pseudospectral method based on prolate spheroidal wave functions for frequency domain electromagnetic simulations we apply prolate spheroidal wave functions of order zero as basis functions in the pseudospectral method for frequency domain electromagnetic simulation problems like the traditional pseudospectral frequency domain psfd methods based on chebyshev and legendre polynomial series the prolate psfd method yields exponential order of accuracy in terms of the number of samples utilized per wavelength the prolate expansion is superior to the chebyshev and legendre polynomial series by a factor of spl pi 2 in addition the prolate psfd method employs a more uniform spatial grid achieving better resolution near the center of the domain

a spectral chebyshev method for linear stability analysis of one dimensional exact solutions of gas dynamics we present a spectral numerical method for solving one dimensional systems of partial differential equations pdes which arise from linearization of the euler equations about an exact solution depending on space and time a two domain chebyshev collocation method is used matching of quantities is performed in the space of characteristic variables as suggested by kopriva appl numer math 2 1986 221 j comput phys 125 1996 244 time dependent boundary conditions are handled following an approach proposed by thompson j comput phys 68 1987 1 89 1990 439 an exact numerical stability analysis valid for any explicit three step third order nondegenerate runge kutta scheme is provided the numerical method is tested against exact solutions for the three fundamental modes of a compressible flow entropy vorticity and acoustic modes

an edge weighted centroidal voronoi tessellation model for image segmentation centroidal voronoi tessellations cvts are special voronoi tessellations whose generators are also the centers of mass centroids of the voronoi regions with respect to a given density function and cvt based methodologies have been proven to be very useful in many diverse applications in science and engineering in the context of image processing and its simplest form cvt based algorithms reduce to the well known k means clustering and are easy to implement in this paper we develop an edge weighted centroidal voronoi tessellation ewcvt model for image segmentation and propose some efficient algorithms for its construction our ewcvt model can overcome some deficiencies possessed by the basic cvt model in particular the new model appropriately combines the image intensity information together with the length of cluster boundaries and can handle very sophisticated situations we demonstrate through extensive examples the efficiency effectiveness robustness and flexibility of the proposed method

a block pseudospectral method for maxwell s equations a block pseudospectral bps method is proposed as a new way to couple pseudospectral discretizations across interfaces in computations for a linear hyperbolic system the coupling is achieved via discretized derivative matching conditions obtained from the system compared to the standard technique of imposing compatibility conditions based on characteristics of the system the bps method offers better stability and accuracy especially in the case where equation coefficients are discontinuous computational examples for maxwell s equations in nonhomogeneous media demonstrate that bps retains high accuracy over times that are orders of magnitude larger than those for not only low order methods such as yee s but also high order methods such as characteristic based spectral elements

numerical study of pseudospectral methods in shock wave applications abstract in this paper we use shock capturing spectral methods to simulate compressible flows in the presence of shock waves three applications are considered the first is an interaction of a one dimensional shock with an entropy wave the second case deals with interactions between shock wave and an entropy wave in two space dimensions and the third case is two dimensional shock vortex interactions the first two applications are found in the study of turbulence in high speed flow the last application is a key element in understanding the acoustic dynamics in aeroacoustic and in design of supersonic jet in aerodynamics the purpose of this study is to show the feasibility of simulating shocked flow with spectral methods the numerical methods involved are the chebyshev and fourier collocation methods the euler equations of gas dynamics is discretized by pseudospectral collocation methods in space and a nonlinearly stable third order runge kutta methods in time the fluxes are evaluated pointwise directly and not by the cell averaging technique a significant reduction in cpu time and storage usage are achieved by incorporating several well established numerical techniques such as grid transformation and filtering into the spectral algorithm the results of this study indicate that spectral method is well suited not only for smooth problems but also for those with discontinuity

active contours without edges we propose a new model for active contours to detect objects in a given image based on techniques of curve evolution mumford shah 1989 functional for segmentation and level sets our model can detect objects whose boundaries are not necessarily defined by the gradient we minimize an energy which can be seen as a particular case of the minimal partition problem in the level set formulation the problem becomes a mean curvature flow like evolving the active contour which will stop on the desired boundary however the stopping term does not depend on the gradient of the image as in the classical active contour models but is instead related to a particular segmentation of the image we give a numerical algorithm using finite differences finally we present various experimental results and in particular some examples for which the classical snakes methods based on the gradient are not applicable also the initial curve can be anywhere in the image and interior contours are automatically detected

a stable penalty method for the compressible navier stokes equations iii multidimensional domain decomposition schemes this paper concluding the trilogy develops schemes for the stable solution of wave dominated unsteady problems in general three dimensional domains the schemes utilize a spectral approximation in each subdomain and asymptotic stability of the semidiscrete schemes is established the complex computational domains are constructed by using nonoverlapping quadrilaterals in the two dimensional case and hexahedrals in the three dimensional space to illustrate the ideas underlying the multidomain method a stable scheme for the solution of the three dimensional linear advection diffusion equation in general curvilinear coordinates is developed the analysis suggests a novel yet simple stable treatment of geometric singularities like edges and vertices the theoretical results are supported by a two dimensional implementation of the scheme the main part of the paper is devoted to the development of a spectral multidomain scheme for the compressible navier stokes equations on conservation form and a unified approach for dealing with the open boundaries and subdomain boundaries is presented well posedness and asymptotic stability of the semidiscrete scheme is established in a general curvilinear volume with special attention given to a hexahedral domain the treatment includes a stable procedure for dealing with boundary conditions at a solid wall the efficacy of the scheme for the compressible navier stokes equations is illustrated by obtaining solutions to subsonic and supersonic boundary layer flows with various types of boundary conditions the results are found to agree with the solution of the compressible boundary layer equations

image segmentation using local variation and edge weighted centroidal voronoi tessellations the classic centroidal voronoi tessellation cvt model and its generalizations work quite well at extracting uniformly colored objects but often fail to handle images with distinct color distribution or strong inhomogeneous intensity to resolve this problem within the cvt methodology in this paper we incorporate the information of local variation of colors intensities and the length of boundaries into the energy functional and develop a new model called the local variation and edge weighted centroidal voronoi tessellation lvewcvt for image segmentation its mathematical formulation and practical implementations are also discussed and given we test the lvewcvt method on various type of segments and also compare it with several state of art algorithms using extensive segmentation examples the results demonstrate excellent performance and competence of the proposed method

high order point value enhanced finite volume method for two dimensional hyperbolic equations on unstructured meshes abstract presently an approximate delta function adf is defined in multi dimensional space in the form of a finite order polynomial that holds identical integral properties to the dirac delta function when used in conjunction with a finite order polynomial integrand spanning a finite domain by using this adf over a two dimensional unstructured mesh a compact high order point value enhanced finite volume method pfv is constructed the corresponding scheme is capable of storing and updating cell averaged values inside each element as well as the unknown quantities and their derivatives when needed on vertex points the sharing of vertex information with surrounding elements reduces the number of degrees of freedom relative to other compact and high order methods of comparable convergence rate to ensure conservation cell averaged values are updated using an identical approach to the one traditionally followed in the finite volume method to verify the performance of the pfv scheme at successive orders its accuracy and stability are vetted using benchmark problems associated with the two dimensional wave and euler equations encompassing a total of six standard test cases

multidomain spectral solution of the euler gas dynamics equations abstract we present interface treatments for computing the euler gas dynamics equations by a multidomain chebyshev spectral collocation method these treatments are suitable for use at the corners of subdomains and for patched or overlapping subdomains they can be applied to interfaces placed in subsonic supersonic or transonic regions of a flow computed results indicate that the solutions are spectrally accurate can be more accurate and more efficient than a single domain calculation and that reflections of waves at interfaces are not significant

optimal decomposition of the domain in spectral methods for wave like phenomena a strategy for determining the optimal number of grid points and subdomains in a spectral method with domain decomposition on a serial computer is presented the rapidly growing computational cost for large numbers of grid points in each subdomain is balanced against the exponential convergence for spectral approximation of smooth functions and the optimum is found as the number of grid points and subdomains that gives the minimal computational cost for a given accuracy the typical length scale of the problem is found to influence the number of subdomains but not the number of grid points within each subdomain

a novel strategy for deriving high order stable boundary closures based on global conservation i basic formulas abstract it is well known that for initial boundary value problems one may need to decrease the order of boundary closures to ensure strict stability also called time stability of finite difference schemes for high order schemes this often reduces the global convergence rate significantly to cure this issue we derive high order accurate boundary closures that satisfy a global conservation property we show that the boundary closures cannot be both high order accurate and conservative in the l 2 inner product if the grid is equidistant therefore we derive particular sets of nonuniform solution points and quadrature weights near the domain boundaries the new schemes are high order accurate on the modified grids and conservative in the derived quadrature rules although we have no theoretical stability proof numerical eigenvalue analysis suggests that the new schemes are strictly stable up to eleventh order global accuracy for scalar linear advection equations numerical experiments with one and two dimensional linear equations corroborate the design orders of the schemes

globally constraint preserving fr dg scheme for maxwell s equations at all orders abstract computational electrodynamics ced the numerical solution of maxwell s equations plays an incredibly important role in several problems in science and engineering high accuracy solutions are desired and the discontinuous galerkin dg method is one of the better ways of delivering high accuracy in numerical ced maxwell s equations have a pair of involution constraints for which mimetic schemes that globally satisfy the constraints at a discrete level are highly desirable balsara and kappeli 2019 presented a von neumann stability analysis of globally constraint preserving dg schemes for ced up to fourth order that paper was focused on developing the theory and documenting the superior dissipation and dispersion of dgtd schemes in media with constant permittivity and permeability in this paper we present working dgtd schemes for ced that go up to fifth order of accuracy and analyze their performance when permittivity and permeability vary strongly in space our dgtd schemes achieve constraint preservation by collocating the electric displacement and magnetic induction as well as their higher order modes in the faces of the mesh our first finding is that at fourth and higher orders of accuracy one has to evolve some zone centered modes in addition to the face centered modes it is well known that the limiting step in dg schemes causes a reduction of the optimal accuracy of the scheme though the schemes still retain their formal order of accuracy with weno type limiters in this paper we document simulations where permittivity and permeability vary by almost an order of magnitude without requiring any limiting of the dg scheme this very favorable second finding ensures that dgtd schemes retain optimal accuracy even in the presence of large spatial variations in permittivity and permeability we also study the conservation of electromagnetic energy in these problems our third finding shows that the electromagnetic energy is conserved very well even when permittivity and permeability vary strongly in space as long as the conductivity is zero

analysis of an hp nonconforming discontinuous galerkin spectral element method for wave propagation we analyze the consistency stability and convergence of an hp discontinuous galerkin spectral element method of kopriva j comput phys 128 1996 pp 475 488 and kopriva woodruff and hussaini internat j numer methods engrg 53 2002 pp 105 122 the analysis is carried out simultaneously for acoustic elastic coupled elastic acoustic and electromagnetic wave propagation our analytical results are developed for both conforming and nonconforming approximations on hexahedral meshes using either exact integration with legendre gauss quadrature or inexact integration with legendre gauss lobatto quadrature a mortar based nonconforming approximation is developed to treat both h and p nonconforming meshes simultaneously the mortar approach is constructed in such a way that consistency stability and convergence analyses for nonconforming approximations follow the conforming counterparts with minimal modifications in particular it casts hp nonconforming interfaces into equiv

normalized cuts and image segmentation we propose a novel approach for solving the perceptual grouping problem in vision rather than focusing on local features and their consistencies in the image data our approach aims at extracting the global impression of an image we treat image segmentation as a graph partitioning problem and propose a novel global criterion the normalized cut for segmenting the graph the normalized cut criterion measures both the total dissimilarity between the different groups as well as the total similarity within the groups we show that an efficient computational technique based on a generalized eigenvalue problem can be used to optimize this criterion we applied this approach to segmenting static images as well as motion sequences and found the results to be very encouraging

a discrete splitting finite element method for numerical simulations of incompressible navier stokes flows the presence of the pressure and the convection terms in incompressible navier stokes equations makes their numerical simulation a challenging task the indefinite system as a consequence of the absence of the pressure in continuity equation is ill conditioned this difficulty has been overcome by various splitting techniques but these techniques incur the ambiguity of numerical boundary conditions for the pressure as well as for the intermediate velocity whenever introduced we present a new and straightforward discrete splitting technique which never resorts to numerical boundary conditions the non linear convection term can be treated by four different approaches and here we present a new linear implicit time scheme these two new techniques are implemented with a finite element method and numerical verifications are made copyright 2005 john wiley sons ltd

least squares quantization in pcm it has long been realized that in pulse code modulation pcm with a given ensemble of signals to handle the quantum values should be spaced more closely in the voltage regions where the signal amplitude is more likely to fall it has been shown by panter and dite that in the limit as the number of quanta becomes infinite the asymptotic fractional density of quanta per unit voltage should vary as the one third power of the probability density per unit voltage of signal amplitudes in this paper the corresponding result for any finite number of quanta is derived that is necessary conditions are found that the quanta and associated quantization intervals of an optimum finite quantization scheme must satisfy the optimization criterion used is that the average quantization noise power be a minimum it is shown that the result obtained here goes over into the panter and dite result as the number of quanta become large the optimum quautization schemes for 2 b quanta b 1 2 cdots 7 are given numerically for gaussian and for laplacian distribution of signal amplitudes

numerical simulation of transitional flow past a wing using flux reconstruction method in this paper the capabilities of a high order flux reconstruction scheme for the implicit large eddy simulations of a transitional flow at a low reynolds number of 60 000 around the sd7003 wing are examined this is the case posed in the first and second international workshops on the high order computational fluid dynamics method held in 2012 and 2013 the correction function used in the flux reconstruction scheme is the radau polynomial which is equivalent to the discontinuous galerkin scheme a time accurate implicit lower upper symmetric gauss seidel solution algorithm for the application of the flux reconstruction scheme to complex unsteady flows is developed and it is found to be able to produce comparable results to the explicit runge kutta scheme while achieving better computational efficiency simulations are carried out at 4 and 8 deg with polynomials of degree p 1 2 and 3 resulting in second third and fourth order accurate flux reconstruction schemes respectively two structured he

high order flux correction finite difference schemes for strand grids a novel high order method combining unstructured flux correction along body surfaces and high order finite differences normal to surfaces is formulated for unsteady viscous flows on strand grids the flux correction algorithm is applied in each unstructured layer of the strand grid and the layers are then coupled together via a source term containing derivatives in the strand direction strand direction derivatives are approximated to high order via summation by parts operators for first derivatives and second derivatives with variable coefficients we show how this procedure allows for the proper truncation error canceling properties required for the flux correction scheme the resulting scheme possesses third order design accuracy but often exhibits fourth order accuracy when higher order derivatives are employed in the strand direction especially for highly viscous flows we prove discrete conservation for the new scheme and time stability in the absence of the flux correction terms results in two dimensions are presented that demonstrate improvements in accuracy with minimal computational and algorithmic overhead over traditional second order algorithms

a multiphase level set framework for image segmentation using the mumford and shah model we propose a new multiphase level set framework for image segmentation using the mumford and shah model for piecewise constant and piecewise smooth optimal approximations the proposed method is also a generalization of an active contour model without edges based 2 phase segmentation developed by the authors earlier in t chan and l vese 1999 in scale space 99 m nilsen et al eds lncs vol 1682 pp 141 151 and t chan and l vese 2001 ieee ip 10 2 266 277 the multiphase level set formulation is new and of interest on its own by construction it automatically avoids the problems of vacuum and overlaps it needs only log n level set functions for n phases in the piecewise constant cases it can represent boundaries with complex topologies including triple junctionss in the piecewise smooth case only two level set functions formally suffice to represent any partition based on the four color theorem finally we validate the proposed models by numerical results for signal and image denoising and segmentation implemented using the osher and sethian level set method

towards efficient tracking of inertial particles with high order multidomain methods this paper develops an efficient particle tracking algorithm to be used in fluid simulations approximated by a high order multidomain discretization of the navier stokes equations we discuss how to locate a particle s host subdomain how to interpolate the flow field to its location and how to integrate its motion in time a search algorithm for the nearest subdomain and quadrature point tuned to a typical quadrilateral isoparametric spectral subdomain takes advantage of the inverse of the linear blending equation we show that to compute particle laden flows a sixth order lagrangian polynomial that uses points solely within a subdomain is sufficiently accurate to interpolate the carrier phase variables to the particle position time integration of particles with a lower order adams bashforth scheme rather than the fourth order runge kutta scheme often used for the integration of the carrier phase increases computational efficiency while maintaining engineering accuracy we verify the tracking algorithm with numerical tests on a steady channel flow and an unsteady backward facing step flow

a simple efficient and high order accurate curved sliding mesh interface approach to spectral difference method on coupled rotating and stationary domains this paper presents a simple efficient and high order accurate sliding mesh interface approach to the spectral difference sd method we demonstrate the approach by solving the two dimensional compressible navier stokes equations on quadrilateral grids this approach is an extension of the straight mortar method originally designed for stationary domains 7 8 our sliding method creates curved dynamic mortars on sliding mesh interfaces to couple rotating and stationary domains on the nonconforming sliding mesh interfaces the related variables are first projected from cell faces to mortars to compute common fluxes and then the common fluxes are projected back from the mortars to the cell faces to ensure conservation to verify the spatial order of accuracy of the sliding mesh spectral difference ssd method both inviscid and viscous flow cases are tested it is shown that the ssd method preserves the high order accuracy of the sd method meanwhile the ssd method is found to be very efficient in terms of computational cost this novel sliding mesh interface method is very suitable for parallel processing with domain decomposition it can be applied to a wide range of problems such as the hydrodynamics of marine propellers the aerodynamics of rotorcraft wind turbines and oscillating wing power generators etc

curve evolution implementation of the mumford shah functional for image segmentation denoising interpolation and magnification we first address the problem of simultaneous image segmentation and smoothing by approaching the mumford shah 1989 paradigm from a curve evolution perspective in particular we let a set of deformable contours define the boundaries between regions in an image where we model the data via piecewise smooth functions and employ a gradient flow to evolve these contours each gradient step involves solving an optimal estimation problem for the data within each region connecting curve evolution and the mumford shah functional with the theory of boundary value stochastic processes the resulting active contour model offers a tractable implementation of the original mumford shah model i e without resorting to elliptic approximations which have traditionally been favored for greater ease in implementation to simultaneously segment and smoothly reconstruct the data within a given image in a coupled manner various implementations of this algorithm are introduced to increase its speed of convergence we also outline a hierarchical implementation of this algorithm to handle important image features such as triple points and other multiple junctions next by generalizing the data fidelity term of the original mumford shah functional to incorporate a spatially varying penalty we extend our method to problems in which data quality varies across the image and to images in which sets of pixel measurements are missing this more general model leads us to a novel pde based approach for simultaneous image magnification segmentation and smoothing thereby extending the traditional applications of the mumford shah functional which only considers simultaneous segmentation and smoothing

constrained centroidal voronoi tessellations for surfaces centroidal voronoi tessellations are useful for subdividing a region in euclidean space into voronoi regions whose generators are also the centers of mass with respect to a prescribed density function of the regions their extensions to general spaces and sets are also available for example tessellations of surfaces in a euclidean space may be considered in this paper a precise definition of such constrained centroidal voronoi tessellations ccvts is given and a number of their properties are derived including their characterization as minimizers of an energy deterministic and probabilistic algorithms for the construction of ccvts are presented and some analytical results for one of the algorithms are given computational examples are provided which serve to illustrate the high quality of ccvt point sets finally ccvt point sets are applied to polynomial interpolation and numerical integration on the sphere

an optimal runge kutta method for steady state solutions of hyperbolic systems an optimal two stage runge kutta time integration scheme is derived to compute steady state approximations to hyperbolic equations the analysis is general in the sense that it requires only that the eigenvalues of the derivative matrix lie in the right half of the complex plane thus it is applicable to spatial discretizations which do not have uniformly spaced points as examples the method is applied to two hyperbolic problems which have been discretized in space by chebyshev spectral collocation

on the eddy resolving capability of high order discontinuous galerkin approaches to implicit les under resolved dns of euler turbulence we present estimates of spectral resolution power for under resolved turbulent euler flows obtained with high order discontinuous galerkin dg methods the 1 rule based on linear dispersion diffusion analysis introduced by moura et al 2015 10 is here adapted for 3d energy spectra and validated through the inviscid taylor green vortex problem the 1 rule estimates the wavenumber beyond which numerical diffusion induces an artificial dissipation range on measured energy spectra as the original rule relies on standard upwinding different riemann solvers are tested very good agreement is found for solvers which treat the different physical waves in a consistent manner relatively good agreement is still found for simpler solvers the latter however displayed spurious features attributed to the inconsistent treatment of different physical waves it is argued that in the limit of vanishing viscosity such features might have a significant impact on robustness and solution quality the estimates proposed are regarded as useful guidelines for no model dg based simulations of free turbulence at very high reynolds numbers

impact of number representation for high order implicit large eddy simulations high order numerical methods for unstructured grids combine the superior accuracy of high order spectral or finite difference methods with the geometric flexibility of low order finite volume or fi

a staggered grid multidomain spectral method for the compressible navier stokes equations we present a flexible non conforming staggered grid chebyshev spectral multidomain method for the solution of the compressible navier stokes equations in this method subdomain corners are not included in the approximation thereby simplifying the subdomain connectivity to allow for local refinement of the polynomial order or subdomain subdivision non conforming subdomains are treated by a mortar method spectral accuracy is shown in one and two dimensional linear and non linear problems application is made to four compressible flow problems the couette flow a steady boundary layer over a flat plate steady transonic flow in a nozzle and unsteady flow over a cylinder at a reynolds number of 75

blobworld image segmentation using expectation maximization and its application to image querying retrieving images from large and varied collections using image content as a key is a challenging and important problem we present a new image representation that provides a transformation from the raw pixel data to a small set of image regions that are coherent in color and texture this blobworld representation is created by clustering pixels in a joint color texture position feature space the segmentation algorithm is fully automatic and has been run on a collection of 10 000 natural images we describe a system that uses the blobworld representation to retrieve images from this collection an important aspect of the system is that the user is allowed to view the internal representation of the submitted image and the query results similar systems do not offer the user this view into the workings of the system consequently query results from these systems can be inexplicable despite the availability of knobs for adjusting the similarity metrics by finding image regions that roughly correspond to objects we allow querying at the level of objects rather than global image properties we present results indicating that querying for images using blobworld produces higher precision than does querying using color and texture histograms of the entire image in cases where the image contains distinctive objects

short note a comparison of the discontinuous galerkin and spectral difference method on triangulations using pkd polynomials this paper gives a first numerical comparison of the discontinuous galerkin dg and spectral difference method sd under almost equivalent conditions for smooth test cases

a weak legendre collocation spectral method for the solution of the incompressible navier stokes equations in unstructured quadrilateral subdomains a weak legendre spectral method is developed for the solution of the primitive variable formulation of the unsteady incompressible navier stokes equations in general two dimensional and axisymmetric geometries a semi implicit projection method is utilized for the temporal approximation and for decoupling the velocity field from the pressure field a series of elliptic boundary value problems arises from the above procedure each of which is spatially discretized by a weak collocation method in multiple nonoverlapping subdomains in particular a modified variational formulation of the partial differential equations is presented which leads after discretization to a weak multidomain approximation of the corresponding problems a weak formalism for the influence matrix technique is also developed which is consistent with the spatial discretization scheme and successfully separate the equations for the internal nodes from the ones governing the interface unknowns a method of dealing with the singularity problem faced by the weak formulation at axisymmetric problems is proposed while a combination of direct methods is studied for tackling effectively the linear algebraic systems resulting from the full discretization exponential convergence is demonstrated for a plethora of stokes and navier stokes simulations

a skew symmetric discontinuous galerkin spectral element discretization and its relation to sbp sat finite difference methods this paper shows that the discontinuous galerkin collocation spectral element method with gauss lobatto points dgsem gl satisfies the discrete summation by parts sbp property and can thus be classified as an sbp sat simultaneous approximation term scheme with a diagonal norm operator in the same way sbp sat finite difference schemes can be interpreted as discontinuous galerkin type methods with a corresponding weak formulation based on an inner product formulation common in the finite element community this relation allows the use of matrix vector notation common in the sbp sat finite difference community to show discrete conservation for the split operator formulation of scalar nonlinear conservation laws for dgsem gl and diagonal norm sbp sat based on this result a skew symmetric energy stable discretely conservative dgsem gl formulation applicable to general diagonal norm sbp sat schemes for the nonlinear burgers equation is constructed

equivalence between the energy stable flux reconstruction and filtered discontinuous galerkin schemes the aim of this paper is to demonstrate the equivalence between filtered discontinuous galerkin dg schemes and the energy stable flux reconstruction esfr schemes expanding on previous demonstrations in 1d 1 and for straight sided elements in 3d 2 we first derive the dg and esfr schemes in strong form and compare the respective flux penalization terms while highlighting the implications of the fundamental assumptions for stability in the esfr formulations notably that all esfr scheme correction fields can be interpreted as modally filtered dg correction fields we present the result in the general context of all higher dimensional curvilinear element formulations through a demonstration that there exists a weak form of the esfr schemes which is both discretely and analytically equivalent to the strong form we then extend the results obtained for the strong formulations to demonstrate that esfr schemes can be interpreted as a dg scheme in weak form where discontinuous edge flux is substituted for numerical edge flux correction theoretical derivations are then verified with numerical results obtained from a 2d euler testcase with curved boundaries given the current choice of high order dg type schemes and the question as to which might be best to use for a specific application the main significance of this work is the bridge that it provides between them clearly outlining the similarities between the schemes results in the important conclusion that it is always less efficient to use esfr schemes as opposed to the weak dg scheme when solving problems implicitly

spectral element method for linear fan tone noise radiation a numerical method for prediction of acoustic spinning mode radiation from turbofan inlets is presented sound propagation is modeled by the linearized mass conservation equation for irrotational flows and solved in the frequency domain the mean flow through the inlet is obtained as a solution of the full potential equation both the mean flow and the acoustic problem are approximated by galerkin projection in spectral element spaces of continuous piecewise polynomials defined on the same grid the gauss chebyshev lobatto points within the elements are generated via transfinite interpolation and cad projection procedures embedded within the code the linear algebraic systems obtained are then solved using either direct or sparse iterative solvers based on the message passing interface standard for interprocessor communication the singularity appearing in the acoustic integrals on the symmetry axis is treated by the use of a collocation operator based on the gauss chebyshev instead of the gauss chebyshev lobatto points to eliminate reflections from the radiation boundaries a novel frequency domain formulation of the matched layer technique wherein waves entering the layer are exponentially damped is proposed the overall computing procedure is first validated on a tone radiation problem from a semi infinite cylinder and then applied to an experimental jt15d turbofan inlet setup

multiscale superpixels and supervoxels based on hierarchical edge weighted centroidal voronoi tessellation superpixels and supervoxels play an important role in many computer vision applications such as image segmentation object recognition and video analysis in this paper we propose a new hierarchical edge weighted centroidal voronoi tessellation hewcvt method for generating superpixels supervoxels in multiple scales in this method we model the problem as a multilevel clustering process superpixels supervoxels in one level are clustered to obtain larger size superpixels supervoxels in the next level in the finest scale the initial clustering is directly conducted on pixels voxels the clustering energy involves both color similarities and boundary smoothness of superpixels supervoxels the resulting superpixels supervoxels can be easily represented by a hierarchical tree which describes the nesting relation of superpixels supervoxels across different scales we first investigate the performance of obtained superpixels supervoxels under different parameter settings then we evaluate and compare the proposed method with several state of the art superpixel supervoxel methods on standard image and video data sets both quantitative and qualitative results show that the proposed hewcvt method achieves superior or comparable performances with other methods

non oscillatory spectral element chebyshev method for shock wave calculations a new algorithm based on spectral element discretization and non oscillatory ideas is developed for the solution of hyperbolic partial differential equations a conservative formulation is proposed based on cell averaging and reconstruction procedures that employs a staggered grid of gauss chebyshev and gauss lobatto chebyshev discretizations the non oscillatory reconstruction procedure is based on ideas similar to those proposed by cai et al math comput 52 389 1989 but employs a modified technique which is more robust and simpler in terms of determining the location and strength of a discontinuity it is demonstrated through model problems of linear advection inviscid burgers equation and one dimensional euler system that the proposed algorithm leads to stable non oscillatory accurate results exponential accuracy away from the discontinuity is realized for the inviscid burgers equation example

revisiting the spectral analysis for high order spectral discontinuous methods the spectral analysis is a basic tool to characterise the behaviour of any convection scheme by nature the solution projected onto the fourier basis enables to estimate the dissipation and the dispersion associated with the spatial discretisation of the hyperbolic linear problem in this paper we wish to revisit such analysis focusing attention on two key points the first point concerns the effects of time integration on the spectral analysis it is shown with standard high order finite difference schemes dedicated to aeroacoustics that the time integration has an effect on the required number of points per wavelength the situation depends on the choice of the coupled schemes one for time integration one for space derivative and one for the filter and here the compact scheme with its eighth order filter seems to have a better spectral accuracy than the considered dispersion relation preserving scheme with its associated filter especially in terms of dissipation secondly such a coupled space time approach is applied to the new class of high order spectral discontinuous approaches focusing especially on the spectral difference method a new way to address the specific spectral behaviour of the scheme is introduced first for wavenumbers in 0 0 following the matrix power method for wavenumbers above an aliasing phenomenon always occurs but it is possible to understand and to control the aliasing of the signal it is shown that aliasing depends on the polynomial degree and on the number of time steps a new way to define dissipation and dispersion is introduced and applied to wavenumbers larger than since the new criteria recover the previous results for wavenumbers below the new proposed approach is an extension of all the previous ones dealing with dissipation and dispersion errors at last since the standard finite difference schemes can serve as reference solution for their capability in aeroacoustics it is shown that the spectral difference method is as accurate as or even more accurate than the considered finite difference schemes

the ode formulation of hyperbolic pdes discretized by the spectral collocation method we formulate systems of hyperbolic partial differential equations pdes with characteristic boundary conditions as pure initial value problems of ordinary differential equations odes this enables a straightforward application of any explicit or implicit method for the time integration of the spatially discretized system we also show how this method relates to the correctional method of treating the boundary points to exemplify we work out the ode formulation for the one dimensional compressible euler equations and a simple two dimensional linear system and conclude with some numerical calculations on these using both explicit and implicit runge kutta methods

an evaluation of the bouwer and rice method of slug test analysis the method of bouwer and rice 1976 for analyzing slug test data is widely used to estimate hydraulic conductivity k based on steady state flow assumptions this method is specifically intended to be applicable to unconfined aquifers therefore it is of practical value to investigate the limits of accuracy of the k estimates obtained with this method accordingly using a numerical model for transient flow we evaluate the method from two perspectives first we apply the method to synthetic slug test data and study the error in estimated values of k second we analyze the logical basis of the method parametric studies helped assess the role of the effective radius parameter specific storage screen length and well radius on the estimated values of k the difference between unconfined and confined systems was studied via conditions on the upper boundary of the flow domain for the cases studied the bouwer and rice analysis was found to give good estimates of k with errors ranging from 10 to 100 we found that the estimates of k were consistently superior to those obtained with hvorslev s 1951 basic time lag method in general the bouwer and rice method tends to underestimate k the greatest errors occurring in the presence of a damaged zone around the well or when the top of the screen is close to the water table when the top of the screen is far removed from the upper boundary of the system no difference is manifest between confined and unconfined conditions it is reasonable to infer from the simulated results that when the screen is close to the upper boundary the results of the bouwer and rice method agree more closely with a confined idealization than an unconfined idealization in effect this method treats the aquifer system as an equivalent radial flow permeameter with an effective radius re which is a function of the flow geometry our transient simulations suggest that re varies with time and specific storage thus the effective radius may be reasonably viewed as a time averaged mean value the fact that the method provides reasonable estimates of hydraulic conductivity suggests that the empirical electric analog experiments of bouwer and rice have yielded shape factors that are better than the shape factors implicit in the hvorslev method

a conservative staggered grid chebyshev multidomain method for compressible flows ii a semi structured method we present a chebyshev multidomain method that can solve systems of hyperbolic equations in conservation form on an unrestricted quadrilateral subdivision of a domain within each subdomain the solutions and fluxes are approximated by a staggered grid chebyshev method thus the method is unstructured in terms of the subdomain decomposition but strongly structured within the subdomains communication between subdomains is done by a mortar method in such a way that the method is globally conservative the method is applied to both linear and nonlinear test problems and spectral accuracy is demonstrated

geometry imbedded darcy s law and transient subsurface flow the traditional interpretation of darcy s experiment views it as a valuable means for setting up the partial differential equation of transient or steady state subsurface fluid flow in the present work darcy s observations are viewed from a different perspective enabling the statement of transient subsurface fluid flow in terms of an equation defined over finite domains of space and time two new notions namely geometry imbedding and location of average are introduced the equation describes transient flow along a flow tube with arbitrarily varying cross section consisting of materials with properties dependent on fluid potential this equation based on its own postulates is fully consistent within itself and exists independently of the classical partial differential equation this technical note presents preliminary ideas on what appears to be a promising new line of inquiry that departs from the traditional approach based on continuum mechanics further work is in progress

self validated labeling of markov random fields for image segmentation this paper addresses the problem of self validated labeling of markov random fields mrfs namely to optimize an mrf with unknown number of labels we present graduated graph cuts ggc a new technique that extends the binary s t graph cut for self validated labeling specifically we use the split and merge strategy to decompose the complex problem to a series of tractable subproblems in terms of gibbs energy minimization a suboptimal labeling is gradually obtained based upon a set of cluster level operations by using different optimization structures we propose three practical algorithms tree structured graph cuts tsgc net structured graph cuts nsgc and hierarchical graph cuts hgc in contrast to previous methods the proposed algorithms can automatically determine the number of labels properly balance the labeling accuracy spatial coherence and the labeling cost i e the number of labels and are computationally efficient independent to initialization and able to converge to good local minima of the objective energy function we apply the proposed algorithms to natural image segmentation experimental results show that our algorithms produce generally feasible segmentations for benchmark data sets and outperform alternative methods in terms of robustness to noise speed and preservation of soft boundaries

intrinsic manifold slic a simple and efficient method for computing content sensitive superpixels superpixels are perceptually meaningful atomic regions that can effectively capture image features among various methods for computing uniform superpixels simple linear iterative clustering slic is popular due to its simplicity and high performance in this paper we extend slic to compute content sensitive superpixels i e small superpixels in content dense regions with high intensity or colour variation and large superpixels in content sparse regions rather than using the conventional slic method that clusters pixels in mathbb r 5 we map the input image i to a 2 dimensional manifold mathcal m subset mathbb r 5 whose area elements are a good measure of the content density in i we propose a simple method called intrinsic manifold slic imslic for computing a geodesic centroidal voronoi tessellation gcvt a uniform tessellation on mathcal m which induces the content sensitive superpixels in i in contrast to the existing algorithms imslic characterizes the content sensitivity by measuring areas of voronoi cells on mathcal m using a simple and fast approximation to a closed form solution the method can compute the gcvt at a very low cost and guarantees that all voronoi cells are simply connected we thoroughly evaluate imslic and compare it with eleven representative methods on the bsds500 dataset and seven representative methods on the nyuv2 dataset computational results show that imslic outperforms existing methods in terms of commonly used quality measures pertaining to superpixels such as compactness adherence to boundaries and achievable segmentation accuracy we also evaluate imslic and seven representative methods in an image contour closure application and the results on two datasets whd and wsd show that imslic achieves the best foreground segmentation performance

a point value enhanced finite volume method based on approximate delta functions abstract we revisit the concept of an approximate delta function adf introduced by huynh 2011 1 in the form of a finite order polynomial that holds identical integral properties to the dirac delta function when used in conjunction with a finite order polynomial integrand over a finite domain we show that the use of generic adf polynomials can be effective at recovering and generalizing several high order methods including taylor based and nodal based discontinuous galerkin methods as well as the correction procedure via reconstruction based on the adf concept we then proceed to formulate a point value enhanced finite volume pfv method which stores and updates the cell averaged values inside each element as well as the unknown quantities and if needed their derivatives on nodal points the sharing of nodal information with surrounding elements saves the number of degrees of freedom compared to other compact methods at the same order to ensure conservation cell averaged values are updated using an identical approach to that adopted in the finite volume method here the updating of nodal values and their derivatives is achieved through an adf concept that leverages all of the elements within the domain of integration that share the same nodal point the resulting scheme is shown to be very stable at successively increasing orders both accuracy and stability of the pfv method are verified using a fourier analysis and through applications to the linear wave and nonlinear burgers equations in one dimensional space

generalized edge weighted centroidal voronoi tessellations for geometry processing in this paper we propose a generalized edge weighted centroidal voronoi tessellation gewcvt model and corresponding solution algorithms then apply them for geometry processing such as curve surface smoothing and reconstruction the main idea of the method is to seek a good way to discretize the similarity and regularity measures of the objective functional in the context of centroidal voronoi tessellation methodology so that its minimization can be done by clustering type algorithms through various numerical examples the proposed gewcvt based method is shown to be an effective and robust tool for such applications

a hybrid multilevel method for high order discretization of the euler equations on unstructured meshes higher order discretization has not been widely successful in industrial applications to compressible flow simulation among several reasons for this one may identify the lack of tailor suited best practice relaxation techniques that compare favorably to highly tuned lower order methods such as finite volume schemes in this paper we investigate solution algorithms in conjunction with high order spectral difference discretization for the euler equations using such techniques as multigrid and matrix free implicit relaxation methods in particular we present a novel hybrid multilevel relaxation method that combines optionally matrix free implicit relaxation techniques with explicit multistage smoothing using geometric multigrid furthermore we discuss efficient implementation of these concepts using such tools as automatic differentiation

image segmentation using active contours driven by the bhattacharyya gradient flow this paper addresses the problem of image segmentation by means of active contours whose evolution is driven by the gradient flow derived from an energy functional that is based on the bhattacharyya distance in particular given the values of a photometric variable or of a set thereof which is to be used for classifying the image pixels the active contours are designed to converge to the shape that results in maximal discrepancy between the empirical distributions of the photometric variable inside and outside of the contours the above discrepancy is measured by means of the bhattacharyya distance that proves to be an extremely useful tool for solving the problem at hand the proposed methodology can be viewed as a generalization of the segmentation methods in which active contours maximize the difference between a finite number of empirical moments of the ldquoinsiderdquo and ldquooutsiderdquo distributions furthermore it is shown that the proposed methodology is very versatile and flexible in the sense that it allows one to easily accommodate a diversity of the image features based on which the segmentation should be performed as an additional contribution a method for automatically adjusting the smoothness properties of the empirical distributions is proposed such a procedure is crucial in situations when the number of data samples supporting a certain segmentation class varies considerably in the course of the evolution of the active contour in this case the smoothness properties of the empirical distributions have to be properly adjusted to avoid either over or underestimation artifacts finally a number of relevant segmentation results are demonstrated and some further research directions are discussed

a wavenumber based extrapolation and interpolation method for use in conjunction with high order finite difference schemes the errors incurred in using extrapolation and interpolation in large scale computations are analyzed and quantified in the wavenumber space if a large extrapolation stencil is used the errors in the low wavenumbers can be significantly reduced however the errors in the high wavenumbers are at the same time greatly increased the opposite is true if the stencil size is reduced based on the wavenumber analysis an optimized extrapolation and interpolation method is proposed the optimization is carried out over a selected band of wavenumbers it is known that extrapolation often leads to numerical instability the instability is the result of large error amplification in the high wavenumber range to reduce the tendency to trigger numerical instability it is proposed that an extra constraint be imposed on the optimized extrapolation method the added constraint aims to reduce error amplification over the high wavenumbers numerical examples are provided to illustrate that accurate and stable numerical results can be obtained in large scale simulation using a high order finite difference scheme and the proposed optimized extrapolation method when the same problems are recomputed using the familiar high order polynomials extrapolation method in the lagrange form in one case the numerical results are plagued by large errors and ultimately instability in another problem it is found that the use of the lagrange polynomials extrapolation method would lead immediately to numerical instability

spectral element formulations on non conforming grids a comparative study of pointwise matching and integral projection methods pointwise matching pm and integral projection ip methods are two widely used techniques to extend the classical weak formulations to include non conforming grids we present spectral element formulations on polynomial p type and geometric h type non conforming grids using both the pm also known as the constrained approximation and ip also known as the mortar element methods we systematically compare the convergence characteristics of pm and ip methods for diffusion convection and convection diffusion equations consistency errors due to the non conforming formulations of the diffusion equation result in convergence problems for the pm method using the maximum rule both non conforming formulations for the unsteady convection operator result in eigenvalue spectrum with positive real values causing convergence problems due to the consistency errors however small physical diffusion in the convection diffusion equation eliminates these problems resulting in spectral convergence for both methods encouraged by this we present spectral element formulations for incompressible navier stokes equations using pm and ip methods on p type and h type non conforming grids and demonstrate spectral convergence for unsteady and steady test cases results for two dimensional lid driven cavity flow at re 1000 are also presented

a computational approach to edge detection this paper describes a computational approach to edge detection the success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points these goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution we define detection and localization criteria for a class of edges and present mathematical forms for these criteria as functionals on the operator impulse response a third criterion is then added to ensure that the detector has only one response to a single edge we use the criteria in numerical optimization to derive detectors for several common image features including step edges on specializing the analysis to step edges we find that there is a natural uncertainty principle between detection and localization performance which are the two main goals with this principle we derive a single operator shape which is optimal at any scale the optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a gaussian smoothed image we extend this simple detector using operators of several widths to cope with different signal to noise ratios in the image we present a general method called feature synthesis for the fine to coarse integration of information from operators at different scales finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge

symmetric quadrature rules for simplexes based on sphere close packed lattice arrangements sphere close packed scp lattice arrangements of points are well suited for formulating symmetric quadrature rules on simplexes as they are symmetric under affine transformations of the simplex unto itself in 2d and 3d as a result scp lattice arrangements have been utilized to formulate symmetric quadrature rules with n p 1 4 10 20 35 and 56 points on the 3 simplex shunn and ham 2012 in what follows the work on the 3 simplex is extended and scp lattices are employed to identify symmetric quadrature rules with n p 1 3 6 10 15 21 28 36 45 55 and 66 points on the 2 simplex and n p 84 points on the 3 simplex these rules are found to be capable of exactly integrating polynomials of up to degree 17 in 2d and up to degree 9 in 3d

chebyshev collocation method and multi domain decomposition for navier stokes equations in complex curved geometries a general multidomain decomposition is proposed for the numerical solution of the 2d incompressible stationary navier stokes equations the solution technique consists in a chebyshev orthogonal collocation method preconditioned by a standard galerkin finite element technique the preconditioned system is then solved through a richardson procedure the domain of interest is decomposed into quadrilaterals curved when needed a gordon transfinite interpolation performs the curvilinear grid generation of the obtained simply connected planar subdomains the interface conditions naturally incorporated into the finite element approach relate neighbour subdomains through the normal jump of appropriate fluxes across internal boundaries where an integral form ofc 1 continuity is consequently achieved at convergence of the iterative processes the study of model stokes problems demonstrates that the current method still behaves spectrally in distorted geometries for curvilinear distortion a loss of several orders of magnitude is observed in the solution accuracy even when the distortion is very limited finally some results of flow simulation in a constricted channel are proposed to illustrate the abilities of the present method to treat navier stokes problems

summation by parts operators for correction procedure via reconstruction the correction procedure via reconstruction cpr formerly known as flux reconstruction is a framework of high order methods for conservation laws unifying some discontinuous galerkin spectral difference and spectral volume methods linearly stable schemes were presented by vincent et al 2011 2015 but proofs of non linear entropy stability in this framework have not been published yet to the knowledge of the authors we reformulate cpr methods using summation by parts sbp operators with simultaneous approximation terms sats a framework popular for finite difference methods extending the results obtained by gassner 2013 for a special discontinuous galerkin spectral element method this reformulation leads to proofs of conservation and stability in discrete norms associated with the method recovering the linearly stable cpr schemes of vincent et al 2011 2015 additionally extending the skew symmetric formulation of conservation laws by additional correction terms entropy stability for burgers equation is proved for general sbp cpr methods not including boundary nodes

block pseudospectral methods for maxwell s equations ii two dimensional discontinuous coefficient case block pseudospectral bps methods are examined for maxwell s equations in two dimensional inhomogeneous media for the case of a rectangular strip with a straight line interface blocks may be coupled via fictitious points or a generalization of characteristic outflow conditions the bps methods generalize to curvilinear strips described by a change of variables such strips can conform to interfaces while overlapping with a high order free space grid to form a composite grid method numerical experiments on strips with dielectrics lossy materials perfect conductors and absorbing layers indicate that the two coupling methods are comparable and accurate with just 3 4 points per wavelength full composite examples are included to demonstrate high accuracy and geometric flexibility

on consistency and rate of convergence of flux reconstruction for time dependent problems this study is directed at a rigorous characterization of the consistency and convergence of discontinuous finite element schemes formulated using flux reconstruction fr we show that the fr formulation is consistent for linear advection and converges to the exact solution for any scheme that is stable in the von neumann sense the numerical solution for a scheme of polynomial order p is composed of p 1p 1 eigenmodes of which one and exactly one is physical such that it exhibits the analytical dispersion behavior in the limit of asymptotic grid resolution the remaining p modes are spurious such that the fraction of energy received by them from the initial condition vanishes in the asymptotic limit on grid refinement the rate of convergence of the numerical solution is a function of time starting from a short time rate at t 0 t 0 associated with interpolation and asymptotically approaching a long time rate as t t associated with numerical differentiation both these rates can be inferred directly from the eigensystem of the numerical derivative operator we verify these analytical expectations using simple experiments in 1 d and 2 d

what does a slug test measure an investigation of instrument response and the effects of heterogeneity 1 we consider parameters determined by the inversion of slug test head recovery data with the homogeneous parameter model of cooper et al 1967 to be weighted spatial averages of transmissivity and storage defined at a smaller scale we quantify the spatial averaging using a power average spatial filter expression we determine the form of the filter function and the power exponent using numerically simulated slug test data the filter function that describes how smaller scale transmissivity is weighted by slug tests displays an approximate 1 r2 behavior with r the radial distance from the well the radius of the cylinderical volume that is averaged by the slug test is inversely proportional to the square root of the storage coefficient larger averaging volume with smaller storage the power exponent grows from 0 19 to 0 345 as the ratio of the characteristic scale of the heterogeneity to the characteristic scale of the averaging volume grows although a power exponent of zero corresponding to geometric averaging provides good results for most simulations our results show that while slug tests are useful to estimate transmissivity they have dubious value for estimating storage coefficients we find that the transmissivity estimate is unbiased and does not appear to be strongly influenced by storage properties the storage coefficient estimate is however strongly influenced by the transmissivity and is biased we investigate the interaction between storage coefficient and transmissivity by examining an analytical slug test model that contains two annular zones each with distinct transmissivity and storage coefficient

the lobatto cell robust explicit higher order fdtd that handles inhomogeneous media to improve numerical dispersion and second order convergence behavior of the traditional yee finite difference time domain fdtd algorithm various higher order finite difference implementations have been proposed many have difficulty handling interfaces between distinct dielectric media or metallic sheets because the high order taylor expansions on which these codes are based are invalidated by field or derivative discontinuities one sided extensions extrapolations are a common approach to remedy interface discontinuities here another approach based upon whitney form mass lumped finite elements is pursued to develop the ldquolobatto cell rdquo a high order replacement for the yee cell with appropriate continuity behavior at contrasting media interfaces the lobatto cell retains many robust features of the yee method discrete conservation laws a guarantee of conditional stability and straightforward explicit updating but provides higher order interpolation and dispersion error convergence a notable drawback of the method is larger modeling granularity staircasing which is managed here by combining the lobatto cell method with preexisting robust subgridding techniques

a strategy for the efficient simulation of viscous compressible flows using a multi domain pseudospectral method abstract a new multi domain pseudospectral method is developed to simulate viscous compressible flow in a quasi one dimensional nozzle the flow variables at the interface points are advanced in time using the same second order time marching scheme as the interior points the spatial derivatives of the inviscid flux vector are evaluated at the interface points using a spectrally accurate modification of van leer s flux vector splitting method the derivatives of the viscous flux vector are evaluated alternately from neighboring sub domains the scheme is found to be spectrally accurate shock waves are resolved without oscillations for moderate reynolds numbers

convergence analysis of shock capturing and shock fitting solutions on unstructured grids a new shock fitting technique for unstructured two and three dimensional meshes has been recently proposed and developed by the authors in the present paper both global and local a posteriori grid convergence analysis is used to quantitatively measure the discretization error and order of convergence of the numerical solutions obtained using this new unstructured shock fitting technique specifically the analysis has considered the numerical solutions of two different flows characterized by the presence of strong shocks a transonic source flow and an hypersonic flow past a circular cylinder it is shown that the shock fitting technique allows to compute numerical solutions that converge both pointwise and in a global sense with an observed order of accuracy that is very close to the design order of the spatial discretization scheme and with very small discretization errors

multidomain spectral solution of compressible viscous flows abstract we develop a nonoverlapping multidomain spectral collocation method to solve compressible viscous flows at the interfaces the advection terms are treated with a characteristic correction method the diffusion terms are treated with a penalty method spectral accuracy is demonstrated on linear model problems in one and two space dimensions the method is applied to a subsonic and a supersonic flow over a flat plate the results are compared to solutions of the boundary layer equations which show that two digit accuracy in the adiabatic plate temperature is obtained with 16 points in the boundary layer for a freestream mach number of two a second application is to a transonic flow in a two dimensional converging diverging nozzle where the computed results are compared to experimental data

a new flux splitting scheme a new flux splitting scheme is proposed the scheme is remarkably simple and yet its accuracy rivals and in some cases surpasses that of roe s solver in the euler and navier stokes solutions carried out in this study the scheme is robust and converges as fast as the roe splitting we propose an appropriately defined cell face advection mach number using values from the two straddling cells via associated characteristic speeds this interface mach number is then used to determine the upwind extrapolation for the convective quantities accordingly the name of the scheme is coined as the advection upstream splitting method ausm we also introduce a new pressure splitting which is shown to behave successfully yielding much smoother results than other existing pressure splittings of particular interest is the supersonic blunt body problem in which the roe scheme gives anomalous solutions the ausm produces correct solutions without difficulty for a wide range of flow conditions as well as grids

prior knowledge level set representations visual grouping in this paper we propose a level set method for shape driven object extraction we introduce a voxel wise probabilistic level set formulation to account for prior knowledge to this end objects are represented in an implicit form constraints on the segmentation process are imposed by seeking a projection to the image plane of the prior model modulo a similarity transformation the optimization of a statistical metric between the evolving contour and the model leads to motion equations that evolve the contour toward the desired image properties while recovering the pose of the object in the new image upon convergence a solution that is similarity invariant with respect to the model and the corresponding transformation are recovered promising experimental results demonstrate the potential of such an approach

computation of electromagnetic scattering with a non conforming discontinuous spectral element method in this paper we solve electromagnetic scattering problems by approximating maxwell s equations in the time domain with a high order quadrilateral discontinuous spectral element method dsem the method is a collocation form of the discontinuous galerkin method for hyperbolic systems where the solution is approximated by a tensor product legendre expansion and inner products are replaced with gauss legendre quadratures to increase flexibility of the method we use a mortar element method to couple element faces mortars provide a means for coupling element faces along which the polynomial orders differ which allows the flexibility to choose the approximation order within an element by considering only local resolution requirements mortars also permit local subdivision of a mesh by connecting element faces that do not share a full side we present evidence showing that the convergence of the non conforming approximations is spectral along with examples of their use copyright 2001 john wiley sons ltd

a conservative staggered grid chebyshev multidomain method for compressible flows we present a new multidomain spectral collocation method that uses a staggered grid for the solution of compressible flow problems the solution unknowns are defined at the nodes of a gauss quadrature rule the fluxes are evaluated at the nodes of a gauss lobatto rule the method is conservative free stream preserving and exponentially accurate a significant advantage of the method is that subdomain corners are not included in the approximation making solutions in complex geometries easier to compute

connections between the filtered discontinuous galerkin method and the flux reconstruction approach to high order discretizations the purpose of this paper is to provide new insights on the connections that exist between the discontinuous galerkin method dg the flux reconstruction method fr and the recently identified energy stable flux reconstruction method esfr when solving time dependent conservation laws all these schemes appear to be quite similar and it is important to understand how they are related in this paper we first review results on the stability of the discontinuous galerkin method and extend it to the filtered discontinuous galerkin method we then consider the flux reconstruction approach and show its connections with dg in particular we show how the energy stable flux reconstruction method introduced by vincent et al is equivalent to a filtered dg method hence giving a new proof of its stability also it allows the use of the method without having to know the special form of the flux correction polynomials finally we underline some fundamental differences that exist between fr and dg

minimization of region scalable fitting energy for image segmentation intensity inhomogeneities often occur in real world images and may cause considerable difficulties in image segmentation in order to overcome the difficulties caused by intensity inhomogeneities we propose a region based active contour model that draws upon intensity information in local regions at a controllable scale a data fitting energy is defined in terms of a contour and two fitting functions that locally approximate the image intensities on the two sides of the contour this energy is then incorporated into a variational level set formulation with a level set regularization term from which a curve evolution equation is derived for energy minimization due to a kernel function in the data fitting term intensity information in local regions is extracted to guide the motion of the contour which thereby enables our model to cope with intensity inhomogeneity in addition the regularity of the level set function is intrinsically preserved by the level set regularization term to ensure accurate computation and avoids expensive reinitialization of the evolving level set function experimental results for synthetic and real images show desirable performances of our method

a fuzzy edge weighted centroidal voronoi tessellation model for image segmentation the centroidal voronoi tessellation cvt is a special voronoi tessellation whose generators are also the centers of mass of the corresponding voronoi regions the edge weighted centroidal voronoi tessellation ewcvt greatly improves the classic cvt model by adding an edge energy term in the energy functional and has been proven to be very effective and efficient for image segmentation in this paper we propose a fuzzy edge weighted centroidal voronoi tessellation fewcvt model which generalizes the ewcvt clustering with fuzzy membership information the fewcvt model novelly introduces an edge energy based on fuzzy clustering and naturally combines it into the ewcvt model and thus appropriately combines the image intensity information with the length of cluster boundaries in a fuzzy form in its simplest form fewcvt model reduces to the classic ewcvt model an iterative algorithm is proposed for the fewcvt model based on energy minimization in the experiments we apply the fewcvt method to segment various types of images and also compare it with several existing fuzzy clustering methods to demonstrate its performance

vcells simple and efficient superpixels using edge weighted centroidal voronoi tessellations vcells the proposed edge weighted centroidal voronoi tessellations ewcvts based algorithm is used to generate superpixels i e an oversegmentation of an image for a wide range of images the new algorithm is capable of generating roughly uniform subregions and nicely preserving local image boundaries the undersegmentation error is effectively limited in a controllable manner moreover vcells is very efficient with core computational cost at o k nc n in which k nc and n are the number of iterations superpixels and pixels respectively extensive qualitative discussions are provided together with the high quality segmentation results of vcells on a wide range of complex images the simplicity and efficiency of our model are demonstrated by complexity analysis time and accuracy evaluations

spectral methods for hyperbolic problems we review the current state of fourier and chebyshev collocation methods for the solution of hyperbolic problems with an eye to basic questions of accuracy and stability of the numerical approximations throughout the discussion we emphasize recent developments in the area such as spectral penalty methods the use of filters the resolution of the gibbs phenomenon and issues related to the solution of nonlinear conservations laws such as conservation and convergence we also include a brief discussion on the formulation of multi domain methods for hyperbolic problems and conclude with a few examples of the application of pseudospectral collocation methods for solving nontrivial systems of conservation laws

stability of energy stable flux reconstruction for the diffusion problem using the interior penalty and bassi and rebay ii numerical fluxes for linear triangular elements abstract the flux reconstruction fr method has gained popularity within the research community the approach has been demonstrated to recover high order methods such as the discontinuous galerkin dg method stability analyses have been conducted for a linear advection problem leading to the energy stable flux reconstruction esfr methods also named vincent castonguay jameson huynh vcjh methods esfr schemes can be viewed as dg schemes with modally filtered correction fields using this class of methods the linear advection diffusion problem has been shown to be stable using the local discontinuous galerkin scheme ldg to compute the viscous numerical flux this stability proof has been extended for linear triangular and tetrahedra elements although the ldg scheme is commonly used it requires on particular meshes a wide stencil which raises the computational cost as a consequence many prefer the compact interior penalty ip or the bassi and rebay ii br2 numerical fluxes this article for the first time derives for both schemes a condition on the penalty term to ensure the stability for the linear diffusion equation the derivations are based on gauss legendre flux points and on periodic boundary conditions moreover the article proposes that for both the ip and br2 numerical fluxes the stability of the esfr scheme is independent of the auxiliary correction field a von neumann analysis is conducted to study the maximal time step of various esfr methods

shape factors for constant head double packer permeameters 1 local estimates of hydraulic conductivity are often obtained from constant head double packer tests the tests yield ratios of flow against head difference these are converted to values of hydraulic conductivity by dividing by a shape factor previously used shape factors have generally assumed that the packers are infinitely large such shape factors lead to overestimates of hydraulic conductivity as they ignore the effect of water flow around the packers a semianalytical solution is derived for a constant head double packer permeameter test the solution is compared with existing approximate techniques including the spheroidal equipotential solution the narrow packer approximation of rehbinder 1996 and the long packer approximation of rehbinder 2005 generally it is shown that ignoring the length of the packer and assuming a fully cased well lead to an overestimate of hydraulic conductivity the significance of this reduces with increasing well screen aspect ratio evaluation of the solution is nontrivial for this reason a polynomial relationship between shape factor well screen aspect ratio and packer length obtained by curve fitting with the semianalytical solution is provided

centroidal voronoi tessellations applications and algorithms a centroidal voronoi tessellation is a voronoi tessellation whose generating points are the centroids centers of mass of the corresponding voronoi regions we give some applications of such tessellations to problems in image compression quadrature finite difference methods distribution of resources cellular biology statistics and the territorial behavior of animals we discuss methods for computing these tessellations provide some analyses concerning both the tessellations and the methods for their determination and finally present the results of some numerical experiments