three dimensional volume conserving immersed boundary model for two phase fluid flows abstract we present a volume preserving scheme for two phase immiscible incompressible flows using an immersed boundary method ibm in a three dimensional space the two phase ibm employs a mixture of eulerian and lagrangian variables where the fluid interface is represented by discrete lagrangian markers exerting surface tension forces to the eulerian fluid domain and the markers are advected by the fluid velocity the interactions between the lagrangian markers and the fluid variables are linked by the discretized dirac delta function the present study extends the previous two dimensional research li et al volume preserving immersed boundary methods for two phase fluid flows int j numer meth fluids 69 2012 842 858 to the three dimensional space the key idea of the proposed method is relocating surface points along the normal directions to conserve the total volume we perform a number of numerical experiments to show the efficiency and accuracy of the proposed method

simulating the dynamics of inextensible vesicles by the penalty immersed boundary method in this paper we develop an immersed boundary ib method to simulate the dynamics of inextensible vesicles interacting with an incompressible fluid in order to take into account the inextensibility constraint of the vesicle the penalty immersed boundary pib method is used to virtually decouple the fluid and vesicle dynamics as numerical tests of our current pib method the dynamics of single and multiple inextensible vesicles under shear flows have been extensively explored and compared with the previous literature the method is also validated by a series of convergence study which confirms its consistent first order accuracy on the velocity field the vesicle configuration the vesicle area and the perimeter errors in addition the method is also applied to study a binary component vesicle problem

the overlapped radial basis function finite difference rbf fd method a generalization of rbf fd abstract we present a generalization of the rbf fd method that computes rbf fd weights in finite sized neighborhoods around the centers of rbf fd stencils by introducing an overlap parameter 0 1 such that 1 recovers the standard rbf fd method and 0 results in a full decoupling of stencils we provide experimental evidence to support this generalization and develop an automatic stabilization procedure based on local lebesgue functions for the stable selection of stencil weights over a wide range of values we provide an a priori estimate for the speedup of our method over rbf fd that serves as a good predictor for the true speedup we apply our method to parabolic partial differential equations with time dependent inhomogeneous boundary conditions neumann in 2d and dirichlet in 3d our results show that our method can achieve as high as a 60 speedup in 3d over existing rbf fd methods in the task of forming differentiation matrices

fast and accurate computation of hypersingular integrals in galerkin surface integral equation formulations via the direct evaluation method hypersingular 4 d integrals arising in the galerkin discretization of surface integral equation formulations are computed by means of the direct evaluation method the proposed scheme extends the basic idea of the singularity cancellation methods usually employed for the regularization of the singular integral kernel by utilizing a series of coordinate transformations combined with a reordering of the integrations the overall algebraic manipulation results in smooth 2 d integrals that can be easily evaluated via standard quadrature rules finally the reduction of the dimensionality of the original integrals together with the smooth behavior of the associated integrands lead up to unmatched accuracy and efficiency

a fast numerical method for solving the three dimensional stokes equations in the presence of suspended particles abstract a new fast numerical method for solving the three dimensional stokes equations in the presence of suspended particles is presented the fluid dynamics equations are solved on a lattice a particle is represented by a set of points each of which moves at the local fluid velocity and is not constrained to lie on the lattice these points are coupled by forces which resist deformation of the particle these forces contribute to the force density in the stokes equations as a result a single set of fluid dynamics equations holds at all points of the domain and there are no internal boundaries particle size shape and deformability may be prescribed computational work increases only linearly with the number of particles so large numbers 500 1000 of particles may be studied efficiently the numerical method involves implicit calculation of the particle forces by minimizing an energy function and solution of a finite difference approximation to the stokes equations using the fourier toeplitz method the numerical method has been implemented to run on all cray computers the implementation exploits the cray s vectorized arithmetic and on machines with insufficient central memory it performs efficient disk 1 o while storing most of the data on disk applications of the method to sedimentation of one two and many particle systems are described trajectories and settling speeds for two particle sedimentation and settling speed for multiparticle sedimentation from initial distributions on a cubic lattice or at random give good quantitative agreement with existing theories

stable and accurate pressure approximation for unsteady incompressible viscous flow how to properly specify boundary conditions for pressure is a longstanding problem for the incompressible navier stokes equations with no slip boundary conditions an analytical resolution of this issue stems from a recently developed formula for the pressure in terms of the commutator of the laplacian and leray projection operators here we make use of this formula to a improve the accuracy of computing pressure in two kinds of existing time discrete projection methods implicit in viscosity only and b devise new higher order accurate time discrete projection methods that extend a slip correction idea behind the well known finite difference scheme of kim and moin we test these schemes for stability and accuracy using various combinations of c 0 finite elements for all three kinds of time discretization one can obtain third order accuracy for both pressure and velocity without a time step stability restriction of diffusive type furthermore two kinds of projection methods are found stable using piecewise linear elements for both velocity and pressure

gradient iteration with lp norm constraints abstract gradient iterations with l p norm constrains have been studied recently both in the context of inverse problem and of compressed sensing use of l p norm constrains p 2 is often advocated when a sparse solution is expected a constrained gradient iteration is usually implemented via a shrinkage operator in this note we establish the l 2 norm convergence of such a constrained gradient iteration when p 1 2

sound quality characteristics of refrigerator noise in real living environments with relation to psychoacoustical and autocorrelation function parameters psychoacoustical and autocorrelation function acf parameters were employed to describe the temporal fluctuations of refrigerator noise during starting transition into from the stationary phase and termination of operation the temporal fluctuations of refrigerator noise include a click at start up followed by a rapid increase in volume a change of pitch and termination of the operation subjective evaluations of the noise of 24 different refrigerators were conducted in a real living environment the relationship between objective measures and perceived noisiness was examined by multiple regression analysis sound quality indices were developed based on psychoacoustical and acf parameters the psychoacoustical parameters found to be important for evaluating noisiness in the stationary phase were loudness and roughness the relationship between noisiness and acf parameters shows that sound energy and its fluctuations are important for evaluating noisiness also refrigerator sounds that had a fluctuat

dissimilarity judgments in relation to temporal and spatial factors for the sound field in an existing hall in relation to the temporal and spatial factors of sound fields dissimilarity judgments for different source locations on a stage were performed this study is based on the model of the auditory brain system which consists of the autocorrelation and crosscorrelation mechanisms for sound signals arriving at two ears and the specialization of human cerebral hemispheres there are three temporal factors 1 1 and e extracted from the autocorrelation function and four spatial factors ll iacc iacc and w iacc from the interaural crosscorrelation function of binaural signals in addition to these temporal and spatial factors the orthogonal factors of the subjective preference for sound field t 1 and t sub were taken into account the psychological distance between sound fields of different source locations on the stage were calculated by using these temporal spatial and orthogonal factors of sound fields using these distances and their linear combination dissimilarity can be calculated results of multivariable analysis show that the calculated scale values of dissimilarity agree well with the measured scale values

a comparison of implicit solvers for the immersed boundary equations explicit time discretizations of the immersed boundary method are known to require small timesteps to maintain stability a number of implicit methods have been introduced to alleviate this restriction to allow for a more ecient method but many of these methods still have a stability restriction on the timestep furthermore almost no comparisons have appeared in the literature of the relative computational costs of the implicit methods and the explicit method a recent paper e p newren a l fogelson r d guy and r m kirby unconditionally stable discretizations of the immersed boundary equations journal of computational physics vol 222 702 719 2007 addressed the confusion over stability of immersed boundary discretizations this paper identified the cause of instability in previous immersed boundary discretizations as lack of conservation of energy and introduced a new semi implicit discretization proven to be unconditionally stable i e it has bounded discrete energy the current paper addresses the issue of the eciency of the implicit solvers existing and new methods to solve implicit immersed boundary equations are described systematic comparisons of computational cost are presented for a number of these solution methods for our stable semi implicit immersed boundary discretization and an explicit discretization for two distinct test problems these comparisons show that two of the implicit methods are at least competitive with the explicit method on one test problem and outperform it on the other test problem in which the elastic stiness of the boundary does not dictate the timescale of the fluid motion

projected gradient iteration for nonlinear operator equation abstract in this paper we use a projected gradient algorithm to solve a nonlinear operator equation with l p norm 1 p 2 constraint gradient iterations with l p norm constraints have been studied recently both in the context of inverse problem and of compressed sensing in this paper the constrained gradient iteration is implemented via a projected operator we establish the l 2 norm convergence of sequence constructed by the constrained gradient iteration when p 1 2 the performance of the method is testified by a numerical example

a one domain approach for modeling and simulation of free fluid over a porous medium we propose a one domain approach based on the brinkman model for the modeling and simulation of the transport phenomenon between free fluid and a porous medium a thin transition layer is introduced between the free fluid region and the porous media region across which the porosity and permeability undergo a rapid but continuous change we study the behavior of the solution to the one domain model analytically and numerically using the method of matched asymptotic expansion we recover the beavers joseph saffman bjs interface condition as the thickness of the transition layer goes to zero we also calculate the error estimates between the leading order solution of the one domain model and the standard darcy stokes model of two domain model with bjs condition numerical methods are developed for both the one domain model and the two domain model numerical results are presented to support the analytical results thereby justifying the one domain model as a good approximation to the two domain stokes darcy model

eulerian lagrangian treatment of nondilute two phase gels we develop a three dimensional eulerian lagrangian two phase mixture model for a gel in which fluid is represented in eulerian coordinates and network in lagrangian coordinates the equations of motion and boundary conditions in their respective frames are derived using a principle of virtual power the volume fractions of each material at each point of eulerian space are calculated using the position and volume density of network particles network and fluid have separate velocity fields and the model includes viscous elastic and applied forces as well as those due to chemical potentials pressure and intermaterial drag we also develop a second order accurate numerical method for solving the model equations in one dimension illustrations of model behavior under a variety of conditions are shown

measurement of regional environmental noise by use of a pc based system an application to the noise near airport g marconi in bologna abstract measurements of aircraft noise were made at the airport g marconi in bologna by using a measurement system for regional environmental noise the system is based on the model of the human auditory brain system which is based on the interplay of autocorrelators and an interaural cross correlator acting on the pressure signals arriving at the ear entrances and takes into account the specialization of left and right human cerebral hemispheres see reference 8 measurements were taken through dual microphones at ear entrances of a dummy head the aircraft noise was characterized with the following physical factors calculated from the autocorrelation function acf and interaural cross correlation function iacf for binaural signals from the acf analysis 1 energy represented at the origin of delay 0 2 effective duration of the envelope of the normalized acf e 3 the delay time of the first peak 1 and 4 its amplitude 1were extracted from the iacf analysis 5 iacc 6 interaural delay time at which the iacc is defined iacc and 7 width of the iacf at the iacc wiaccwere extracted the factor 0 can be represented as the geometrical mean of the energies at both ears a noise source may be identified by these factors as timbre

acoustical properties of aircraft noise measured by temporal and spatial factors abstract acoustical properties of aircraft noise were investigated by means of temporal and spatial factors in sound fields based on the model of auditory brain system see reference 10 the model consists of the autocorrelation and crosscorrelation mechanisms for sound signals arriving at two ears and the specialization of human cerebral hemisphere there are four temporal factors extracted from the autocorrelation function acf 1 sound energy 0 2 effective duration of acf e 3 delay time of the first peak 1 and 4 its amplitude 1 from the interaural crosscorrelation function iacf three spatial factors are extracted as 1 magnitude of the interaural crosscorrelation iacc 2 interaural delay time at iacc iacc and 3 width of the maximum peak of the iacf wiacc it is found that the acoustical properties are well represented by the factors extracted from the acf and the iacf

implicit second order immersed boundary methods with boundary mass abstract the immersed boundary method is a computational framework for problems involving the interaction of a fluid and immersed elastic structures immersed boundary computations typically evaluate the elastic forces explicitly in the configuration of the immersed elastic structure in many applications this results in a severe restriction on the time step we present a semi implicit and a fully implicit second order accurate immersed boundary method the methods provide a natural way to handle mass on the immersed elastic structures we demonstrate their performance for a prototypical fluid structure interaction problem the methods are shown to possess superior stability properties that significantly alleviate the typically severe time step restriction of explicit computations

an immersed boundary method with formal second order accuracy and reduced numerical viscosity a formally second order accurate immersed boundary method is presented and tested in this paper we apply this new scheme to simulate the flow past a circular cylinder and study the effect of numerical viscosity on the accuracy of the computation by comparing the numerical results with those of a first order method the numerical evidence shows that the new scheme has less numerical viscosity and is therefore a better choice for the simulation of high reynolds number flows with immersed boundaries

a level set approach for computing solutions to incompressible two phase flow a level set approach for computing solutions to incompressible two phase flow is presented the interface between the two fluids is considered to be sharp and is described as the zero level set of a smooth function a new treatment of the level set method allows us to efficiently maintain the level set function as the signed distance from the interface we never have to explicitly reconstruct or find the zero level set consequently we are able to handle arbitrarily complex topologies large density and viscosity ratios and surface tension on relatively coarse grids we use a second order projection method along with a second order upwinded procedure for advecting the momentum and level set equations we consider the motion of air bubbles and water drops we also compute flows with multiple fluids such as air oil and water

a least squares method for linear elasticity using a patch reconstructed space abstract we propose a discontinuous least squares finite element method for solving the linear elasticity the approximation space is obtained by patch reconstruction with only one unknown per element we apply the l 2 norm least squares principle with the weak imposition of the continuity across the interior faces to the stress displacement formulation the optimal convergence order under the energy norm is attained numerical results of the linear elasticity are presented to verify the error estimates our method enjoys the advantages of discontinuous galerkin methods and in addition we illustrate the great simplicity in implementation the robustness and the improved efficiency of our method

adaptive mesh refinement and superconvergence for two dimensional interface problems adaptive mesh refinement and the borgers algorithm are combined to generate a body fitted mesh which can resolve the interface with fine geometric details standard linear finite element method bas

a quadratically convergent unstructured remeshing strategy for shape optimization a novel unstructured remeshing environment for gradient based shape optimization using triangular finite elements is presented the remeshing algorithm is based on a truss structure analogy in solving for the equilibrium position of the truss system the quadratically convergent newton s method is used exact analytical sensitivity information is therefore made available to the shape optimization algorithm the overall computational efficiency in gradient based shape optimization is very high in solving the truss structure analogy we compare our quadratically convergent newton solver with a previously proposed forward euler solver this includes notes regarding mesh uniformity element quality convergence rates and efficiency we present three numerical examples it is then shown that remeshing may introduce discontinuities and local minima we demonstrate that the effects of these on gradient based algorithms are alleviated to some extent through mesh refinement and may largely be overcome with a simple multi start strategy copyright 2005 john wiley sons ltd

a level set based topology optimization method targeting metallic waveguide design problems in this paper we propose a level set based topology optimization method targeting metallic waveguide design problems where the skin effect must be taken into account since the metallic waveguides are generally used in the high frequency range where this effect critically affects performance one of the most reasonable approaches to represent the skin effect is to impose an electric field constraint condition on the surface of the metal to implement this approach we develop a boundary tracking scheme for the arbitrary lagrangian eulerian ale mesh pertaining to the zero iso contour of the level set function that is given in an eulerian mesh and impose dirichlet boundary conditions at the nodes on the zero iso contour in the ale mesh to compute the electric field since the ale mesh accurately tracks the zero iso contour at every optimization iteration the electric field is always appropriately computed during optimization for the sensitivity analysis we compute the nodal coordinate sensitivities in the ale mesh and smooth them by solving a helmholtz type partial differential equation the obtained smoothed sensitivities are used to compute the normal velocity in the level set equation that is solved using the eulerian mesh and the level set function is updated based on the computed normal velocity finally the utility of the proposed method is discussed through several numerical examples copyright 2011 john wiley sons ltd

the immersed boundary method for advection electrodiffusion with implicit timestepping and local mesh refinement we describe an immersed boundary method for problems of fluid solute structure interaction the numerical scheme employs linearly implicit timestepping allowing for the stable use of timesteps that are substantially larger than those permitted by an explicit method and local mesh refinement making it feasible to resolve the steep gradients associated with the space charge layers as well as the chemical potential which is used in our formulation to control the permeability of the membrane to the possibly charged solute low reynolds number fluid dynamics are described by the time dependent incompressible stokes equations which are solved by a cell centered approximate projection method the dynamics of the chemical species are governed by the advection electrodiffusion equations and our semi implicit treatment of these equations results in a linear system which we solve by gmres preconditioned via a fast adaptive composite grid fac solver numerical examples demonstrate the capabilities of this methodology as well as its convergence properties

an efficient semi implicit immersed boundary method for the navier stokes equations the immersed boundary method is one of the most useful computational methods in studying fluid structure interaction on the other hand the immersed boundary method is also known to require small time steps to maintain stability when solved with an explicit method many implicit or approximately implicit methods have been proposed in the literature to remove this severe time step stability constraint but none of them give satisfactory performance in this paper we propose an efficient semi implicit scheme to remove this stiffness from the immersed boundary method for the navier stokes equations the construction of our semi implicit scheme consists of two steps first we obtain a semi implicit discretization which is proved to be unconditionally stable this unconditionally stable semi implicit scheme is still quite expensive to implement in practice next we apply the small scale decomposition to the unconditionally stable semi implicit scheme to construct our efficient semi implicit scheme unlike other implicit or semi implicit schemes proposed in the literature our semi implicit scheme can be solved explicitly in the spectral space thus the computational cost of our semi implicit schemes is comparable to that of an explicit scheme our extensive numerical experiments show that our semi implicit scheme has much better stability property than an explicit scheme this offers a substantial computational saving in using the immersed boundary method

annoyance of noise stimuli in relation to the spatial factors extracted from the interaural cross correlation function abstract while considering auditory brain model for subjective responses effects of spatial factors extracted from the interaural cross correlation function iacf on annoyance of noise stimuli are examined the previously developed indices to measure sound pressure levels spl and frequency characteristics cannot fully explain the psychological effects of noise in the first experiment subjects judged their annoyance by changing fluctuations in the magnitude of interaural cross correlation function iacc and the spl in the second they judged their annoyance by changing fluctuations in the interaural time delay iacc and the spl results show that 1 annoyance increased by increasing the fluctuations of iacc as well as the spl 2 annoyance increased by increasing the fluctuations of iacc as well as the spl

near field imaging of infinite rough surfaces this paper is concerned with an inverse rough surface scattering problem in near field optical imaging which is to reconstruct the scattering surface with a resolution beyond the diffraction limit the surface is assumed to be a small and smooth deformation of a plane surface based on a transformed field expansion the boundary value problem with complex scattering surface is converted into a successive sequence of two point boundary value problems in the frequency domain where an analytic solution for the direct scattering problem is derived from the method of integrated solution by neglecting the high order terms in the power series expansion the nonlinear inverse problem is linearized and an explicit inversion formula is obtained a spectral cut off regularization is adopted to suppress the exponential growth of the noise in the evanescent wave components which carry high spatial frequency of the scattering surface and contribute to the superresolution in the near field regime the method works f

the loudness of complex noise in relation to the factors extracted from the auto correlation function abstract the loudness of complex signals which include bandpass noises with different center frequencies complex noise is examined while changing the effective duration of the autocorrelation function e based on a model of the human auditory brain system for subjective response to a sound field the center frequencies of each component of the complex noises were 2000 and 3000 hz so that the perceived pitch was centered on 1000 hz the bandwidth of each component was changed by using a 2068 db octave sharp filter to control the e of the source signal the scale values for the loudness of the complex noises were obtained using a paired comparison method the results showed that the loudness increases with the eof the source signal similar to that of the single noise component centered on 1000 hz the loudness of complex noises having equal sound pressure levels is not constant within the critical band 160 hz

on the order of accuracy of the immersed boundary method higher order convergence rates for sufficiently smooth problems the immersed boundary method is both a mathematical formulation and a numerical scheme for problems involving the interaction of a viscous incompressible fluid and a visco elastic structure in m c lai simulations of the flow past an array of circular cylinders as a test of the immersed boundary method ph d thesis courant institute of mathematical sciences new york university 1998 m c lai c s peskin an immersed boundary method with formal second order accuracy and reduced numerical viscosity j comput phys 160 2000 705 719 lai and peskin introduced a formally second order accurate immersed boundary method but the convergence properties of their algorithm have only been examined computationally for problems with nonsmooth solutions consequently in practice only first order convergence rates have been observed in the present work we describe a new formally second order accurate immersed boundary method and demonstrate its performance for a prototypical fluid structure interaction problem involving an immersed viscoelastic shell of finite thickness studied over a broad range of reynolds numbers we consider two sets of material properties for the viscoelastic structure including a case where the material properties of the coupled system are discontinuous at the fluid structure interface for both sets of material properties the true solutions appear to possess sufficient smoothness for the method to converge at a second order rate for fully resolved computations

a multirate time integrator for regularized stokeslets the method of regularized stokeslets is a numerical approach to approximating solutions of fluid structure interaction problems in the stokes regime regularized stokeslets are fundamental solutions to the stokes equations with a regularized point force term that are used to represent forces generated by a rigid or elastic object interacting with the fluid due to the linearity of the stokes equations the velocity at any point in the fluid can be computed by summing the contributions of regularized stokeslets and the time evolution of positions can be computed using standard methods for ordinary differential equations rigid or elastic objects in the flow are usually treated as immersed boundaries represented by a collection of regularized stokeslets coupled together by virtual springs which determine the forces exerted by the boundary in the fluid for problems with boundaries modeled by springs with large spring constants the resulting ordinary differential equations become stiff and hence the time step for explicit time integration methods is severely constrained unfortunately the use of standard implicit time integration methods for the method of regularized stokeslets requires the solution of dense nonlinear systems of equations for many relevant problems here an alternate strategy using an explicit multirate time integration scheme based on spectral deferred corrections is incorporated that in many cases can significantly decrease the computational cost of the method the multirate methods are higher order methods that treat different portions of the ode explicitly with different time steps depending on the stiffness of each component numerical examples on two nontrivial three dimensional problems demonstrate the increased efficiency of the multi explicit approach with no significant increase in numerical error

the mini mixed finite element for the stokes problem an experimental investigation abstract o h 3 2 superconvergence in pressure and velocity has been experimentally investigated for the two dimensional stokes problem discretized with the mini mixed finite element even though the classic mixed finite element theory for the mini element guarantees linear convergence for the total error recent theoretical results indicate that superconvergence of order o h 3 2 in pressure and of the linear part of the computed velocity to the piecewise linear nodal interpolation of the exact velocity is in fact possible with structured three directional triangular meshes the numerical experiments presented here suggest a more general validity of o h 3 2 superconvergence possibly to automatically generated and unstructured triangulations in addition the approximating properties of the complete computed velocity have been compared with the approximating properties of the piecewise linear part of the computed velocity finding that the former is generally closer to the exact velocity whereas the latter conserves mass better

two dimensional simulations of valveless pumping using the immersed boundary method flow driven by pumping without valves is examined motivated by biomedical applications cardiopulmonary resuscitation cpr and the human fetus before the development of the heart valves the direction of flow inside a loop of tubing which consists of almost rigid and flexible parts is investigated when the boundary of one end of the flexible segment is forced periodically in time despite the absence of valves net flow around the loop may appear in these simulations the magnitude and even the direction of this flow depend on the driving frequency of the periodic forcing

a computational method for the coupled solution of reaction diffusion equations on evolving domains and manifolds in this paper we devise a moving mesh finite element method for the approximate solution of coupled bulk surface reaction diffusion equations on an evolving two dimensional domain fundamental to the success of the method is the robust generation of bulk and surface meshes for this purpose we use a novel moving mesh partial differential equation mmpde approach the developed method is applied to model problems with known analytical solutions these experiments indicate second order spatial and temporal accuracy coupled bulk surface problems occur frequently in many areas in particular in the modelling of eukaryotic cell migration and chemotaxis we apply the method to a model of the two way interaction of a migrating cell in a chemotactic field where the bulk region corresponds to the extracellular region and the surface to the cell membrane

generalized finite differences using fundamental solutions summary it is well known that solutions for linear partial differential equations may be given in terms of fundamental solutions the fundamental solutions solve the homogeneous equation exactly and are obtained from the solution of the inhomogeneous equation where the inhomogeneous term is described by a dirac delta distribution fundamental solutions are the building blocks of the boundary element method and of the method of fundamental solutions and are traditionally used to build boundary only global approximations in the domain of interest in this work the same characteristic of the fundamental solutions that of solving the homogeneous equation exactly is used but not to build a global approximation on the contrary local approximations are built in such a manner that it is possible to construct finite difference operators that are free from any form of structured grid copyright q 2009 john wiley sons ltd

qualitative measures for initial meshes this paper reviews geometric measures used to assess the shape of finite elements in two and three dimensional meshes measures have been normalized and made scale invariant whenever possible this paper also introduces a universal similarity region that enhances comparisons of triangles and their measures as a byproduct the usr provides a dynamic way to compare improved triangular meshes copyright 2000 john wiley sons ltd

cues for localization in the median plane as extracted from the auto correlation function abstract this study evaluates using factors extracted from the autocorrelation function acf as cues for sound localization of the median plane the amplitude of the transfer function for sound incident from the median plane to the ear entrances measured see reference 6 is translated into the acf it is shown that the sound localization in the median plane can be characterized by factors extracted from the acf these cues are the effective duration of the normalized acf e the delay time of the first peak 1 and its amplitude 1

nodal flow simulations by the immersed boundary method experimental work in developmental biology has recently shown that fluid flow driven by rotating cilia in the node which is a structure present in the early stage of growth of vertebrate embryos is responsible for determining the normal development of the left right asymmetry with the heart on the left of the body the liver on the right and so on the role of physics particularly of fluid dynamics in this process is one of the important questions that remain to be answered we apply a computational technique based on the immersed boundary method to the 3d nodal flow problem and investigate the fluid dynamics of the nodal flow in the developing embryo numerical simulations allow us to find the optimal condition for the maximal leftward flow in the node which is qualitatively comparable to experimental and theoretical findings in addition we explore how the leftward flow is affected by the change of the following parameter values the rigidity of the rotating cilia the rotational frequency and

a fast robust and non stiff immersed boundary method we propose a fast and non stiff approach for the solutions of the immersed boundary method for newtonian incompressible flows in two or three dimensions the proposed methodology is built on a robust semi implicit discretization introduced by peskin in the late 70s which is solved efficiently through the novel use of a fast treecode strategy to compute flow structure interactions optimal multipole type expansions are performed numerically by solving a least squares problem with a new fast iterative algorithm the new immersed boundary method is particularly well suited for three dimensional applications and or for problems where the number of immersed boundary points is large we demonstrate the efficacy and superiority of the method over existing approaches with two simple but illustrative examples in 3d

online planning of multiaxial loading path for elastic material identification while anisotropic materials provide more capabilities than regular isotropic materials the directional behavior of the anisotropic materials complicates their elastic and inelastic behavior such nonlinear behavior can be effectively observed and characterized by multiaxial testing but how to plan the loading path of a multiaxial test given a specimen and sensor readings while identifying material properties remains as an untouched issue this paper presents a methodology that updates the loading path at every sensor reading to identify reliable elastic moduli of anisotropic materials the multiaxial test must be quantified in order to find an effective loading path the proposed methodology uses distinguishability and uniqueness as such quantities by firstly analyzing the specimen on a continuum basis and then applying singular value decomposition svd associating the distinguishability and uniqueness to the reliability of elastic moduli the path planning problem is formulated such that an effective loading path can be found efficiently by a standard optimization method numerical examples first investigate the validity of the distinguishability and the uniqueness as performance measures to evaluate loading paths and the reliability of elastic moduli identified the efficacy of the proposed methodology has been then confirmed by analyzing it with and applying it to identification of elastic moduli

finite element approximation of convection diffusion problems using an exponentially graded mesh we present the analysis of an h version finite element method for the approximation of the solution to convection diffusion problems the method uses piece wise polynomials of degree p 1 defined on an exponentially graded mesh optimally constructed for the approximation of exponential layers we consider a model convection diffusion problem posed on the unit square and establish robust optimal convergence rates in the energy and in the maximum norm we also present the results of some numerical computations that illustrate our theoretical findings and compare the proposed method with others found in the literature

generalization performance of bipartite ranking algorithms with convex losses abstract previous works describing the generalization performance of bipartite ranking algorithms are usually based on the assumption of 0 1 loss or the area under the receiver operating characteristic roc curve in this paper we go far beyond this classical framework by investigating the generalization performance of bipartite ranking algorithms with convex losses over reproducing kernel hilbert spaces based on the mcdiarmid inequality and rademacher complexity we establish the upper bound on the generalization error for a bipartite ranking algorithm the theoretical analysis is different from the previous results on error analysis and shows the attractive uniform convergence property of regularized bipartite ranking algorithms

a poroelastic immersed boundary method with applications to cell biology the immersed boundary method is a widely used mixed eulerian lagrangian framework for simulating the motion of elastic structures immersed in viscous fluids in the traditional immersed boundary method the fluid and structure move with the same velocity field in this work a model based on the immersed boundary method is presented for simulating poroelastic media in which the fluid permeates a porous elastic structure of small volume fraction that moves with its own velocity field two distinct methods for calculating elastic stresses are presented and compared the methods are validated on a radially symmetric test problem by comparing with a finite difference solution of the classical equations of poroelasticity finally two applications of the modeling framework to cell biology are provided cellular blebbing and cell crawling it is shown that in both examples poroelastic effects are necessary to explain the relevant mechanics

superconvergence property of an over penalized discontinuous galerkin finite element gradient recovery method a polynomial preserving recovery method is introduced for over penalized symmetric interior penalty discontinuous galerkin solutions to a quasi linear elliptic problem as a post processing method the polynomial preserving recovery is superconvergent for the linear and quadratic elements under specified meshes in the regular and chevron patterns as well as general meshes satisfying condition by means of the averaging technique we prove the polynomial preserving recovery method for averaged solutions is superconvergent satisfying similar estimates as those for conforming finite element methods we deduce superconvergence of the recovered gradient directly from discontinuous solutions and naturally construct an a posteriori error estimator consequently the a posteriori error estimator based on the recovered gradient is asymptotically exact extensive numerical results consistent with our analysis are presented

unconditionally stable discretizations of the immersed boundary equations the immersed boundary ib method is known to require small timesteps to maintain stability when solved with an explicit or approximately implicit method many implicit methods have been proposed to try to mitigate this timestep restriction but none are known to be unconditionally stable and the observed instability of even some of the fully implicit methods is not well understood in this paper we prove that particular backward euler and crank nicolson like discretizations of the nonlinear immersed boundary terms of the ib equations in conjunction with unsteady stokes flow can yield unconditionally stable methods we also show that the position at which the spreading and interpolation operators are evaluated is not relevant to stability so as long as both operators are evaluated at the same location in time and space we further demonstrate through computational tests that approximate projection methods which do not provide a discretely divergence free velocity field appear to have a stabilizing influence for these problems and that the implicit methods of this paper when used with the full navier stokes equations are no longer subject to such a strict timestep restriction and can be run up to the cfl constraint of the advection terms

perturbation based stochastic multi scale computational homogenization method for the determination of the effective properties of composite materials with random properties quantifying uncertainty in the overall elastic properties of composite materials arising from randomness in the material properties and geometry of composites at microscopic level is crucial in the stochastic analysis of composites in this paper a stochastic multi scale finite element method which couples the multi scale computational homogenization method with the second order perturbation technique is proposed to calculate the statistics of the overall elasticity properties of composite materials in terms of the mean value and standard deviation the uncertainties associated with the material properties of the constituents are considered performance of the proposed method is evaluated by comparing mean values and coefficients of variation for components of the effective elastic tensor against corresponding values calculated using monte carlo simulation for three numerical examples results demonstrate that the proposed method has sufficient accuracy to capture the variability in effective elastic properties of the composite induced by randomness in the constituent material properties

2 d parachute simulation by the immersed boundary method parachute aerodynamics involves an interaction between the flexible elastic porous parachute canopy and the high speed airflow relative to the parachute through which the parachute falls computer simulation of parachute dynamics typically simplifies the problem in various ways e g by considering the parachute as a rigid bluff body here we avoid such simplification by using the immersed boundary ib method to study the full fluid structure interaction the ib method is generalized to handle porous immersed boundaries and the generalized method is used to study the influence of porosity on parachute stability

a local radial basis function method for advection diffusion reaction equations on complexly shaped domains abstract time dependent advection diffusion reaction and diffusion reaction equations are used as models in biology chemistry physics and engineering as representative examples we focus on a chemotaxis model and a turing system from biology and apply a local radial basis function method to numerically approximate the solutions the numerical method can efficiently approximate large scale problems in complexly shaped domains

loudness in relation to iterated rippled noise abstract this study examined the loudness of iterated rippled noises irns with different number of iterations under conditions of equal sound pressure the scale values of loudness were obtained using a paired comparison method the results showed that the loudness of irns was not constant even though the sound pressure level was equivalent the loudness of irns increased with increasing iteration number this indicated that repetitive components of sounds might affect their loudness

a coupled immersed boundary lattice boltzmann method for incompressible flows through moving porous media in this work we propose a numerical framework to simulate fluid flows in interaction with moving porous media of complex geometry it is based on the lattice boltzmann method including porous effects via a brinkman forchheimer darcy force model coupled to the immersed boundary method to handle complex geometries and moving structures the coupling algorithm is described in detail and it is validated on well established literature test cases for both stationary and moving porous configurations the proposed method is easy to implement and efficient in terms of cpu cost and memory management compared to alternative methods which can be used to deal with moving immersed porous media e g re meshing at each time step or use of a moving chimera mesh an overall good agreement was obtained with reference results opening the way to the numerical simulation of moving porous media for flow control applications

planar morphometry shear and optimal quasi conformal mappings to characterize the diversity of planar shapes in such instances as insect wings and plant leaves we present a method for the generation of a smooth morphometric mapping between two planar domains which matches a number of homologous points our approach tries to balance the competing requirements of a descriptive theory which may not reflect mechanism and a multi parameter predictive theory that may not be well constrained by experimental data specifically we focus on aspects of shape as characterized by local rotation and shear quantified using quasi conformal maps that are defined precisely in terms of these fields to make our choice optimal we impose the condition that the maps vary as slowly as possible across the domain minimizing their integrated squared gradient we implement this algorithm numerically using a variational principle that optimizes the coefficients of the quasi conformal map between the two regions and show results for the recreation of a sample historical grid deformation mapping of d arcy thompson we also deploy our method to compare a variety of drosophila wing shapes and show that our approach allows us to recover aspects of phylogeny as marked by morphology

a finite element method for the numerical solution of the coupled cahn hilliard and navier stokes system for moving contact line problems in this paper a semi implicit finite element method is presented for the coupled cahn hilliard and navier stokes equations with the generalized navier boundary condition for the moving contact line problems in our method the system is solved in a decoupled way for the cahn hilliard equations a convex splitting scheme is used along with a p1 p1 finite element discretization the scheme is unconditionally stable a linearized semi implicit p2 p0 mixed finite element method is employed to solve the navier stokes equations with our method the generalized navier boundary condition is extended to handle the moving contact line problems with complex boundary in a very natural way the efficiency and capacity of the present method are well demonstrated with several numerical examples

a simple mesh generator in matlab creating a mesh is the first step in a wide range of applications including scientific computing and computer graphics an unstructured simplex mesh requires a choice of meshpoints vertex nodes

the laplacian eigenvalues of a polygon the difficulties are almost always at the boundary that statement applies to the solution of partial differential equations with a given boundary and also to shape optimization with an unknown boundary these problems require two decisions closely related but not identical o1 how to discretize the boundary conditions 2 how to discretize the boundary itself that second problem is the one we discuss here the region w is frequently replaced by a polygon or polyhedron the approximate boundary email protected n may be only a linear interpolation of the true boundary email protected a perturbation theory that applies to smooth changes of domain is often less successful for a polygon this paper concentrates on a model problem the simplest we could find and we look at eigenvalues of the laplacian the boundary email protected will be the unit circle the approximate boundary email protected n is the regular inscribed polygon with n equal sides it seems impossible that the eigenvalues of regular polygons have not been intensively studied but we have not yet located an authoritative reference the problem will be approached numerically from three directions without attempting a general theory those directions are o1 finite element discretizations of the polygons w n 2 a taylor series based on piecewise smooth perturbations of the circle 3 a series expansion of the eigenvalues in powers of 1 n the second author particularly wishes that we could have consulted george fix about this problem his harvard thesis demonstrated the tremendous improvement that singular elements can bring to the finite element method particularly when w has a reentrant corner or even a crack his numerical experiments in 1 came at the beginning of a long and successful career in applied mathematics we only wish it had been longer

efficient solutions to robust semi implicit discretizations of the immersed boundary method the immersed boundary method is a versatile tool for the investigation of flow structure interaction in a large number of applications the immersed boundaries or structures are very stiff and strong tangential forces on these interfaces induce a well known severe time step restriction for explicit discretizations this excessive stability constraint can be removed with fully implicit or suitable semi implicit schemes but at a seemingly prohibitive computational cost while economical alternatives have been proposed recently for some special cases there is a practical need for a computationally efficient approach that can be applied more broadly in this context we revisit a robust semi implicit discretization introduced by peskin in the late 1970s which has received renewed attention recently this discretization in which the spreading and interpolation operators are lagged leads to a linear system of equations for the interface configuration at the future time when the interfacial force is linear however this linear system is large and dense and thus it is challenging to streamline its solution moreover while the same linear system or one of similar structure could potentially be used in newton type iterations nonlinear and highly stiff immersed structures pose additional challenges to iterative methods in this work we address these problems and propose cost effective computational strategies for solving peskin s lagged operators type of discretization we do this by first constructing a sufficiently accurate approximation to the system s matrix and we obtain a rigorous estimate for this approximation this matrix is expeditiously computed by using a combination of pre calculated values and interpolation the availability of a matrix allows for more efficient matrix vector products and facilitates the design of effective iterative schemes we propose efficient iterative approaches to deal with both linear and nonlinear interfacial forces and simple or complex immersed structures with tethered or untethered points one of these iterative approaches employs a splitting in which we first solve a linear problem for the interfacial force and then we use a nonlinear iteration to find the interface configuration corresponding to this force we demonstrate that the proposed approach is several orders of magnitude more efficient than the standard explicit method in addition to considering the standard elliptical drop test case we show both the robustness and efficacy of the proposed methodology with a 2d model of a heart valve

two finite element approaches for darcy and darcy brinkman flow through deformable porous media mixed method vs nurbs based isogeometric continuity abstract porous media problems with coupled finite deformations and flow are still quite challenging if large deformations occur a non homogeneous porosity field is almost inevitable as the porosity can vary due to deformation or due to flow and pore pressure from a numerical point of view this significantly changes the mathematical description of the problem in this contribution we will analyze the consequences of the occurrence of porosity gradients on the finite element formulations of saturated two phase porous media for darcy and darcy brinkman flow we will present two approaches which are capable of fulfilling the numerical requirements for convergence the first will be an approach based on nurbs shape functions the second is a mixed formulation including the porosity as primary solution field in addition we will propose a method to include no penetration or no slip constraints into the monolithic system using a dual lagrange multiplier method the potential of the proposed methods for solving porous flow structure interaction undergoing large deformations will be illustrated by numerical examples

an immersed boundary element method for level set based topology optimization summary in this paper we propose a new bem for level set based topology optimization in the proposed bem the nodal coordinates of the boundary element are replaced with the nodal level set function and the nodal coordinates of the eulerian mesh that maintains the level set function because this replacement causes the nodal coordinates of the boundary element to disappear the boundary element mesh appears to be immersed in the eulerian mesh therefore we call the proposed bem an immersed bem the relationship between the nodal coordinates of the boundary element and the nodal level set function of the eulerian mesh is clearly represented and therefore the sensitivities with respect to the nodal level set function are strictly derived in the immersed bem furthermore the immersed bem completely eliminates grayscale elements that are known to cause numerical difficulties in topology optimization by using the immersed bem we construct a concrete topology optimization method for solving the minimum compliance problem we provide some numerical examples and discuss the usefulness of the constructed optimization method on the basis of the obtained results copyright 2012 john wiley sons ltd

a numerical study of a semi algebraic multilevel preconditioner for the local discontinuous galerkin method in this work we consider the local discontinuous galerkin ldg method applied to second order elliptic problems arising in the modeling of single phase flows in porous media it has been recently proven that the spectral condition number of the stiffness matrix exhibits an asymptotic behavior of o h 2 on structured and unstructured meshes where h is the mesh size thus efficient preconditioners are mandatory we present a semi algebraic multilevel preconditioner for the ldg method using local lagrange type interpolatory basis functions we show numerically that its performance does not degrade or at least the number of iterations increases very slowly as the number of unknowns augments the preconditioner is tested on problems with high jumps in the coefficients which is the typical scenario of problems arising in porous media

on the role of polynomials in rbf fd approximations ii numerical solution of elliptic pdes rbf generated finite differences rbf fd have in the last decade emerged as a very powerful and flexible numerical approach for solving a wide range of pdes we find in the present study that combining polyharmonic splines phs with multivariate polynomials offers an outstanding combination of simplicity accuracy and geometric flexibility when solving elliptic equations in irregular or regular regions in particular the drawbacks on accuracy and stability due to runge s phenomenon are overcome once the rbf stencils exceed a certain size due to an underlying minimization property test problems include the classical 2 d driven cavity and also a 3 d global electric circuit problem with the earth s irregular topography as its bottom boundary the results we find are fully consistent with previous results for data interpolation

effect of domain shape modeling and measurement errors on the 2 d d bar method for eit the d bar algorithm based on nachman s 2 d global uniqueness proof for the inverse conductivity problem nachman 1996 is implemented on a chest shaped domain the scattering transform is computed on this chest shaped domain using trigonometric and adjacent current patterns and the complete electrode model for the forward problem is computed with the finite element method in order to obtain simulated voltage measurements the robustness and effectiveness of the method is demonstrated on a simulated chest with errors in input currents output voltages electrode placement and domain modeling

simulating flexible fiber suspensions using a scalable immersed boundary algorithm we present an approach for numerically simulating the dynamics of flexible fibers in a three dimensional shear flow using a scalable immersed boundary ib algorithm based on guermond and minev s pseudo compressible fluid solver the fibers are treated as one dimensional neutrally buoyant kirchhoff rods that resist stretching bending and twisting within the generalized ib framework we perform a careful numerical comparison against experiments on single fibers performed by s g mason and co workers who categorized the fiber dynamics into several distinct orbit classes we show that the orbit class may be determined using a single dimensionless parameter for low reynolds flows lastly we simulate dilute suspensions containing up to hundreds of fibers using a distributed memory computer cluster these simulations serve as a stepping stone for studying more complex suspension dynamics involving aggregation of fibers or flocculation and particle sedimentation due to added mass

on the hyper elastic formulation of the immersed boundary method abstract the immersed boundary ib method is both a mathematical formulation and a numerical method for fluid structure interaction problems in which immersed incompressible visco elastic bodies or boundaries interact with an incompressible fluid previous formulations of the ib method were not able to treat appropriately immersed materials of finite nonzero thickness modeled by general hyper elastic constitutive laws because of the lack of appropriate transmission conditions between the immersed body and the surrounding fluid in the case of a nonzero jump in normal stress at the solid fluid interface such a jump does not arise when the solid is comprised of fibers that run parallel to the interface but typically does arise in other cases e g when the solid contains elastic fibers that terminate at the solid fluid interface we present a derivation of the ib method that takes into account in an appropriate way the missing term the derivation presented in this paper starts from a separation of the stress that appears in the principle of virtual work the stress is divided into its fluid like and solid like components and each of these two terms is treated in its natural framework i e the eulerian framework for the fluid like stress and the lagrangian framework for the solid like stress we describe how the ib method can be used in conjunction with standard formulations of continuum mechanics models for immersed incompressible elastic materials and present some illustrative numerical experiments

a computational model of the cochlea using the immersed boundary method this thesis describes a two dimensional computational model of the cochlea inner ear solved using a modified form of peskin s immersed boundary method this method is an extension of peskin s method that was originally applied to solving a model of the heart 1972 this method solves the time dependent incompressible navier stokes equations in the presence of immersed boundaries the fluid equations are specified on a fixed eulerian grid while the immersed boundaries are specified on a moving lagrangian grid the immersed boundaries are used to represent the structures of the cochlea the rigid bone the actively moving stapes and the flexible membranes the immersed boundaries exert forces locally on the fluid these local forces are seen by the fluid as external forces that are added to the other forces pressure and viscous acting on the fluid the computational method divides into three separate parts first the forces exerted by the points of the immersed boundary are calculated and extended to the fluid grid second the fluid equations are solved and the velocities are restricted to the immersed boundary points finally the immersed boundary points are moved to their new locations at the new local velocities the immersed boundary forces are either specified such that the boundary moves at a given velocity zero or non zero or they are specified such that the forces obey some given force law for example hooke s law these forces can be calculated either explicitly or implicitly or a combination of both for the fluid the navier stokes equations are solved on a doubly periodic rectangular grid in a second order accurate manner using a projection method developed by bell colella and glaz 1988 the extension and restriction of the boundary forces and fluid velocities to and from the fluid grid are also done in a second order accurate manner the cochlea is modelled as two fluid chambers separated by a flexible partition whose stiffness varies exponentially along its length the stapes is represented by a moving piston and the bony outer walls are allowed to be either straight or tapered a travelling wave propagates along the flexible partition under the influence of the moving piston and the dependence of this wave on cochlea geometry and partition stiffness is studied also included are studies of bone conduction and transient signal analysis finally comparisons of the model results are made to experimental data and asymptotic results

the method of fundamental solutions applied to boundary eigenvalue problems we develop methods based on fundamental solutions to compute the steklov wentzell and laplace beltrami eigenvalues in the context of shape optimization in the class of smooth simply connected two dimensional domains the numerical method is accurate and fast a theoretical error bound is given along with comparisons with mesh based methods we illustrate the use of this method in the study of a wide class of shape optimization problems in two dimensions we extend the method to the computation of the laplace beltrami eigenvalues on surfaces and we investigate some spectral optimal partitioning problems

stencil reduction algorithms for the local discontinuous galerkin method the problem of reducing the stencil of the local discontinuous galerkin method applied to second order differential operator is discussed heuristic algorithms to minimize the total number of non zero blocks of the reduced stiffness matrix are presented and tested on a wide variety of unstructured and structured grids in 2d and 3d copyright 2009 john wiley sons ltd

diagnostic system based on the human auditory brain model for measuring environmental noise an application to railway noise abstract measurements of railway noise were conducted by use of a diagnostic system of regional environmental noise the system is based on the model of the human auditory brain system the model consists of the interplay of autocorrelators and an interaural crosscorrelator acting on the pressure signals arriving at the ear entrances and takes into account the specialization of left and right human cerebral hemispheres different kinds of railway noise were measured through binaural microphones of a dummy head to characterize the railway noise physical factors extracted from the autocorrelation functions acf and interaural crosscorrelation function iacf of binaural signals were used the factors extracted from acf were 1 energy represented at the origin of the delay 0 2 effective duration of the envelope of the normalized acf e 3 the delay time of the first peak 1 and 4 its amplitude o 1 the factors extracted from iacf were 5 iacc 6 interaural delay time at which the iacc is defined iacc and 7 width of the iacf at the iacc w iacc the factor 0 can be represented as a geometrical mean of energies at both ears as listening level ll

on the radius edge condition in the control volume method in this paper we show that the control volume algorithm for the solution of poisson s equation in three dimensions will converge even if the mesh contains a class of very flat tetrahedra slivers these tetrahedra are characterized by the fact that they have modest ratios of diameter to shortest edge but large circumscribing to inscribed sphere radius ratios and therefore may have poor interpolation properties elimination of slivers is a notoriously difficult problem for automatic mesh generation algorithms we also show that a discrete poincare inequality will continue to hold in the presence of slivers

a discrete forcing immersed boundary method for the fluid structure interaction of an elastic slender body we present an immersed boundary ib method for the simulation of flow around an elastic slender body the present method is based on the discrete forcing ib method for a stationary rigid body proposed by kim kim and choi 2001 25 the discrete forcing approach is used to relieve the limitation on the computational time step size the incompressible navier stokes equations are implicitly coupled with the dynamic equation for an elastic slender body motion the first is solved in the eulerian coordinate and the latter is described in the lagrangian coordinate the elastic slender body is modeled as a thin and flexible solid and is segmented by finite number of thin blocks each block is moved by external and internal forces such as the hydrodynamic elastic and buoyancy forces where the hydrodynamic force is obtained directly from the discrete forcing used in the ib method all the spatial derivative terms are discretized with the second order central difference scheme the present method is applied to three different fluid structure interaction problems flows around a flexible filament a flapping flag in a free stream and a flexible flapping wing in normal hovering respectively computations are performed at maximum cfl numbers of 0 75 1 the results obtained agree very well with those from previous studies

improved volume conservation in the computation of flows with immersed elastic boundaries this paper introduces a recipe for the construction of a finite difference divergence operator the coefficients of which are completely determined once an interpolation scheme has been chosen substitution of this divergence operator for the previously used divergence based on central differences makes a dramatic improvement in the overall volume conservation that is observed in an immersed boundary computation this improvement is particularly important for computations in which an elastic boundary separates chambers containing fluid at substantially different pressures a situation which is prominent in cardiac fluid dynamics during the contraction of the ventricles

computational cost of the fekete problem i the forces method on the 2 sphere here we study the computational complexity of the fekete point problem namely we give an exhaustive description of the main properties of an algorithm for the minimization of the logarithmic potential energy on the 2 sphere and we characterize the probability distribution of the cost of the different minima in particular we show that a local minimum can be found with an average cost of about o n 2 8

numerical quadrature over smooth closed surfaces the numerical approximation of definite integrals or quadrature often involves the construction of an interpolant of the integrand and its subsequent integration in the case of one dimension it is natural to rely on polynomial interpolants however their extension to two or more dimensions can be costly and unstable an efficient method for computing surface integrals on the sphere is detailed in the literature reeger fornberg 2016 stud appl math 137 174 188 doi 10 1111 sapm 12106 the method uses local radial basis function interpolation to reduce computational complexity when generating quadrature weights for any given node set this article generalizes this method to arbitrary smooth closed surfaces

a meshfree generalized finite difference method for surface pdes abstract in this paper we propose a novel meshfree generalized finite difference method gfdm approach to discretize pdes defined on manifolds derivative approximations for the same are done directly on the tangent space in a manner that mimics the procedure followed in volume based meshfree gfdms as a result the proposed method not only does not require a mesh it also does not require an explicit reconstruction of the manifold in contrast to some existing methods it avoids the complexities of dealing with a manifold metric while also avoiding the need to solve a pde in the embedding space a major advantage of this method is that all developments in usual volume based numerical methods can be directly ported over to surfaces using this framework we propose discretizations of the surface gradient operator the surface laplacian and surface diffusion operators possibilities to deal with anisotropic and discontinuous surface properties with large jumps are also introduced and a few practical applications are presented

fast high dimensional node generation with variable density abstract we present an algorithm for producing discrete distributions with a prescribed nearest neighbor distance function our approach is a combination of quasi monte carlo q mc methods and weighted riesz energy minimization the initial distribution is a stratified q mc sequence with some modifications a suitable energy functional on the configuration space is then minimized to ensure local regularity the resulting node sets are good candidates for building meshless solvers and interpolants as well as for other purposes where a point cloud with a controlled separation covering ratio is required applications of a three dimensional implementation of the algorithm in particular to atmospheric modeling are also given