an unconditionally stable fully conservative semi lagrangian method semi lagrangian methods have been around for some time dating back at least to 3 researchers have worked to increase their accuracy and these schemes have gained newfound interest with the recent widespread use of adaptive grids where the cfl based time step restriction of the smallest cell can be overwhelming since these schemes are based on characteristic tracing and interpolation they do not readily lend themselves to a fully conservative implementation however we propose a novel technique that applies a conservative limiter to the typical semi lagrangian interpolation step in order to guarantee that the amount of the conservative quantity does not increase during this advection in addition we propose a new second step that forward advects any of the conserved quantity that was not accounted for in the typical semi lagrangian advection we show that this new scheme can be used to conserve both mass and momentum for incompressible flows for incompressible flows we further explore properly conserving kinetic energy during the advection step but note that the divergence free projection results in a velocity field which is inconsistent with conservation of kinetic energy even for inviscid flows where it should be conserved for compressible flows we rely on a recently proposed splitting technique that eliminates the acoustic cfl time step restriction via an incompressible style pressure solve then our new method can be applied to conservatively advect mass momentum and total energy in order to exactly conserve these quantities and remove the remaining time step restriction based on fluid velocity that the original scheme still had

a regularized lagrangian finite point method for the simulation of incompressible viscous flows in this paper we present a regularized lagrangian finite point method rlfpm for the numerical simulation of incompressible viscous flows a lagrangian finite point scheme is applied to the projection method for the incompressible navier stokes equations the approximation of spatial derivatives is obtained by the weighted least squares method the pressure poisson equation with neumann boundary condition is solved by a stabilized finite point method a key aspect of the present approach is the periodic redistribution of the particle locations which are being distorted by the flow again weighted least squares approximation is implemented to interpolate the properties of the old particles onto the new particle locations with the proposed regularization technique problems associated with the flow induced irregularity of particle distribution in the lagrangian finite point scheme are circumvented three numerical examples taylor green flow lid driven flow in a cavity and flow through a periodic lattice of cylinders are presented to validate the proposed methodology the problem of extra diffusion caused by regularization is discussed the results demonstrate that rlfpm is able to perform accurate and stable simulations of incompressible viscous flows

scale space and edge detection using anisotropic diffusion a new definition of scale space is suggested and a class of algorithms used to realize a diffusion process is introduced the diffusion coefficient is chosen to vary spatially in such a way as to encourage intraregion smoothing rather than interregion smoothing it is shown that the no new maxima should be generated at coarse scales property of conventional scale space is preserved as the region boundaries in the approach remain sharp a high quality edge detector which successfully exploits global information is obtained experimental results are shown on a number of images parallel hardware implementations are made feasible because the algorithm involves elementary local operations replicated over the image

analysis of hybrid selection maximal ratio combining in correlated nakagami fading we present an analysis of a hybrid selection maximal ratio combining diversity system over an evenly correlated slow frequency nonselective nakagami fading channel where the correlation coefficient between any pair of the diversity branch gain amplitudes is the same and all average branch signal to noise ratios snrs are equal in this system the l branches with the largest instantaneous snr out of n available branches are selected and combined using maximal ratio combining from the joint characteristic function cf of the instantaneous branch snrs we obtain an expression for the cf of the combiner output snr as a series of elementary cfs the expression can be conveniently used to obtain the symbol error probability of coherent detection of different m ary modulation schemes we illustrate our methodology using m ary phase shift keying as an example

an mgf based unified framework to determine the joint statistics of partial sums of ordered random variables order statistics find applications in various areas of communications and signal processing in this paper we introduce an unified analytical framework to determine the joint statistics of partial sums of ordered random variables rvs with the proposed approach we can systematically derive the joint statistics of any partial sums of ordered statistics in terms of the moment generating function mgf and the probability density function pdf our mgf based approach applies not only when all the k ordered rvs are involved but also when only the ks ks k best rvs are considered in addition we present the closed form expressions for the exponential rv special case these results apply to the performance analysis of various wireless communication systems over fading channels

an implicit corrected sph formulation for thermal diffusion with linear free surface boundary conditions the smoothed particle hydrodynamics sph method has proven useful for modeling large deformation of fluids including fluids with stress free surfaces because of the lagrangian nature of the method it is well suited to address the thermal evolution of these free surface flows boundary conditions at the interface of the fluid with a solid wall are usually enforced through the use of boundary particles however applying conditions at free surfaces in particular gradient boundary conditions can be problematic with traditional sph formulations due to the degradation of the gradient approximation in these regions compounding this difficulty is that traditional approximations of the laplacian operator suffer a similar degradation near free surfaces a new sph formulation of the laplacian operator is presented which improves the accuracy near free surface boundaries this new form is based on a gradient approximation commonly used in thermal viscous and pressure projection problems but includes higher order terms in the appropriate taylor series comparisons with other approximations of second order derivatives are given the discretization is tested by solving steady state and transient problems of thermal diffusion using the backward euler method with a gmres solver boundary conditions are imposed through an augmented matrix copyright 2008 john wiley sons ltd

accuracy and stability in incompressible sph isph based on the projection method and a new approach the stability and accuracy of three methods which enforce either a divergence free velocity field density invariance or their combination are tested here through the standard taylor green and spin down vortex problems while various approaches to incompressible sph isph have been proposed in the past decade the present paper is restricted to the projection method for the pressure and velocity coupling it is shown that the divergence free isph method cannot maintain stability in certain situations although it is accurate before instability sets in the density invariant isph method is stable but inaccurate with random noise like disturbances the combined isph combining advantages in divergence free isph and density invariant isph can maintain accuracy and stability although at a higher computational cost redistribution of particles on a fixed uniform mesh is also shown to be effective but the attraction of a mesh free method is lost a new divergence free isph approach is proposed here which maintains accuracy and stability while remaining mesh free without increasing computational cost by slightly shifting particles away from streamlines although the necessary interpolation of hydrodynamic characteristics means the formulation ceases to be strictly conservative this avoids the highly anisotropic particle spacing which eventually triggers instability importantly pressure fields are free from spurious oscillations up to the highest reynolds numbers tested

speckle reducing anisotropic diffusion this paper provides the derivation of speckle reducing anisotropic diffusion srad a diffusion method tailored to ultrasonic and radar imaging applications srad is the edge sensitive diffusion for speckled images in the same way that conventional anisotropic diffusion is the edge sensitive diffusion for images corrupted with additive noise we first show that the lee and frost filters can be cast as partial differential equations and then we derive srad by allowing edge sensitive anisotropic diffusion within this context just as the lee 1980 1981 1986 and frost 1982 filters utilize the coefficient of variation in adaptive filtering srad exploits the instantaneous coefficient of variation which is shown to be a function of the local gradient magnitude and laplacian operators we validate the new algorithm using both synthetic and real linear scan ultrasonic imagery of the carotid artery we also demonstrate the algorithm performance with real sar data the performance measures obtained by means of computer simulation of carotid artery images are compared with three existing speckle reduction schemes in the presence of speckle noise speckle reducing anisotropic diffusion excels over the traditional speckle removal filters and over the conventional anisotropic diffusion method in terms of mean preservation variance reduction and edge localization

analysis of a new variational model for multiplicative noise removal in this paper we consider a new variational model for multiplicative noise removal we prove the existence and uniqueness of the minimizer for the variational problem furthermore we derive the existence and uniqueness of weak solutions for the associated evolution equation finally some numerical experiments are shown to compare the proposed model with the model given by aubert and aujol

virtual branch analysis of symbol error probability for hybrid selection maximal ratio combining in rayleigh fading we derive analytical expressions for the symbol error probability sep for a hybrid selection maximal ratio combining h s mrc diversity system in multipath fading wireless environments with h s mrc l out of n diversity branches are selected and combined using maximal ratio combining mrc we consider coherent detection of m ary phase shift keying mpsk and quadrature amplitude modulation mqam using h s mrc for the case of independent rayleigh fading with equal signal to noise ratio averaged over the fading the proposed problem is made analytically tractable by transforming the ordered physical diversity branches which are correlated into independent and identically distributed i i d virtual branches which results in a simple derivation of the sep for arbitrary l and n we further obtain a canonical structure for the sep of h s mrc as a weighted sum of the elementary seps which are the seps using mrc with i i d diversity branches in rayleigh fading or equivalently the seps of the nondiversity single branch system in nakagami fading whose closed form expressions are well known we present numerical examples illustrating that h s mrc even with l spl lt n can achieve a performance close to that of n branch mrc

a new incompressibility discretization for a hybrid particle mac grid representation with surface tension we take a particle based approach to incompressible free surface flow motivated by the fact that an explicit representation of the interface geometry and internal deformations gives precise feedback to an implicit solver for surface tension methods that enforce incompressibility directly on the particles are typically numerically inefficient compared to those that utilize a background grid however background grid discretizations suffer from inaccuracy near the free surface where they do not properly capture the interface geometry therefore our incompressibility discretization utilizes a particle based projection near the interface and a background mac grid based projection for efficiency in the vast interior of the liquid domain as well as a novel method for coupling these two disparate projections together we show that the overall coupled elliptic solver is second order accurate and remains second order accurate when used in conjunction with an appropriate temporal discretization for parabolic problems a similar second order accurate discretization is derived when the mac grid unknowns are located on faces as opposed to cell centers so that navier stokes viscosity can be solved for implicitly as well finally we present a fully implicit approach to surface tension that is robust enough to achieve a steady state solution in a single time step beyond stable implicit surface tension for our novel hybrid discretization we demonstrate preliminary results for both standard front tracking and the particle level set method

a variational approach to removing multiplicative noise this paper focuses on the problem of multiplicative noise removal we draw our inspiration from the modeling of speckle noise by using a map estimator we can derive a functional whose minimizer corresponds to the denoised image we want to recover although the functional is not convex we prove the existence of a minimizer and we show the capability of our model on some numerical examples we study the associated evolution problem for which we derive existence and uniqueness results for the solution we prove the convergence of an implicit scheme to compute the solution

analysis of hybrid selection maximal ratio combining in rayleigh fading we use a novel virtual branch technique to succinctly derive the mean and variance of the combiner output signal to noise ratio for hybrid selection maximal ratio combining in a multipath fading environment

behavioral analysis of anisotropic diffusion in image processing in this paper we analyze the behavior of the anisotropic diffusion model of perona and malik 1990 the main idea is to express the anisotropic diffusion equation as coming from a certain optimization problem so its behavior can be analyzed based on the shape of the corresponding energy surface we show that anisotropic diffusion is the steepest descent method for solving an energy minimization problem it is demonstrated that an anisotropic diffusion is well posed when there exists a unique global minimum for the energy functional and that the ill posedness of a certain anisotropic diffusion is caused by the fact that its energy functional has an infinite number of global minima that are dense in the image space we give a sufficient condition for an anisotropic diffusion to be well posed and a sufficient and necessary condition for it to be ill posed due to the dense global minima the mechanism of smoothing and edge enhancement of anisotropic diffusion is illustrated through a particular orthogonal decomposition of the diffusion operator into two parts one that diffuses tangentially to the edges and therefore acts as an anisotropic smoothing operator and the other that flows normally to the edges and thus acts as an enhancement operator

high order particle method for solving incompressible navier stokes equations within a mixed lagrangian eulerian framework abstract owing to the fact that the poisson equation of pressure for incompressible fluid flow is purely elliptic it is therefore computationally improper to compute pressure on irregularly distributed moving particles as addressed in the recent moving particle with embedded pressure mesh mppm method in the current work a modified mppm method known as the mixed lagrangian eulerian mle method is proposed for solving the incompressible navier stokes equations in the current velocity pressure formulation the momentum and continuity equations are approximated on the moving particles lagrangian and the uniform cartesian grid points respectively meanwhile the total derivative of velocity terms appeared in the momentum equations are estimated by simply advecting the moving particles thereby eliminating the convection stability problem and increasing the flow accuracy without introducing false diffusion error in the conventional moving particle semi implicit mps and mppm methods numerical accuracies of the laplacian and gradient operators are strongly dependent on the regularity of the particle distribution in some implicit schemes the gradient and laplacian terms are of second order and first order accuracy respectively in the current work the second order accuracies of these differential terms exhibited on moving particles are realized by interpolating the derivative values from the uniform cartesian grids calculated by using the high order combined compact difference ccd scheme from the numerical results of laplacian term approximation by using various numerical schemes it is shown that the new mle scheme is at least second order accurate the proposed mixed lagrangian eulerian mle method can be easily applied to simulate fluid flow problems ranging from low to high reynolds number it is found that the numerical results compare well with the benchmark solutions moreover it is more accurate than the recently proposed mppm method

a strongly degenerate quasilinear equation the parabolic case we prove the existence and uniqueness of entropy solutions of the neumann problem for the quasilinear parabolic equation ut a u du where a z f z and f is a convex function of with linear growth as satisfying other additional assumptions in particular this class includes the case where f z z 0 and is a convex function with linear growth as

cyclic schemes for pde based image analysis we investigate a class of efficient numerical algorithms for many partial differential equations pdes in image analysis they are applicable to parabolic or elliptic pdes that have bounded coefficients and lead to space discretisations with symmetric matrices our schemes are easy to implement and well suited for parallel implementations on gpus since they are based on the explicit diffusion scheme in the parabolic case and the jacobi method in the elliptic case by supplementing these methods with cyclically varying time step sizes or relaxation parameters we achieve efficiency gains of several orders of magnitude we call the resulting algorithms fast explicit diffusion fed and fast jacobi fj methods to achieve a good compromise between efficiency and accuracy we show that one should use parameter cycles that result from factorisations of box filters for these cycles we establish stability results in the euclidean norm our schemes perform favourably in a number of applications including isotropic nonlinear diffusion filters with widely varying diffusivities as well as anisotropic diffusion methods for image filtering inpainting and regularisation in computer vision moreover they are equally suited for higher dimensional problems as well as higher order pdes and they can also be interpreted as efficient first order methods for smooth optimisation problems

analysis of minimum selection h s mrc in rayleigh fading we analyze the error performance of an improved hybrid selection maximal ratio combining h s mrc technique called minimum selection h s mrc in flat rayleigh fading for coherent digital modulation schemes here the minimum number of diversity branches are selected such that their combined signal to noise ratio is above a given threshold we derive a closed form expression for the distribution of the number of selected branches this distribution is used to obtain the symbol error probability

a stable sph discretization of the elliptic operator with heterogeneous coefficients smoothed particle hydrodynamics sph has been extensively used to model high and low reynolds number flows free surface flows and collapse of dams study pore scale flow and dispersion elasticity and thermal problems in different applications it is required to have a stable and accurate discretization of the elliptic operator with homogeneous and heterogeneous coefficients in this paper the stability and approximation analysis of different sph discretization schemes traditional and new of the diagonal elliptic operator for homogeneous and heterogeneous media are presented the optimum and new discretization scheme of specific shape satisfying thetwo point flux approximation nature is also proposed this scheme enhances the laplace approximation brookshaw s scheme 1985 and schwaiger s scheme 2008 used in the sph community for thermal viscous and pressure projection problems with an isotropic elliptic operator the numerical results are illustrated by numerical examples where the comparison between different versions of the meshless discretization methods are presented

adaptive smoothing via contextual and local discontinuities a novel adaptive smoothing approach is proposed for noise removal and feature preservation where two distinct measures are simultaneously adopted to detect discontinuities in an image inhomogeneity underlying an image is employed as a multiscale measure to detect contextual discontinuities for feature preservation and control of the smoothing speed while local spatial gradient is used for detection of variable local discontinuities during smoothing unlike previous adaptive smoothing approaches two discontinuity measures are combined in our algorithm for synergy in preserving nontrivial features which leads to a constrained anisotropic diffusion process that inhomogeneity offers intrinsic constraints for selective smoothing thanks to the use of intrinsic constraints our smoothing scheme is insensitive to termination times and the resultant images in a wide range of iterations are applicable to achieve nearly identical results for various early vision tasks our algorithm is formally analyzed and related to anisotropic diffusion comparative results indicate that our algorithm yields favorable smoothing results and its application in extraction of hydrographic objects demonstrates its usefulness as a tool for early vision

lagrangian formulations to solve free surface incompressible inviscid fluid flows abstract a particle method is presented for the solution of the incompressible inviscid fluid flow equation using a lagrangian formulation the interpolated function are those used in meshless approximations and the time integration is introduced in a semi implicit way by a fractional step method in this manner both classical stabilization terms used in incompressible euler equations are unnecessary numerical diffusion for convective terms are unnecessary due to the lagrangian formulation and stabilization of pressure due to the incompressibility constraint for equal order interpolations is eliminated using the fractional step method

a stabilized fractional step runge kutta taylor sph algorithm for coupled problems in geomechanics abstract failure of geomaterials with pores filled with fluids is an important research area in both civil and geological engineering many finite element formulations for coupled problems present difficulties such as overestimating failure loads or mesh alignment dependence resulting on spurious failure mechanisms moreover the spaces where field variables are approximated have to fulfill additional requirements ensuring stability stress velocity pore pressure formulations in fe analysis provide accurate results for wave propagation and failure analysis however finite elements present important limitations when deformations are large the purpose of this paper is to present a stabilized fractional step sph algorithm which combines the advantages of the sph method for large deformation problems with those of the taylor galerkin algorithm used within the finite element framework

adaptive richardson iteration based on leja points an adaptive richardson iteration method is presented for the solution of large linear systems of equations with a sparse symmetric positive definite matrix the relaxation parameters for richardson iteration are chosen to be reciprocal values of leja points for an interval a b on the positive real axis and the endpoints a and b are determined adaptively by computing certain modified moments during the iterations computed examples show that the adaptive richardson method can be competitive with the conjugate gradient algorithm

hyperbolic phenomena in a strongly degenerate parabolic equation we consider the equation u t u u x x where 0 and where is a strictly increasing function with lim s we solve the associated cauchy problem for an increasing initial function and discuss to what extent the solution behaves qualitatively like solutions of the first order conservation law u t u x equations of this type arise for example in the theory of phase transitions where the corresponding free energy functional has a linear growth rate with respect to the gradient

a doubly degenerate diffusion model based on the gray level indicator for multiplicative noise removal multiplicative noise removal is a challenging task in image processing inspired by the impressive performance of nonlinear diffusion models in additive noise removal we address this problem in the view of nonlinear diffusion equation theories rather than the traditional variation methods we develop a nonlinear diffusion filter denoising framework which considers not only the information of the gradient of the image but also the information of gray levels of the image furthermore under this framework we propose a doubly degenerate diffusion model for multiplicative noise removal which is analyzed with respect to some of its properties and behavior in denoising process in numerical aspects we present an efficient scheme which uses a stabilization by fast explicit diffusion for the implementation of the multiplicative noise removal model finally the experimental results illustrate effectiveness and efficiency of the proposed model

a conservative adaptive projection method for the variable density incompressible navier stokes equations in this paper we present a method for solving the equations governing time dependent variable density incompressible flow in two or three dimensions on an adaptive hierarchy of grids the method is based on a projection formulation in which we first solve advection diffusion equations to predict intermediate velocities and then project these velocities onto a space of approximately divergence free vector fields our treatment of the first step uses a specialized second order upwind method for differencing the nonlinear convection terms that provides a robust treatment of these terms suitable for inviscid and high reynolds number flow density and other scalars are advected in such a way as to maintain conservation if appropriate and free stream preservation our approach to adaptive refinement uses a nested hierarchy of logically rectangular girds with simultaneous refinement of the girds in both space and time the integration algorithm on the grid hierarchy is a recursive procedure in which coarse grids are advanced in time fine grids are advanced multiple steps to reach the same time as the coarse grids and the data at different levels are then synchronized the single grid algorithm is described briefly but the emphasis here is on the time stepping procedure for the adaptive hierarchy numerical examples are presented to demonstrate the algorithms s accuracy and convergence properties and illustrate the behavior of the method an additional example demonstrates the performance of the method on a more realistic problem namely a three dimensional variable density shear layer

closed form statistics for the sum of squared nakagami m variates and its applications we present closed form expressions for the probability density function pdf and the cumulative distribution function cdf of the sum of non identical squared nakagami m random variables rvs with integer order fading parameters as it is shown they can be written as a weighted sum of erlang pdfs and cdfs respectively while the analysis includes both independent and correlated sums of rvs the proposed formulation significantly improves previously published results which are either in the form of infinite sums or higher order derivatives of the fading parameter m the obtained formulas can be applied to the performance analysis of diversity combining receivers operating over nakagami m fading channels

a simplified approach to enhance the performance of smooth particle hydrodynamics methods this paper presents an approach to improve the accuracy and stability of smooth particle hydrodynamics sph techniques and describes how this correction procedure can be combined with kernel correction to formulate a complete form of the corrected smooth particle hydrodynamics csph method the development and theory of this new approach is presented in the context of the solution of poisson equations successful implementation of the theory is verified via various numerical examples

computing a null divergence velocity field using smoothed particle hydrodynamics a new use of smoothed particle hydrodynamics sph in fluid simulation is presented an algorithm solving the helmholtz hodge decomposition using sph in order to find the null divergence velocity field for incompressible flow simulation accordingly a new version of the laplacian for a vector field is proposed here in order to improve the accuracy of the sph technique the paper also presents some test problems for understanding the limitations of different kinds of gradient and laplacian approximation formulas

oriented speckle reducing anisotropic diffusion ultrasound imaging systems provide the clinician with noninvasive low cost and real time images that can help them in diagnosis planning and therapy however although the human eye is able to derive the meaningful information from these images automatic processing is very difficult due to noise and artifacts present in the image the speckle reducing anisotropic diffusion filter was recently proposed to adapt the anisotropic diffusion filter to the characteristics of the speckle noise present in the ultrasound images and to facilitate automatic processing of images we analyze the properties of the numerical scheme associated with this filter using a semi explicit scheme we then extend the filter to a matrix anisotropic diffusion allowing different levels of filtering across the image contours and in the principal curvature directions we also show a relation between the local directional variance of the image intensity and the local geometry of the image which can justify the choice of the gradient and the principal curvature directions as a basis for the diffusion matrix finally different filtering techniques are compared on a 2 d synthetic image with two different levels of multiplicative noise and on a 3 d synthetic image of a y junction and the new filter is applied on a 3 d real ultrasound image of the liver

modeling low reynolds number incompressible flows using sph the method of smoothed particle hydrodynamics sph is extended to model incompressible flows of low reynolds number for such flows modification of the standard sph formalism is required to minimize errors associated with the use of a quasi incompressible equation of state treatment of viscosity state equation kernel interpolation and boundary conditions are described simulations using the method show close agreement with series solutions for couette and poiseuille flows furthermore comparison with finite element solutions for flow past a regular lattice of cylinders shows close agreement for the velocity and pressure fields the sph results exhibit small pressure fluctuations near curved boundaries further improvements to the boundary conditions may be possible which will reduce these errors a similar method to that used here may permit the simulation of other flows at low reynolds numbers using sph further development will be needed for cases involving free surfaces or substantially different equations of state