a second order kinetic scheme for gas dynamics on arbitrary grids cartesian meshes for domains with complicated boundaries give rise to cut cells with arbitrarily small volumes explicit integration schemes over such meshes have a time step restriction proportional to the smallest cell volume we present an implementation of the kinetic scheme for gas dynamics by perthame b perthame boltzmann type schemes for gas dynamics and the entropy property siam j num anal 27 1990 1405 1421 on arbitrary cartesian meshes the formulation allows a time step based on the underlying regular cell size and retains l 1 stability positivity and second order convergence numerical convergence studies on arbitrary grids are presented

robust image analysis with sparse representation on quantized visual features recent techniques based on sparse representation sr have demonstrated promising performance in high level visual recognition exemplified by the highly accurate face recognition under occlusion and other sparse corruptions most research in this area has focused on classification algorithms using raw image pixels and very few have been proposed to utilize the quantized visual features such as the popular bag of words feature abstraction in such cases besides the inherent quantization errors ambiguity associated with visual word assignment and misdetection of feature points due to factors such as visual occlusions and noises constitutes the major cause of dense corruptions of the quantized representation the dense corruptions can jeopardize the decision process by distorting the patterns of the sparse reconstruction coefficients in this paper we aim to eliminate the corruptions and achieve robust image analysis with sr toward this goal we introduce two transfer processes ambiguity transfer and mis detection transfer to account for the two major sources of corruption as discussed by reasonably assuming the rarity of the two kinds of distortion processes we augment the original sr based reconstruction objective with mmbl0 norm regularization on the transfer terms to encourage sparsity and hence discourage dense distortion transfer computationally we relax the nonconvex mmbl0 norm optimization into a convex mmbl1 norm optimization problem and employ the accelerated proximal gradient method to optimize the convergence provable updating procedure extensive experiments on four benchmark datasets caltech 101 caltech 256 corel 5k and cmu pose illumination and expression manifest the necessity of removing the quantization corruptions and the various advantages of the proposed framework

metric subregularity and the proximal point method we examine the linear convergence rates of variants of the proximal point method for finding zeros of maximal monotone operators we begin by showing how metric subregularity is sufficient for local linear convergence to a zero of a maximal monotone operator this result is then generalized to obtain convergence rates for the problem of finding a common zero of multiple monotone operators by considering randomized and averaged proximal methods

a simplified h box method for embedded boundary grids we present a simplified h box method for integrating time dependent conservation laws on embedded boundary grids using an explicit finite volume scheme by using a method of lines approach with a strong stability preserving runge kutta method in time the complexity of our previously introduced h box method is greatly reduced a stable accurate and conservative approximation is obtained by constructing a finite volume method where the numerical fluxes satisfy a certain cancellation property for a model problem in one space dimension using appropriate limiting strategies the resulting method is shown to be total variation diminishing in two space dimensions stability is maintained by using rotated h boxes as introduced in previous work m j berger and r j leveque comput systems engrg 1 1990 pp 305 311 c helzel m j berger and r j leveque siam j sci comput 26 2005 pp 785 809 but in the new formulation h box gradients are taken solely from the underlying cartesian grid which also reduces the computational cost

a second order accurate conservative front tracking method in one dimension this paper presents a conservative front tracking method for shocks and contact discontinuities that is second order accurate it is based on a volume of fluid method that treats the moving front with concepts similar to those of an embedded boundary method special care is taken in the centering of the data to ensure the right order of accuracy at the front and a redistribution step guarantees conservation a suite of test problems for tracking both shocks and contact discontinuities is presented that confirms that the method is second order accurate

component averaged row projections a robust block parallel scheme for sparse linear systems a new method for the parallel solution of large sparse linear systems is introduced it proceeds by dividing the equations into blocks and operating in block parallel iterative mode i e all the blocks are processed in parallel and the partial results are merged to form the next iterate the new scheme performs kaczmarz row projections within the blocks and merges the results by certain component averaging operations hence it is called component averaged row projections or carp the system matrix can be general nonsymmetric and ill conditioned and the division into blocks is unrestricted for partial differential equations pdes if the blocks are domain based then only variables at the boundaries between domains are averaged thereby minimizing data transfer between processors carp is very robust its application to test cases of linear systems derived from pdes shows that it converges in difficult cases where state of the art methods fail it is also very memory efficient and exhibits an almost linear speedup ratio with efficiency greater than unity in some cases a formal proof of convergence is presented it is shown that the component averaging operations are equivalent to row projections in a certain superspace so the convergence properties of carp are identical to those of kaczmarz s algorithm in the superspace carp and its convergence proof also apply to the consistent convex feasibility problem

an efficient robust adaptive filtering algorithm based on parallel subgradient projection techniques this paper presents a novel robust adaptive filtering scheme based on the interactive use of statistical noise information and the ideas developed originally for efficient algorithmic solutions to the convex feasibility problems the statistical noise information is quantitatively formulated as stochastic property closed convex sets by the simple design formulae developed in this paper a simple set theoretic inspection also leads to an important statistical reason for the sensitivity to noise of the affine projection algorithm apa the proposed adaptive algorithm is computationally efficient and robust to noise because it requires only an iterative parallel projection onto a series of closed half spaces that are highly expected to contain the unknown system to be identified and is free from the computational load of solving a system of linear equations the numerical examples show that the proposed adaptive filtering scheme realizes dramatically fast and stable convergence for highly colored excited speech like input signals in severe noise situations

summed squared distance error reduction by simultaneous multiprojections and applications a parallel projection scheme in which projections are performed simultaneously on all constraints at each iteration is presented it is a multiprojections scheme because different distance functions can be minimized for each projection as long as they are based on weighted l 2 norms the use of multiple distance functions enables simplifications of the various projection operations leading to an efficient implementation of this algorithm this is true especially for constrained deconvolution type problems due to the inherent parallelism of the algorithm projections onto more than two sets can be performed even if one or more of the sets are nonconvex maintaining a monotone decrease of a cost functional with no further restrictions this is in contrast to the serial projections onto convex sets pocs algorithm where no more than two sets can be treated if one of the sets is nonconvex our method is a special case of a multiprojections method proposed by censor and elfving where generalized distance functions of the bregman type are used the restriction to weighted l 2 norms leads to a simple and explicit form of this algorithm and allows relaxation and the use of nonconvex sets

block iterative surrogate projection methods for convex feasibility problems abstract a unified framework is presented for studying the convergence of projection methods for finding a common point of finitely many closed convex sets in r n every iteration approximates each set by a half space given either by an approximate projection of the current iterate or by an aggregate inequality derived from the convex inequalities describing this set the next iterate is found by projecting the current one on a surrogate half space formed by taking a convex combination of the half space inequalities convergence to a solution is established under weak conditions that allow various acceleration techniques and choices of aggregating weights the resulting methods are block iterative and hence lend themselves to parallel implementation we show that the idea of forming cut maps via surrogate inequalities encompasses many classical as well as recently proposed methods for set intersection problems and convex feasibility problems with nondifferentiable inequalities and linear equations and inequalities

adjoint sensitivity computations for an embedded boundary cartesian mesh method we present a new approach for the computation of shape sensitivities using the discrete adjoint and flow sensitivity methods on cartesian meshes with general polyhedral cells cut cells at the wall boundaries by directly linearizing geometric constructors of the cut cells an efficient and robust computation of shape sensitivities is achieved for problems governed by the euler equations the accuracy of the linearization is verified by the use of a model problem with an exact solution verification studies show that the convergence rate of gradients is second order for design variables that do not alter the boundary shape and is reduced to first order for shape design problems the approach is applied to several three dimensional problems including inverse design and shape optimization of a re entry capsule in hypersonic flow the results show that reliable approximations of the gradient are obtained in all cases the approach is well suited for geometry control via computer aided design and is especially effective for conceptual design studies with complex geometry where fast turn around time is required

a sharp interface immersed boundary method for compressible viscous flows an immersed boundary method for computing viscous subsonic compressible flows with complex shaped stationary immersed boundaries is presented the method employs a ghost cell technique for imposing the boundary conditions on the immersed boundaries the current approach leads to a sharp representation of the immersed boundaries a property that is especially useful for flow simulations at high reynolds numbers another unique feature of the method is that it can be applied on cartesian as well as generalized body non conformal curvilinear meshes a mixed second order central difference quick scheme is used which allows a high degree of control over the numerical damping a bilinear interpolation scheme used in conjunction with the ghost cell approach results in second order global as well as local spatial accuracy the solver is parallelized for distributed memory platforms using domain decomposition and message passing interface mpi and salient features of the parallel algorithm are presented the accuracy fidelity and efficiency of the solver are examined by simulating flow past circular cylinders and airfoils and comparing against experimental data and other established results finally we present results from a simulation of wing tip flow at a relatively high reynolds number in order to demonstrate the ability of the solver to model complex non canonical three dimensional flows

logically rectangular grids and finite volume methods for pdes in circular and spherical domains we describe a class of logically rectangular quadrilateral and hexahedral grids for solving pdes in circular and spherical domains including grid mappings for the circle the surface of the sphere and the three dimensional ball the grids are logically rectangular and the computational domain is a single cartesian grid compared to alternative approaches based on a multiblock data structure or unstructured triangulations this approach simplifies the implementation of numerical methods and the use of adaptive refinement a more general domain with a smooth boundary can be gridded by composing one of the mappings from this paper with another smooth mapping from the circle or sphere to the desired domain although these grids are highly nonorthogonal we show that the high resolution wave propagation algorithm implemented in clawpack can be used effectively to approximate hyperbolic problems on these grids since the ratio between the largest and smallest grids is below 2 for most of our grid mappings explicit finite volume methods such as the wave propagation algorithm do not suffer from the center or pole singularities that arise with polar or latitude longitude grids numerical test calculations illustrate the potential use of these grids for a variety of applications including euler equations shallow water equations and acoustics in a heterogeneous medium pattern formation from a reaction diffusion equation on the sphere is also considered all examples are implemented in the clawpack software package and full source code is available on the web along with matlab routines for the various mappings

a cartesian grid embedded boundary method for hyperbolic conservation laws we present a second order godunov algorithm to solve time dependent hyperbolic systems of conservation laws on irregular domains our approach is based on a formally consistent discretization of the conservation laws on a finite volume grid obtained from intersecting the domain with a cartesian grid we address the small cell stability problem associated with such methods by hybridizing our conservative discretization with a stable nonconservative discretization at irregular control volumes and redistributing the difference in the mass increments to nearby cells in a way that preserves stability and local conservation the resulting method is second order accurate in l 1 for smooth problems and is robust in the presence of large amplitude discontinuities intersecting the irregular boundary

a conservative three dimensional eulerian method for coupled solid fluid shock capturing a new method is presented for the explicit eulerian finite difference computation of shock capturing problems involving multiple resolved material phases in three dimensions we solve separately for each phase the equations of fluid dynamics or solid mechanics using as interface boundary conditions artificially extended representations of the individual phases for fluids we use a new 3d spatially unsplit implementation of the piecewise parabolic ppm method of colella and woodward for solids we use the 3d spatially unsplit eulerian solid mechanics method of miller and colella vacuum and perfectly incompressible obstacles may also be employed as phases a separate problem is the time evolution of material interfaces which are represented by planar segments constructed with a volume of fluid method the volume fractions are advanced in time using a second order 3d spatially unsplit advection routine with a velocity field determined by solution of interface normal two phase riemann problems from the riemann problem solutions we also determine cross interface momentum and energy fluxes the volume fractions in mixed cells may be arbitrarily small which would ordinarily make the courant friedrichs lewy time step stability limit arbitrarily small as well we overcome this limitation using the mass redistribution formalism to conservatively redistribute generalized mass in the neighborhood of the split cells we present an application of this method to an explosion contained in a metal can a reactive fluid approximating pbx 9404 is encased within an elastic plastic solid approximating copper surrounded by vacuum our implementation is in parallel and with adaptive mesh refinement

on projection algorithms for solving convex feasibility problems due to their extraordinary utility and broad applicability in many areas of classical mathematics and modern physical sciences most notably computerized tomography algorithms for solving convex feasibility problems continue to receive great attention to unify generalize and review some of these algorithms a very broad and flexible framework is investigated several crucial new concepts which allow a systematic discussion of questions on behaviour in general hilbert spaces and on the quality of convergence are brought out numerous examples are given

heuristic algorithm for generating multilevel cartesian meshes inmultidimensional regions with moving boundaries universal algorithm for fully automated generation of multilevel cartesian mesh in arbitrary planar regions with moving boundaries is developed and discussed in details it uses multilevel tree technology and heuristic enabling flexible mesh adaptation to changes of boundaries efficient mixed coding for mesh storing is presented suggested algorithm generates meshes with properties most desirable for computing various field distribution problems main parts of elaborated algorithm are generalized for multidimensional meshes

sparsity preserving projections with applications to face recognition dimensionality reduction methods drs have commonly been used as a principled way to understand the high dimensional data such as face images in this paper we propose a new unsupervised dr method called sparsity preserving projections spp unlike many existing techniques such as local preserving projection lpp and neighborhood preserving embedding npe where local neighborhood information is preserved during the dr procedure spp aims to preserve the sparse reconstructive relationship of the data which is achieved by minimizing a l1 regularization related objective function the obtained projections are invariant to rotations rescalings and translations of the data and more importantly they contain natural discriminating information even if no class labels are provided moreover spp chooses its neighborhood automatically and hence can be more conveniently used in practice compared to lpp and npe the feasibility and effectiveness of the proposed method is verified on three popular face databases yale ar and extended yale b with promising results

multidimensional upwind methods for hyperbolic conservation laws abstract we present a class of second order conservative finite difference algorithms for solving numerically time dependent problems for hyperbolic conservation laws in several space variables these methods are upwind and multidimensional in that the numerical fluxes are obtained by solving the characteristic form of the full multidimensional equations at the zone edge and that all fluxes are evaluated and differenced at the same time in particular operator splitting is not used correct behavior at discontinuities is obtained by the use of solutions to the riemann problem and by limiting some of the second order terms numerical results are presented which show that the methods described here yield the same high resolution as the corresponding operator split methods

fourier spectral embedded boundary solution of the poisson s and laplace equations with dirichlet boundary conditions a fourier spectral embedded boundary method for solution of the poisson s equation with dirichlet boundary conditions and arbitrary forcing functions including zero forcing function is presented in this paper this iterative method begins by transformation of the dirichlet boundary conditions from the physical boundaries to some corresponding regular grid points which are called the numerical boundaries using a second order interpolation method then the transformed boundary conditions and the forcing function are extended to a square smoothly and periodically via multiplying them by some suitable error functions instead of direct solution of the resulting extended poisson s problem it is suggested to define and solve an equivalent transient diffusion problem on the regular domain until achievement of the steady solution which is considered as the solution of the original problem without need of any numerical time integration method time advancement of the solution is obtained directly from the exact solution of the transient problem in the fourier space consequently timestep sizes can be chosen without stability limitations which it means higher rates of convergence in comparison with the classical relaxation methods the method is presented in details for one and two dimensional problems and a new emerged phenomenon which is called the saturation state is illustrated both in the physical and spectral spaces the numerical experiments have been performed on the one and two dimensional irregular domains to show the accuracy of the method and its superiority from the rate of convergence viewpoint to the other classical relaxation methods capability of the method in dealing with complex geometries and in presence of discontinuity at the boundaries has been shown via some numerical experiments on a four leaf shape geometry

on the asymtotic behavior of some alternate smoothing series expansion iterative methods abstract we study the asymptotic behavior of some iterative methods used in image reconstruction from projections these methods combine in each step a major iteration of a standard series expansion algorithm like art followed by the application of a smoothing matrix we prove convergence for a whole family of these methods when the matrix is symmetric and we give counterexamples for other cases

strong convergence of almost simultaneous block iterative projection methods in hilbert spaces abstract we prove strong convergence of a class of block iterative projection methods for finding a common point of a finite family of closed convex subsets in a hilbert space

numerical simulation of two dimensional and three dimensional axisymmetric advection diffusion systems with complex geometries using finite volume methods a finite volume method has been developed that can deal accurately with complicated curved boundaries for both two dimensional and three dimensional axisymmetric advection diffusion systems the motivation behind this is threefold firstly the ability to model the correct geometry of a situation yields more accurate results secondly smooth geometries eliminate corner singularities in the calculation of for example mechanical variables and thirdly different geometries can be tested for experimental applications an example illustrating each of these is given fluid carrying a dye and rotating in an annulus bone fracture healing in mice and using vessels of different geometry in an ultracentrifuge

graph optimization for dimensionality reduction with sparsity constraints graph based dimensionality reduction dr methods play an increasingly important role in many machine learning and pattern recognition applications in this paper we propose a novel graph based learning scheme to conduct graph optimization for dimensionality reduction with sparsity constraints godrsc different from most of graph based dr methods where graphs are generally constructed in advance godrsc aims to simultaneously seek a graph and a projection matrix preserving such a graph in one unified framework resulting in an automatically updated graph moreover by applying an l 1 regularizer a sparse graph is achieved which models the locality structure of data and contains natural discriminating information finally extensive experiments on several publicly available uci and face databases verify the feasibility and effectiveness of the proposed method

an anelastic allspeed projection method for gravitationally stratified flows this paper looks at gravitationally stratified atmospheric flows at low mach and froude numbers and proposes a new algorithm to solve the compressible euler equations in which the asymptotic limits are recovered numerically and the boundary conditions for block structured local refinement methods are well posed the model is non hydrostatic and the numerical algorithm uses a splitting to separate the fast acoustic dynamics from the slower anelastic dynamics the acoustic waves are treated implicitly while the anelastic dynamics is treated semi implicitly and an embedded boundary method is used to represent orography we present an example that verifies our asymptotic analysis and a set of results that compares very well with the classical gravity wave results presented by durran

adaptive moment of fluid method a novel adaptive mesh refinement amr strategy based on the moment of fluid mof method for volume tracking of evolving interfaces is presented moment of fluid method is a new interface reconstruction and volume advection method using volume fractions as well as material centroids the mesh refinement criterion is based on the deviation of the actual centroid obtained by interface reconstruction from the reference centroid given by moment advection process the centroid error indicator detects not only high curvature regions but also regions with complicated subcell structures like filaments a new lagrange remap scheme is presented for advecting moments which includes lagrangian backtracking polygon intersection based remapping and forward tracking to define the material centroid the effectiveness and efficiency of amr mof method is demonstrated with classical test problems such as zalesak s disk and reversible vortex problem the comparison with previously published results for these problems shows the superior accuracy of the amr mof method over other methods in addition two new test cases with severe deformation rates are introduced namely droplet deformation and s shape deformation problems for further demonstration of the capabilities of the amr mof method

asymmetric variational inequality problems over product sets applications and iterative methods in this paper we i describe how several equilibrium problems can be uniformly modelled by a finite dimensional asymmetric variational inequality defined over a cartesian product of sets and ii investigate the local and global convergence of various iterative methods for solving such a variational inequality problem because of the special cartesian product structure these iterative methods decompose the original variational inequality problem into a sequence of simpler variational inequality subproblems in lower dimensions the resulting decomposition schemes often have a natural interpretation as some adjustment processes

a cartesian grid embedded boundary method for the heat equation and poisson s equation in three dimensions we present an algorithm for solving poisson s equation and the heat equation on irregular domains in three dimensions our work uses the cartesian grid embedded boundary algorithm for 2d problems of johansen and colella a cartesian grid embedded boundary method for poisson s equation on irregular domains j comput phys 147 2 1998 60 85 and extends work of mccorquodale colella and johansen a cartesian grid embedded boundary method for the heat equation on irregular domains j comput phys 173 2001 620 635 our method is based on a finite volume discretization of the operator on the control volumes formed by intersecting the cartesian grid cells with the domain combined with a second order accurate discretization of the fluxes the resulting method provides uniformly second order accurate solutions and gradients and is amenable to geometric multigrid solvers

inconsistent signal feasibility problems least squares solutions in a product space presents parallel projection methods to find least squares solutions to inconsistent convex set theoretic signal synthesis problems the problem of finding a signal that minimizes a weighted average of the squares of the distances to constraint sets is reformulated in a product space where it is equivalent to that of finding a point that lies in a particular subspace and at minimum distance from the cartesian product of the original sets a solution is obtained in the product space via methods of alternating projections which naturally lead to methods of parallel projections in the original space the convergence properties of the proposed methods are analyzed and signal synthesis applications are demonstrated

online kernel based classification using adaptive projection algorithms the goal of this paper is to derive a novel online algorithm for classification in reproducing kernel hilbert spaces rkhs by exploiting projection based adaptive filtering tools the paper brings powerful convex analytic and set theoretic estimation arguments in machine learning by revisiting the standard kernel based classification as the problem of finding a point which belongs to a closed halfspace a special closed convex set in an rkhs in this way classification in an online setting where data arrive sequentially is viewed as the problem of finding a point classifier in the nonempty intersection of an infinite sequence of closed halfspaces in the rkhs convex analysis is also used to introduce sparsification arguments in the design by imposing an additional simple convex constraint on the norm of the classifier an algorithmic solution to the resulting optimization problem where new convex constraints are added every time instant is given by the recently introduced adaptive projected subgradient method apsm which generalizes a number of well known projection based adaptive filtering algorithms such as the classical normalized least mean squares nlms and the affine projection algorithm apa under mild conditions the generated sequence of estimates enjoys monotone approximation strong convergence asymptotic optimality and a characterization of the limit point further we show that the additional convex constraint on the norm of the classifier naturally leads to an online sparsification of the resulting kernel series expansion we validate the proposed design by considering the adaptive equalization problem of a nonlinear channel and by comparing it with classical as well as with recently developed stochastic gradient descent techniques

variable selection using svm based criteria we propose new methods to evaluate variable subset relevance with a view to variable selection relevance criteria are derived from support vector machines and are based on weight vector w 2 or generalization error bounds sensitivity with respect to a variable experiments on linear and non linear toy problems and real world datasets have been carried out to assess the effectiveness of these criteria results show that the criterion based on weight vector derivative achieves good results and performs consistently well over the datasets we used

flux limiting embedded boundary technique for electromagnetic fdtd a general approach for incorporating embedded boundaries into an electromagnetic finite difference time domain fdtd code is presented this algorithm is shown to satisfy gauss s law and enforces no magnetic monopoles while maintaining a globally second order result first order at physical boundaries with no added time step restriction theoretically predicted superior results are shown with an 11 time step reduction from the courant stability limit this is achieved through a physics based flux limiting scheme near physical boundaries stability local truncation error and energy conservation analysis are also provided

numerical method for the bone regeneration model defined within the evolving 2d axisymmetric physical domain abstract a numerical algorithm used to obtain a solution for a peri implant osseointegration model is constructed the model is formulated in terms of a system of three nonlinear coupled time dependent advection diffusion reaction equations which are defined within the irregular two dimensional physical domain which evolves in time the embedded boundary method and the level set function which is approximated on the fixed regular rectangular grid are used to track the changes of the irregular geometry of the physical domain the method of lines is applied to separate the discretizations in time and in space the advection diffusion and reaction terms are discretized separately by means of the cell centered finite volume method the exact solution of the riemann problem for the nonstrictly hyperbolic system without genuine nonlinearity is obtained an approach for the determination of the gradients of the unknown variables on the edges of the irregular control volumes is proposed the explicit second order trapezoidal rule is used for the time integration since it allows to maintain positivity of the solution which is critical for the considered problem some results of the numerical simulations are presented contact and distance osteogenesis are predicted for micro rough and smooth implants

cut element based immersed boundary method for moving geometries in compressible liquid flows with cavitation the conservative immersed interface method for representing complex immersed solid boundaries or phase interfaces on cartesian grids is improved and extended to allow for the simulation of weakly compressible fluid flows through moving geometries we demonstrate that an approximation of moving interfaces by a level set field results in unphysical oscillations in the vicinity of sharp corners when dealing with weakly compressible fluids such as water by introducing an exact reconstruction of the cut cell properties directly based on a surface triangulation of the immersed boundary we are able to recover the correct flow evolution free of numerical artifacts the new method is based on cut elements it provides sub cell resolution of the geometry and handles flows through narrow closing or opening gaps in a straightforward manner we validate our method with canonical flows around oscillating cylinders we demonstrate that the method allows for an accurate prediction of flows around moving obstacles in weakly compressible liquid flows with cavitation effects in particular we show that the cavitating flow through a closing fuel injector control valve which is an example for a complex application with interaction of stationary and moving parts can be predicted by the method

a new 3 d numerical approach to the solution of pdes with optimal accuracy on irregular domains and cartesian meshes abstract a new 3 d numerical approach for the time dependent wave and heat equations as well as for the time independent laplace equation on irregular domains with the dirichlet boundary conditions has been developed trivial cartesian meshes and simple 27 point uniform and nonuniform stencil equations are used for 3 d irregular domains the calculation of the coefficients of the stencil equations is based on the minimization of the local truncation error of the stencil equations and yields the optimal order of accuracy of the new technique very small distances 0 1 h 1 0 9 h where h is the grid size between the grid points of a cartesian mesh and the boundary do not worsen the accuracy of the new technique at similar 27 point stencils the accuracy of the new approach is two orders higher than that for the linear finite elements the numerical results for irregular domains show that at the same number of degrees of freedom the new approach is even much more accurate than the high order up to the fifth order tetrahedral finite elements with much wider stencils the wave and heat equations can be uniformly treated with the new approach the order of the time derivative in these equations does not affect the coefficients of the stencil equations of the semi discrete systems the new approach can be directly applied to other partial differential equations

an iterative boundary potential method for the infinite domain poisson problem with interior dirichlet boundaries an iterative method is developed for the solution of poisson s problem on an infinite domain in the presence of interior boundaries held at fixed potential in three dimensions the method combines pre existing fast multigrid based poisson solvers for data represented on cartesian grids with the fast multipole method interior boundaries are represented with the embedded boundary formalism the implementation is in parallel and uses adaptive mesh refinement examples are presented for a smooth interior boundary for which an analytical result is known and for an irregular interior boundary problem second order accuracy in l 1 with respect to the grid resolution is demonstrated for both problems

a fast feature weighting algorithm of data gravitation classification the data gravitation classification dgc model is a new classification method that has gained great research interest in recent years feature weights are the key parameters in dgc models because the classification performances of these models are very sensitive to such feature weights the available dgc models use wrapper like algorithms to obtain their optimised feature weights although such algorithms produce high classification accuracies but they contribute to the high computational complexities of the dgc models in this study we propose a fast feature weight algorithm for dgc models called ffw dgc we use the concepts of feature discrimination and redundancy to measure the importance of a feature after which two fuzzy subsets are constructed to respectively represent these concepts next we combine the two fuzzy subsets to compute the feature weights used in gravitational computing we conduct our experiments on 25 standard data sets and 22 imbalance data sets and compare ffw dgc with 11 kinds of classifiers including the swarm intelligence based dgc pso dgc model competitive results of ffw dgc demonstrate that it can obtain high classification accuracies but also hundreds of times of speedup ratios compared with pso dgc

projection on the intersection of convex sets abstract in this paper we give a solution of the problem of projecting a point onto the intersection of several closed convex sets when a projection on each individual convex set is known the existing solution methods for this problem are sequential in nature here we propose a highly parallelizable method the key idea in our approach is the reformulation of the original problem as a system of semi smooth equations the benefits of the proposed reformulation are twofold a a fast semi smooth newton iterative technique based on clarke s generalized gradients becomes applicable and b the mechanics of the iterative technique is such that an almost decentralized solution method emerges we proved that the corresponding semi smooth newton algorithm converges near the optimal point quadratically these features make the overall method attractive for distributed computing platforms e g sensor networks

a stabilized dg cut cell method for discretizing the linear transport equation we present new stabilization terms for solving the linear transport equation on a cut cell mesh using the discontinuous galerkin dg method in two dimensions with piecewise linear polynomials the

linearized alternating direction method with adaptive penalty and warm starts for fast solving transform invariant low rank textures transform invariant low rank textures tilt is a novel and powerful tool that can effectively rectify a rich class of low rank textures in 3d scenes from 2d images despite significant deformation and corruption the existing algorithm for solving tilt is based on the alternating direction method it suffers from high computational cost and is not theoretically guaranteed to converge to a correct solution to the inner loop in this paper we propose a novel algorithm to speed up solving tilt with guaranteed convergence for the inner loop our method is based on the recently proposed linearized alternating direction method with adaptive penalty to further reduce computation warm starts are also introduced to initialize the variables better and cut the cost on singular value decomposition extensive experimental results on both synthetic and real data demonstrate that this new algorithm works much more efficiently and robustly than the existing algorithm it could be at least five times faster than the previous method

viewing parallel projection methods as sequential ones in convex feasibility problems we show that the parallel projection method with variable weights and one variable relaxation coefficient for obtaining a point in the intersection of a finite number of closed convex sets in a given hilbert space may be interpreted as a semi alternating sequential projection method in a suitably newly constructed hilbert space as such convergence results for the parallel projection method may be derived from those which may be constructed in the semi alternating sequential case

hierarchical convex optimization with primal dual splitting this paper addresses the selection of a desirable solution among all the solutions of a convex optimization problem referred to as the first stage problem mainly for inverse problems in signal processing this is realized in the framework of hierarchical convex optimization i e minimizing another convex function over the solution set of the first stage problem hierarchical convex optimization is an ideal strategy when the first stage problem has infinitely many solutions because of the non strict convexity of its objective function which could arise in various scenarios e g convex feasibility problems to this end first the fixed point set characterization behind a primal dual splitting type method is incorporated into the framework of hierarchical convex optimization which enables the framework to cover a broad class of first stage problem formulations then a pair of efficient algorithmic solutions to the hierarchical convex optimization problem as certain realizations of the hybrid steepest descent method are provided with guaranteed convergence we also present a specialized form of the proposed framework to focus on a typical scenario of inverse problems and show its application to signal interpolation

a second order projection method for the incompressible navier stokes equations in this paper we describe a second order projection method for the time dependent incom pressible navier stokes equations as in the original projection method developed by chorin we first solve diffusion convection equations to predict intermediate velocities which are then projected onto the space of divergence free vector fields by introducing more coupling between the diffusion onvection step and the projection step we obtain a temporal discretiza tion that is second order accurate our treatment of the diffusion convection step uses a specialized higher order godunov method for differencing the nonlinear convective terms that provides a robust treatment of these terms at high reynolds number the godunov procedure is second order accurate for smooth flow and remains stable for discontinuous initial data even in the zero viscosity limit we approximate the projection directly using a galerkin procedure that uses a local basis for discretely divergence free vector fields numerical results are presented validating the convergence properties of the method we also apply the method to doubly periodic shear layers to assess the performance of the method on more difficult

a cut cell finite volume finite element coupling approach for fluid structure interaction in compressible flow we present a loosely coupled approach for the solution of fluid structure interaction problems between a compressible flow and a deformable structure the method is based on staggered dirichlet neumann partitioning the interface motion in the eulerian frame is accounted for by a conservative cut cell immersed boundary method the present approach enables sub cell resolution by considering individual cut elements within a single fluid cell which guarantees an accurate representation of the time varying solid interface the cut cell procedure inevitably leads to non matching interfaces demanding for a special treatment a mortar method is chosen in order to obtain a conservative and consistent load transfer we validate our method by investigating two dimensional test cases comprising a shock loaded rigid cylinder and a deformable panel moreover the aeroelastic instability of a thin plate structure is studied with a focus on the prediction of flutter onset finally we propose a three dimensional fluid structure interaction test case of a flexible inflated thin shell interacting with a shock wave involving large and complex structural deformations

on the behavior of subgradient projections methods for convex feasibility problems in euclidean spaces we study some methods of subgradient projections for solving a convex feasibility problem with general not necessarily hyperplanes or half spaces convex sets in the inconsistent case and propose a strategy that controls the relaxation parameters in a specific self adapting manner this strategy leaves enough user flexibility but gives a mathematical guarantee for the algorithm s behavior in the inconsistent case we present the numerical results of computational experiments that illustrate the computational advantage of the new method

adaptive constrained learning in reproducing kernel hilbert spaces the robust beamforming case this paper establishes a new paradigm for convexly constrained adaptive learning in reproducing kernel hilbert spaces rkhs although the technique is of a general nature we present it in the context of the beamforming problem a priori knowledge like beampattern specifications and constraints concerning robustness against steering vector errors takes the form of multiple closed convex sets in a high possibly infinite dimensional rkhs every robustness constraint is shown to be equivalent to a min max optimization task formed by means of the robust statistics epsiv insensitive loss function such a multiplicity of specifications turns out to obtain a simple expression by using the rich frame of fixed point sets of certain mappings defined in a hilbert space moreover the cost function that the final solution has to optimize is expressed as an infinite sequence of convex nondifferentiable loss functions springing from the sequence of the incoming training data a novel adaptive beamforming design of linear complexity with respect to the number of unknown parameters to such a constrained nonlinear learning problem is derived by employing a very recently developed version of the adaptive projected subgradient method apsm the method produces a sequence that under mild conditions exhibits properties like the strong convergence to a beamformer that satisfies all of the imposed constraints and in the meantime asymptotically minimizes the sequence of the loss functions imposed by the training data the numerical examples demonstrate that the proposed method displays increased resolution in cases where the classical linear beamforming solutions collapse moreover it leads to solutions which are in agreement with the imposed a priori knowledge as opposed to unconstrained online kernel regression techniques

a cartesian grid embedded boundary method for poisson s equation on irregular domains we present a numerical method for solving poisson s equation with variable coefficients and dirichlet boundary conditions on two dimensional regions the approach uses a finite volume discretization which embeds the domain in a regular cartesian grid we treat the solution as a cell centered quantity even when those centers are outside the domain cells that contain a portion of the domain boundary use conservative differencing of second order accurate fluxes on each cell volume the calculation of the boundary flux ensures that the conditioning of the matrix is relatively unaffected by small cell volumes this allows us to use multigrid iterations with a simple point relaxation strategy we have combined this with an adaptive mesh refinement amr procedure we provide evidence that the algorithm is second order accurate on various exact solutions and compare the adaptive and nonadaptive calculations

alternating projections and douglas rachford for sparse affine feasibility the problem of finding a vector with the fewest nonzero elements that satisfies an underdetermined system of linear equations is an np complete problem that is typically solved numerically via convex heuristics or nicely behaved nonconvex relaxations in this work we consider elementary methods based on projections for solving a sparse feasibility problem without employing convex heuristics it has been shown recently that locally the fundamental method of alternating projections must converge linearly to a solution to the sparse feasibility problem with an affine constraint in this paper we apply different analytical tools that allow us to show global linear convergence of alternating projections under familiar constraint qualifications these analytical tools can also be applied to other algorithms this is demonstrated with the prominent douglas rachford algorithm where we establish local linear convergence of this method applied to the sparse affine feasibility problem

iterating bregman retractions the notion of a bregman retraction of a closed convex set in euclidean space is introduced bregman retractions include backward bregman projections and forward bregman projections as well as their convex combinations and are thus quite flexible the main result on iterating bregman retractions unifies several convergence results on projection methods for solving convex feasibility problems it is also used to construct new sequential and parallel algorithms

perturbed projections and subgradient projections for the multiple sets split feasibility problem we study the multiple sets split feasibility problem that requires to find a point closest to a family of closed convex sets in one space such that its image under a linear transformation will be closest to another family of closed convex sets in the image space by casting the problem into an equivalent problem in a suitable product space we are able to present a simultaneous subgradients projections algorithm that generates convergent sequences of iterates in the feasible case we further derive and analyze a perturbed projection method for the multiple sets split feasibility problem and additionally furnish alternative proofs to two known results

visco penalization of the sum of two monotone operators a new type of approximating curve for finding a particular zero of the sum of two maximal monotone operators in a hilbert space is investigated this curve consists of the zeros of perturbed problems in which one operator is replaced with its yosida approximation and a viscosity term is added as the perturbation vanishes the curve is shown to converge to the zero of the sum that solves a particular strictly monotone variational inequality as an off spring of this result we obtain an approximating curve for finding a particular zero of the sum of several maximal monotone operators applications to convex optimization are discussed

successive averages of firmly nonexpansive mappings the problem considered here is to find common fixed points of possibly infinitely many firmly nonexpansive selfmappings in a hilbert space for this purpose we use averaged relaxations of the original mappings the averages being bochner integrals with respect to chosen measures judicious choices of such measures serve to enhance the convergence towards common fixed points since projection operators onto closed convex sets are firmly nonexpansive the methods explored are applicable for solving convex feasibility problems in particular by varying the measures our analysis encompasses recent developments of so called block iterative algorithms we demonstrate convergence theorems which cover and extend many known results

a high resolution rotated grid method for conservation laws with embedded geometries we develop a second order rotated grid method for the approximation of time dependent solutions of conservation laws in complex geometry using an underlying cartesian grid stability for time steps adequate for the regular part of the grid is obtained by increasing the domain of dependence of the numerical method near the embedded boundary by constructing h boxes at grid cell interfaces we describe a construction of h boxes that not only guarantees stability but also leads to an accurate and conservative approximation of boundary cells that may be orders of magnitude smaller than regular grid cells of independent interest is the rotated difference scheme itself on which the embedded boundary method is based

an outer approximation method for the variational inequality problem we study two outer approximation schemes applied to the variational inequality problem in reflexive banach spaces first we propose a generic outer approximation scheme and its convergence analysis unifies a wide class of outer approximation methods applied to the constrained optimization problem as is standard in this setting boundedness and optimality of weak limit points are proved to hold under two alternative conditions i boundedness of the feasible set or ii coerciveness of the operator to develop a convergence analysis where i and ii do not hold we consider a second scheme in which the approximated subproblems use a coercive approximation of the original operator under conditions alternative to both i and ii we obtain standard convergence results furthermore when the space is uniformly convex we establish full strong convergence of the second scheme to a solution

an unsplit 3d upwind method for hyperbolic conservation laws abstract an unsplit upwind method for solving hyperbolic conservation laws in three dimensions is developed this paper derives the algorithm by generalizing a two dimensional advection algorithm of van leer and colella to three dimensions and then making appropriate modifications the method is implemented using the equations of gas dynamics several test problems are computed to both verify and display the behavior of the method these test problems include a 1d blast wave a 2d shock reflection off a 30 ramp and a 3d astrophysical jet

sparse discriminative feature selection as sparse representation based classifier src is developed it has drawn more and more attentions in dimension reduction in this paper we introduce src based measurement criterion into feature selection and then propose a novel method called sparse discriminative feature selection our objective function aims to find a subset of features which minimize the within class reconstruction residual and simultaneously maximize the between class reconstruction residual in the subspace of selected features a greedy algorithm and a joint selection algorithm are devised to efficiently solve the proposed combinatorial optimization formulation in particular our joint selection algorithm adds l 2 1 norm minimization into the objective function which reduces the redundant and learns features weights simultaneously a new iterative algorithm is also developed to optimize the proposed objective function experiments on benchmark data sets demonstrate the performance of our feature selection method highlightsthe proposed method selects features that can preserve the sparse reconstructive relationship of the data a greedy algorithm and a joint selection algorithm are devised to efficiently solve the proposed formulation we incorporate discriminative analysis and l2 1 norm minimization into a joint feature selection

a cell centered adaptive projection method for the incompressible navier stokes equations in three dimensions we present a method for computing incompressible viscous flows in three dimensions using block structured local refinement in both space and time this method uses a projection formulation based on a cell centered approximate projection combined with the systematic use of multilevel elliptic solvers to compute increments in the solution generated at boundaries between refinement levels due to refinement in time we use an l0 stable second order semi implicit scheme to evaluate the viscous terms results are presented to demonstrate the accuracy and effectiveness of this approach

a dimensionally split cartesian cut cell method for hyperbolic conservation laws abstract we present a dimensionally split method for solving hyperbolic conservation laws on cartesian cut cell meshes the approach combines local geometric and wave speed information to determine a novel stabilised cut cell flux and we provide a full description of its three dimensional implementation in the dimensionally split framework of klein et al 1 the convergence and stability of the method are proved for the one dimensional linear advection equation while its multi dimensional numerical performance is investigated through the computation of solutions to a number of test problems for the linear advection and euler equations when compared to the cut cell flux of klein et al it was found that the new flux alleviates the problem of oscillatory boundary solutions produced by the former at higher courant numbers and also enables the computation of more accurate solutions near stagnation points being dimensionally split the method is simple to implement and extends readily to multiple dimensions

a cartesian grid embedded boundary method for the heat equation on irregular domains we present an algorithm for solving the heat equation on irregular time dependent domains it is based on the cartesian grid embedded boundary algorithm of johansen and colella j comput phys 147 2 60 85 for discretizing poisson s equation combined with a second order accurate discretization of the time derivative this leads to a method that is second order accurate in space and time for the case where the boundary is moving we convert the moving boundary problem to a sequence of fixed boundary problems combined with an extrapolation procedure to initialize values that are uncovered as the boundary moves we find that in the moving boundary case the use of crank nicolson time discretization is unstable requiring us to use the l sub 0 stable implicit runge kutta method of twizell gumel and arigu

bregman monotone optimization algorithms a broad class of optimization algorithms based on bregman distances in banach spaces is unified around the notion of bregman monotonicity a systematic investigation of this notion leads to a simplified analysis of numerous algorithms and to the development of a new class of parallel block iterative surrogate bregman projection schemes another key contribution is the introduction of a class of operators that is shown to be intrinsically tied to the notion of bregman monotonicity and to include the operators commonly found in bregman optimization methods special emphasis is placed on the viability of the algorithms and the importance of legendre functions in this regard various applications are discussed

a discrete model for compressible flows in heterogeneous media this work deals with the building of a discrete model able to describe and to predict the evolution of complex gas flows in heterogeneous media in many physical applications large scales numerical simulation is no longer possible because of a lack of computing resources indeed the medium topology may be complex due to the presence of many obstacles walls pipes equipments geometric singularities etc aircraft powerplant compartments are examples where topology is complex due to the presence of pipes ducts coolers and other equipment other important examples are gas explosions and large scale dispersion of hazardous materials in urban places cities or underground involving obstacles such as buildings and various infrastructures in all cases efficient safety responses are required then a new discrete model is built and solved in reasonable execution times for large cells volumes including such obstacles quantitative comparisons between experimental and numerical results are shown for different significant test cases showing excellent agreement

multiaccess interference suppression in orthogonal space time block coded mimo systems by adaptive projected subgradient method this paper introduces adaptive filters that are effective to suppress multiple access interference mai in orthogonal space time block coded multiple input multiple output ostbc mimo systems we define an optimal linear filter that minimizes the mean square error between the filter output and a scaled version of the desired output under a constraint defined by the available channel state information csi the adaptive filters refine a given estimate of the optimal filter by suppressing a sequence of closed convex functions with the adaptive projected subgradient method apsm at each iteration to provide robustness against imperfect csi the adaptive filters use not only the available csi but also estimates of previously transmitted symbols which usually belong to a small finite set in digital communication systems the resulting algorithms employ computationally efficient projections onto hyperplanes or hyperslabs and do not require any matrix inversion an efficient recursive scheme based on such an algorithm is also presented convergence analysis and simulation results show the excellent performance of the proposed schemes

h box methods for the approximation of hyperbolic conservation laws on irregular grids we study generalizations of the high resolution wave propagation algorithm for the approximation of hyperbolic conservation laws on irregular grids that have a time step restriction based on a reference grid cell length that can be orders of magnitude larger than the smallest grid cell arising in the discretization this godunov type scheme calculates fluxes at cell interfaces by solving riemann problems defined over boxes of a reference grid cell length h we discuss stability and accuracy of the resulting so called h box methods for one dimensional systems of conservation laws an extension of the method for the two dimensional case which is based on the multidimensional wave propagation algorithm is also described

an accurate moving boundary formulation in cut cell methods a cut cell method for cartesian meshes to simulate viscous compressible flows with moving boundaries is presented we focus on eliminating unphysical oscillations occurring in cartesian grid methods extended to moving boundary problems in these methods cells either lie completely in the fluid or solid region or are intersected by the boundary for the latter cells the time dependent volume fraction lying in the fluid region can be so small that explicit time integration schemes become unstable and a special treatment of these cells is necessary when the boundary moves a fluid cell may become a cut cell or a solid cell may become a small cell at the next time level this causes an abrupt change in the discretization operator and a suddenly modified truncation error of the numerical scheme this temporally discontinuous alteration is shown to act like an unphysical source term which deteriorates the numerical solution i e it generates unphysical oscillations in the hydrodynamic forces exerted on the moving boundary we develop an accurate moving boundary formulation based on the varying discretization operators yielding a cut cell method which avoids these discontinuities results for canonical two and three dimensional test cases evidence the accuracy and robustness of the newly developed scheme

coincidence points by generalized mann iterates with applications in hilbert spaces this paper deals with the construction of the coincidence points by the generalized mann iterates and their applications in hilbert spaces our results generalize and improve a number of recent results

weak and norm convergence of a parallel projection method in hilbert spaces abstract we show that for a parallel projection method for finding the common point of convex sets in a hilbert space under very mild conditions about the variable weights and the variable relaxation parameters the constructed sequence is weakly convergent to a point of the intersection of the sets we also prove norm convergence of the sequence under additional conditions on the convex sets

a dimensionally split cartesian cut cell method for the compressible navier stokes equations abstract we present a dimensionally split method for computing solutions to the compressible navier stokes equations on cartesian cut cell meshes the method is globally second order accurate in the l 1 norm fully conservative and allows the use of time steps determined by the regular grid spacing we provide a description of the three dimensional implementation of the method and evaluate its numerical performance by computing solutions to a number of test problems ranging from the nearly incompressible to the highly compressible flow regimes all the computed results show good agreement with reference results from theory experiment and previous numerical studies to the best of our knowledge this is the first presentation of a dimensionally split cut cell method for the compressible navier stokes equations in the literature

decomposition through formalization in a product space when an optimization problem is posed in a product space it is classical to decompose this problem the goal of this paper is to show how such an approach can be used when the problem to be solved is not naturally posed in a product space by associating systematically to this problem an equivalent one posed in ann fold cartesian product space we obtain by decomposition of the latter both a splitting of operators and a desintegration of constraints for the former applications to three rather classical mathematical programming problems are given

accelerating the alternating projection algorithm for the case of affine subspaces using supporting hyperplanes abstract the von neumann halperin method of alternating projections converges strongly to the projection of a given point onto the intersection of finitely many closed affine subspaces we propose acceleration schemes making use of two ideas firstly each projection onto an affine subspace identifies a hyperplane of codimension 1 containing the intersection and secondly it is easy to project onto a finite intersection of such hyperplanes we give conditions for which our accelerations converge strongly finally we perform numerical experiments to show that these accelerations perform well for a matrix model updating problem

on the convergence of han s method for convex programming with quadratic objective we present an iterative method for minimizing strictly convex quadratic functions over the intersection of a finite number of convex sets the method consists in computing projections onto the individual sets simultaneously and the new iterate is a convex combination of those projections we give convergence proofs even for the inconsistent case i e when the intersection of the sets is empty

set intersection problems supporting hyperplanes and quadratic programming we study how the supporting hyperplanes produced by the projection process can complement the method of alternating projections and its variants for the convex set intersection problem for the problem of finding the closest point in the intersection of closed convex sets we propose an algorithm that like dykstra s algorithm converges strongly in a hilbert space moreover this algorithm converges in finitely many iterations when the closed convex sets are cones in mathbb r n r n satisfying an alignment condition next we propose modifications of the alternating projection algorithm and prove its convergence the algorithm converges superlinearly in mathbb r n r n under some nice conditions under a conical condition the convergence can be finite lastly we discuss the case where the intersection of the sets is empty

a high order numerical approach with cartesian meshes for modeling of wave propagation and heat transfer on irregular domains with inhomogeneous materials abstract recently we have developed a new numerical approach for pdes with constant coefficients on irregular domains and cartesian meshes in this paper we extend it to a much more general case of pdes with variable coefficients that have a lot of applications e g the modeling of functionally graded materials the inhomogeneous materials obtained by 3 d printing and many others here we consider the 2 d wave and heat equations for isotropic and anisotropic inhomogeneous materials the idea of the extension to the case of pdes with variable coefficients is based on the representation of the stencil coefficients as functions of the mesh size this leads to the increase in the size of the local system of algebraic equations solved for each grid point of the new approach however this does not change the size of the global system of semidiscrete equations and practically does not increase the computational costs of the proposed technique similar to our previous technique the new 2 d approach with compact 9 point stencils uses trivial cartesian meshes for complex irregular domains and provides the fourth order of accuracy for the wave and heat equations with variable coefficients the calculation of the coefficients of the stencil equations is based on the minimization of the local truncation error of the stencil equations and yields the optimal order of accuracy of the new technique at similar 9 point stencils the accuracy of the new approach is much higher than that for the linear finite elements the numerical results for irregular domains show that at the same number of degrees of freedom the new approach is even much more accurate than the high order up to the third order finite elements with much wider stencils the wave and heat equations are uniformly treated with the new approach

an efficient conservative cut cell method for rigid bodies interacting with viscous compressible flows a cartesian cut cell method for viscous flows interacting with freely moving boundaries is presented the method enables a sharp resolution of the embedded boundaries and strictly conserves mass momentum and energy a new explicit runge kutta scheme pc rk is introduced by which the overall computational time is reduced by a factor of up to 2 5 the new scheme is a predictor corrector type reformulation of a popular class of runge kutta methods which substantially reduces the computational effort for tracking the moving boundaries and subsequently reinitializing the solver impairing neither stability nor accuracy the structural motion is computed by an implicit scheme with good stability properties due to a strong coupling strategy and the conservative discretization of the flow solver at the material interfaces a new formulation for the treatment of small cut cells is proposed with high accuracy and robustness for arbitrary geometries based on a weighted taylor series approach solved via singular value decomposition the efficiency and the accuracy of the new method are demonstrated for several three dimensional cases of laminar and turbulent particulate flow it is shown that the new method remains fully conservative even for large displacements of the boundaries leading to a fast convergence of the fluid solid coupling while spurious force oscillations inherent to this class of methods are effectively suppressed the results substantiate the good stability and accuracy properties of the scheme even on relatively coarse meshes an efficient cartesian cut cell method for freely moving solid boundaries is presented the new predictor corrector runge kutta scheme pc rk enables simulation speedups of up to 2 5 mass momentum and energy are strictly conserved at the sharply resolved solid fluid interfaces the method exhibits very good stability and accuracy properties even for large displacements of the boundaries spurious force oscillations inherent to this class of methods are suppressed