first order system least squares for the helmholtz equation this paper develops a multilevel least squares approach for the numerical solution of the complex scalar exterior helmholtz equation this second order equation is first recast into an equivalent first order system by introducing several field variables a combination of scaled l2 and h 1 norms is then applied to the residual of this system to create a least squares functional it is shown that in an appropriate hilbert space the homogeneous part of this functional is equivalent to a squared graph norm that is a product norm on the space of individual variables this equivalence to a norm that decouples the variables means that standard finite element discretization techniques and standard multigrid solvers can be applied to obtain optimal performance however this equivalence is not uniform in the wavenumber k which can signal degrading performance of the numerical solution process as k increases to counter this difficulty we obtain a result that characterizes the error components causing performance degradation we do this by defining a finite dimensional subspace of these components on whose orthogonal complement k uniform equivalence is proved for this functional and an analogous functional that is based only on l2 norms this subspace equivalence motivates a nonstandard multigrid method that attempts to achieve optimal convergence uniformly in k we report on numerical experiments that empirically confirm k uniform optimal performance of this multigrid solver we also report on tests of the error in our discretization that seem to confirm optimal accuracy that is free of the so called pollution effect

recovery procedures in error estimation and adaptivity part ii adaptivity in nonlinear problems of elasto plasticity behaviour the first part of this paper 1 discusses in some detail the use of recovery procedures for stress strain or gradients for efficient error estimator and the methods of arriving at adaptive h refinement in this paper we extend such procedure to deal with elasto plasticity and discuss in detail some special features of such computation

a saddle point least squares approach to mixed methods we investigate new pde discretization approaches for solving variational formulations with different types of trial and test spaces the general mixed formulation we consider assumes a stability lbb condition and a data compatibility condition at the continuous level we expand on the bramble pasciak s least square formulation for solving such problems by providing new ways to choose approximation spaces and new iterative processes to solve the discrete formulations our proposed method has the advantage that a discrete inf sup condition is automatically satisfied by natural choices of test spaces first and corresponding trial spaces second in addition for the proposed iterative solver a nodal basis for the trial space is not required applications of the new approach include discretization of first order systems of pdes such as div curl systems and time harmonic maxwell equations

saddle point least squares iterative solvers for the time harmonic maxwell equations abstract we introduce a least squares method for discretizing the time harmonic maxwell equations written as a first order system the method belongs to the recently introduced least squares approach called the saddle point least squares spls method see bacuta and qirko 2015 2017 it is related to two known methods the bramble and pasciak least squares method for solving electromagnetic problems bramble and pasciak 2004 bramble et al 2005 and the minimum residual dpg method of demkowicz and gopalakrishnan 2010 2013 the proposed discretization is based on reduction to a symmetric saddle point formulation on spaces of piecewise polynomial functions the edge elements are avoided a discrete test space is chosen first among standard conforming finite element spaces and the discrete trial space is chosen second as the image of the first order maxwell differential operator on the discrete test space for the proposed iterative processes a nodal basis for the trial space is not required and the main inversion at each step is done only on the test space the method is efficient for both convex and non convex domains and for a various range of frequencies as shown by the numerical results

fast full search equivalent encoding algorithms for image compression using vector quantization three fast search routines to be used in the encoding phase of vector quantization vq image compression systems are presented these routines which are based on geometric considerations provide the same results as an exhaustive or full search examples show that the proposed algorithms need only 3 20 of the number of mathematical operations required by a full search and fewer than 50 of the operations required by recently proposed alternatives

finite element solution of the helmholtz equation with high wave number part i the h version of the fem abstract the paper addresses the properties of finite element solutions for the helmholtz equation the h version of the finite element method with piecewise linear approximation is applied to a one dimensional model problem new results are shown on stability and error estimation of the discrete model in all propositions assumptions are made on the magnitude of hk only where k is the wavelength and h is the stepwidth of the fe mesh previous analytical results had been shown with the assumption that k 2 h is small for medium and high wavenumber these results do not cover the meshsizes that are applied in practical applications the main estimate reveals that the error in h 1 norm of discrete solutions for the helmholtz equation is polluted when k 2 h is not small the error is then not quasioptimal i e the relation of the fe error to the error of best approximation generally depends on the wavenumber k it is noted that the pollution term in the relative error is of the same order as the phase lead of the numerical solution in the result of this analysis thorough and rigorous understanding of error behavior throughout the range of convergence is gained numerical results are presented that show sharpness of the error estimates and highlight some phenomena of the discrete solution behavior the h p version of the fem is studied in part ii

elastic plastic analysis of arbitrary heterogeneous materials with the voronoi cell finite element method abstract in this paper a voronoi cell finite element method is developed to solve small deformation elastic plasticity problems for arbitrary heterogenous materials dirichlet tessellation of microstructural representative materials results in a network of arbitrary sided polygons called voronoi cells each voronoi cell encompasses one second phase heterogeneity at most these are natural elements for the microstructure representing the basic structural elements of the material in this paper formulations are developed for directly considering voronoi cells as elements in a finite element model without any further dissection furthermore a composite voronoi cell finite element method is developed to account for the presence of the second phase within each polygonal element various numerical elastic plastic examples are executed for validating the effectiveness of this formulation finally studies are conducted to understand the effect of size shape and distribution of second phase on the averaged and true local responses of representative material elements

a first order system least squares method for the helmholtz equation we present a first order system least squares fosls method for the helmholtz equation at high wave number k which always leads to a hermitian positive definite algebraic system by utilizing a non trivial solution decomposition to the dual fosls problem which is quite different from that of the standard finite element methods we give an error analysis to the h p version of the fosls method where the dependence on the mesh size h the approximation order p and the wave number k is given explicitly in particular under some assumption of the boundary of the domain the l 2 norm error estimate of the scalar solution from the fosls method is shown to be quasi optimal under the condition that k h p is sufficiently small and the polynomial degree p is at least o log k numerical experiments are given to verify the theoretical results

optimal discrete transmission conditions for a nonoverlapping domain decomposition method for the helmholtz equation this paper is dedicated to recent developments of a two lagrange multipliers domain decomposition method for the helmholtz equation c farhat et al comput methods appl mech engrg 184 2000 pp 213 240 m j gander f magoules and f nataf siam j sci comput 24 2002 pp 38 60 involving an additional augmented operator along the interface between the subdomains most methods for optimizing the augmented interface operator are based on the discretization of approximations of the continuous transparent operator b despres proceedings of the second international conference on mathematical and numerical aspects of wave propagation r kleinman et al eds siam philadelphia 1993 pp 197 206 j d benamou and b despres j comput phys 136 1997 pp 68 82 p chevalier and f nataf domain decomposition methods 10 ams providence ri 1998 pp 400 407 m j gander proceedings of the 12th international conference on domain decomposition methods chiba japan ddm org 2000 pp 247 254 m j gander f magoules and f nataf siam j sci comput 24 2002 pp 38 60 at the discrete level the optimal operator can be proved to be equal to the schur complement of the outer domain this schur complement can be directly approximated using purely algebraic techniques like sparse approximate inverse methods or incomplete factorization the main advantage of such an algebraic approach is that it is much easier to implement in existing code without any information on the geometry of the interface and the finite element formulation used convergence results and parallel efficiency of several algebraic optimization techniques of an interface operator for acoustic analysis applications will be presented

analysis of the anisotropic viscoplastic damage response of composite laminates continuum basis and computational algorithms the mathematical structure underlying the rate equations of a recently developed constitutive model for the coupled viscoplastic damage response of anisotropic composites is critically examined in this regard a number of tensor projection operators have been identified and their properties were exploited to enable the development of a general computational framework for their numerical implementation using the euler fully implicit integration method in particular this facilitated i the derivation of explicit expressions of the consistent material tangent stiffnesses that are valid for both three dimensional as well as subspace e g plane stress formulations ii the implications of the symmetry or unsymmetry properties of these tangent operators from a thermodynamic standpoint and iii the development of an effective time step control strategy to ensure accuracy and convergence of the solution in addition the special limiting case of inviscid elastoplasticity is treated the results of several numerical simulations are given to demonstrate the effectiveness of the schemes developed

an analysis of a new class of integration algorithms for elastoplastic constitutive relations an accuracy analysis of a new class of integration algorithms for finite deformation elastoplastic constitutive relations recently proposed by the authors is carried out in this paper for simplicity attention is confined to infinitesimal deformations the integration rules under consideration fall within the category of return mapping algorithms and follow in a straightforward manner from the theory of operator splitting applied to elastoplastic constitutive relations general rate independent and rate dependent behaviour with plastic hardening or softening associated or non associated flow rules and nonlinear elastic response can be efficiently treated within the present framework isoerror maps are presented which demonstrate the good accuracy properties of the algorithm even for strain increments much larger than the characteristic strains at yielding

on the implementation of inelastic constitutive equations with special reference to large deformation problems abstract methods for finite element analysis of inelastic problems are reviewed problems with currently popular methods based on rate principles of virtual work are pointed out a formulation is presented based on the exact incremental virtual work equation the procedure for integration of the constitutive rate equations to obtain incremental constitutive equations is based on the assumption of a constant strain rate or straight strain path during the increment full newton raphson iteration is used to solve the resulting set of nonlinear equations the treatment of the constitutive equations in this newton raphson scheme leads to a linearized form which is substantially different from the classical rate equations the procedure is implemented in a finite element program and its effectiveness is shown in a number of examples

multiple galerkin adaptive algebraic multigrid algorithm for the helmholtz equations introduced in this paper is a multiple galerkin adaptive algebraic multigrid algorithm for solving linear discrete equations arising from discretization of partial differential operators with a rich and diverse near kernel standard multigrid methods struggle with solving such equations due to their inability to produce accurate coarse correction to all near kernel components the motivating model problem here is the indefinite helmholtz operators for which the character of near kernel components is at least approximately known in the algorithm some of these components are used to create multiple prolongation operators and consecutive coarse descriptions which collectively approximate the entire near kernel the algorithm consists of two parts with multiple galerkin corrections accelerating a standard multigrid v cycle both parts largely employ standard multigrid techniques the resulting algorithm is then used to precondition the gmres numerical experiments in one and two dimensions are presented

consistent derivation of the constitutive algorithm for plane stress isotropic plasticity part i theoretical formulation abstract a derivation of the projected algorithm for general isotropic three invariant plasticity models under plane stress conditions is presented it is obtained by consistently specializing the 3d formulation to the 2d subspace defined by the plane stress condition closed form intrinsic algorithm linearization and a novel expression of the consistent tangent tensor are provided these are also shown to directly emanate from the analogous quantities pertaining to the fully 3d case a detailed discussion of the proposed implementation along with a representative set of numerical examples is provided in the second part of this paper valoroso n rosati l 2008 consistent derivation of the constitutive algorithm for plane stress isotropic plasticity part ii computational issues international journal of solids and structures 46 92 124

a return mapping algorithm for a class of cyclic plasticity models a return mapping algorithm for a class of cyclic plasticity models is presented the constitutive model includes a quadratic yield criterion and multi component formulations of non linear isotropic and kinematic hardening thus both initially isotropic and anisotropic materials can be described and a proper description of the hysteresis loops and the cyclic hardening response of materials under cyclic loading is obtained the return mapping algorithm employs the closest point projection scheme in combination with a decomposition method to obtain an efficient and robust integration of the constitutive model the consistent tangent operator is derived in closed form and is found to be unsymmetric due to the non linear evolution of the kinematic hardening terms the accuracy and robustness of the algorithm are assessed through numerical examples

an implicit integration algorithm with a projection method for viscoplastic constitutive equations robinson s viscoplastic model a representative of the so called overstress models is integrated by use of the generalized midpoint rule the solution of the non linear system of algebraic equations arising from time discretization of the constitutive equations is determined using a projection method in combination with newton s method consistent tangent moduli are calculated and the quadratic convergence of the global newton equilibrium iteration is shown the time increment size is controlled by the convergence behaviour of the equilibrium iteration and the accuracy of the numerical integration various numerical examples are considered to demonstrate the efficiency of the methods

sweeping preconditioner for the helmholtz equation hierarchical matrix representation the paper introduces the sweeping preconditioner which is highly efficient for iterative solutions of the variable coefficient helmholtz equation including very high frequency problems the first central idea of this novel approach is to construct an approximate factorization of the discretized helmholtz equation by sweeping the domain layer by layer starting from an absorbing layer or boundary condition given this specific order of factorization the second central idea is to represent the intermediate matrices in the hierarchical matrix framework in two dimensions both the construction and the application of the preconditioners are of linear complexity the generalized minimal residual method gmres solver with the resulting preconditioner converges in an amazingly small number of iterations which is essentially independent of the number of unknowns this approach is also extended to the three dimensional case with some success numerical results are provided in both two and three dimensions to demonstrate the efficiency of this new approach

consistent tangent operators for rate independent elastoplasticity abstract it is shown that for problems involving rate constitutive equations such as rate independent elastoplasticity the notion of consistency between the tangent stiffness operator and the integration algorithm employed in the solution of the incremental problem plays a crucial role in preserving the quadratic rate of asymptotic convergence of iterative solution schemes based upon newton s method within the framework of closest point projection algorithms a methodology is presented whereby tangent operators consistent with this class of algorithms may be systematically developed to wit associative j 2 flow rules with general nonlinear kinematic and isotropic hardening rules as well as a class of non associative flow rules are considered the resulting iterative solution scheme preserves the asymptotic quadratic convergence characteristic of newton s method whereas use of the socalled elastoplastic tangent in conjunction with a radial return integration algorithm a procedure often employed results in newton type of algorithms with suboptimal rate of convergence application is made to a set of numerical examples which include saturation hardening laws of exponential type

on different finite element methods for approximating the gradient of the solution to the helmholtz equation abstract we consider the numerical solution of the helmholtz equation by different finite element methods in particular we are interested in finding an efficient method for approximating the gradient of the solution we first approximate the gradient by the standard ritz galerkin method as a second method a two stage method due to aziz and werschulz 1980 is presented it is shown that this method gives the same accuracy in the computed gradient and in the computed solution also in the nonconforming case finally a direct method with asymptotic error estimates is given it turns out that the presented direct method is of lowest computational complexity test examples are presented to illustrate the accuracy of the methods

a fast search algorithm for vector quantization using mean pyramids of codewords one of the most serious problems for vector quantization especially for high dimensional vectors is the high computational complexity of searching for the closest codeword in the codebook design and encoding phases although quantizing high dimensional vectors rather than low dimensional vectors results in better performance the computation time needed for vector quantization grows exponentially with the vector dimension this makes high dimensional vectors unsuitable for vector quantization to overcome this problem a fast search algorithm under the assumption that the distortion is measured by the squared euclidean distance is proposed using the mean pyramids of codewords the algorithm ran reject many codewords that are impossible matches and hence save a great deal of computation time the algorithm is efficient for high dimensional codeword searches experimental results confirm the effectiveness of the proposed method

a formulation of the mitc4 shell element for finite strain elasto plastic analysis abstract a finite strain elasto plastic formulation is developed for the mitc4 shell element the developed formulation is based on lee s multiplicative decomposition of the deformation gradient and on the hyperelastic expression of von mises flow rule expressed in terms of hencky s strain tensor the formulation incorporates thickness stretching degrees of freedom that are condensed at the element level by imposing the classical in layer plane stress condition a symmetric and consistent tangent stiffness matrix is also developed

a micropolar formulation of the desai hierarchical model for elastoplastic porous media in this contribution the desai hierarchical model is extended to the case of 3d elasto plastic two phase micropolar continuum an unconditionally stable implicit euler backward algorithm for integration of the constitutive relations is developed and presented in detail the regularizing effect of the introduction of a length parameter to the classical desai model is demonstrated by means of several case studies of single phase and two phase porous media

a displacement like finite element model for j2 elastoplasticity variational formulation and finite step solution abstract the displacement like finite element formulation for finite step j2 elastoplasticity is revisited in this paper the classical computational strategy according to which plastic loading is tested at the gauss points of each element and an independent return mapping algorithm is performed for given incremental displacements is consistently derived from a suitably discretized version of a min max variational principle the sequence of solution phases to be performed within each load step adopting a full newton s method is illustrated in detail and the importance of a correct update of the plastic strains is emphasized it is further shown that in order to increase the rate of convergence and the stability properties of the newton s method the consistent elastoplastic tangent operator must be exploited even at the first iteration of each load step subsequent to the first yielding of the structural model this is in contrast with the traditional implementation according to which the elastic operator is used at the first iteration of each load step the effectiveness of the present approach is shown by a set of numerical examples referred to plane strain problems

a return mapping algorithm for plane stress elastoplasticity an unconditionally stable algorithm for plane stress elastoplasticity is developed based upon the notion of elastic predictor return mapping plastic corrector enforcement of the consistency condition is shown to reduce to the solution of a simple nonlinear equation consistent elastoplastic tangent moduli are obtained by exact linearization of the algorithm use of these moduli is essential in order to preserve the asymptotic rate of quadratic convergence of newton methods the accuracy of the algorithm is assessed by means of iso error maps the excellent performance of the algorithm for large time steps is illustrated in numerical experiments

fast search algorithms for vector quantization of images using multiple triangle inequalities and wavelet transform the encoding of vector quantization vq needs expensive computation for searching the closest codevector to the input vector this paper presents several fast encoding algorithms based on multiple triangle inequalities and wavelet transform to overcome this problem the multiple triangle inequalities confine a search range using the intersection of search areas generated from several control vectors a systematic way for designing the control vectors is also presented the wavelet transform combined with the partial distance elimination is used to reduce the computational complexity of the distance calculation of vectors the proposed algorithms provide the same coding quality as the full search method the experimental results indicate that the new algorithms perform more efficiently than existing algorithms

the propagation of spherical waves in rate sensitive elastic plastic materials an integral equation method for the analysis of elastic plastic wave propagation is presented the elastic plastic solution is thereby found as the superposition of the corresponding elastic result with waves produced by dynamically induced plastic strains the solutions are represented in the form of integrals with elastodynamic green s functions as integration kernels the spherically symmetric problem of a dynamically loaded spherical cavity is considered and the corresponding green s functions for this geometry are derived in closed form time convolution is carried out analytically over a prescribed time step and the spatial integration is performed by gaussian quadrature if the wave travels within each time step just the distance of one spatial element the evaluation of the integrals leads to a tridiagonal system of algebraic equations numerical results are compared to some known analytical solutions proving the accuracy of the method computations are carried out for rate sensitive power law hardening thermal softening materials

topology and shape optimization for elastoplastic structural response abstract it is a common practice to base both material topology optimization as well as a subsequent shape optimization on linear elastic response however in order to obtain a realistic design it might be essential to base the optimization on a more realistic physical behavior i e to consider geometrically or and materially nonlinear effects in the present paper an elastoplastic von mises material model with linear isotropic hardening softening for small strains is used the objective of the design problem is to maximize the structural ductility in the elastoplastic range while the mass in the design space is prescribed with respect to the specific features of either topology or shape optimization for example the number of optimization variables or their local global influence on the structural response different methods are applied for topology optimization problems the gradient of the ductility is determined by the variational adjoint approach in shape optimization the derivatives of the state variables with respect to the optimization variables are evaluated analytically by a variational direct approach the topology optimization problem is solved by an optimality criteria oc method and the shape optimization problem by a mathematical programming mp method in topology optimization a geometrically adaptive procedure is additionally applied in order to increase the efficiency and to avoid artificial stress singularities the procedures are verified by 2d design problems under plane stress conditions

a fast exact gla based on code vector activity detection this paper introduces a new method for reducing the number of distance calculations in the generalized lloyd algorithm gla which is a widely used method to construct a codebook in vector quantization reduced comparison search detects the activity of the code vectors and utilizes it on the classification of the training vectors for training vectors whose current code vector has not been modified we calculate distances only to the active code vectors a large proportion of the distance calculations can be omitted without sacrificing the optimality of the partition the new method is included in several fast gla variants reducing their running times over 50 on average

a least squares approach based on a discrete minus one inner product for first order systems the purpose of this paper is to develop and analyze a least squares approximation to a first order system the first order system represents a reformulation of a second order elliptic boundary value problem which may be indefinite and or nonsymmetric the approach taken here is novel in that the least squares functional employed involves a discrete inner product which is related to the inner product in h 1 the sobolev space of order minus one on the use of this inner product results in a method of approximation which is optimal with respect to the required regularity as well as the order of approximation even when applied to problems with low regularity solutions in addition the discrete system of equations which needs to be solved in order to compute the resulting approximation is easily preconditioned thus providing an efficient method for solving the algebraic equations the preconditioner for this discrete system only requires the construction of preconditioners for standard second order problems a task which is well understood

a four point integration scheme with quadratic exactness for three dimensional element free galerkin method based on variationally consistent formulation abstract the formulation of three dimensional element free galerkin efg method based on the hu washizu three field variational principle is described the orthogonality condition between stress and strain difference is satisfied by correcting the derivatives of the nodal shape functions this leads to a variationally consistent formulation which has a similar form as the formulation of standard galerkin weak form based on this formulation an integration scheme which employs only four cubature points in each background tetrahedral element cell is rationally developed for three dimensional efg with quadratic approximation the consistency of the corrected nodal derivatives and the satisfaction of patch test conditions for the developed integration scheme are theoretically proved extension of the proposed method to small strain elastoplasticity is also presented the proposed method can exactly pass quadratic patch test that is quadratic exactness is achieved and thus it is named as quadratically consistent 4 point qc4 integration method in contrast efg with standard tetrahedral cubature and the existing linearly consistent 1 point lc1 integration fail to exactly pass quadratic patch test numerical results of elastic examples demonstrate the superiority of the proposed method in accuracy convergence efficiency and stability the capability of the proposed qc4 scheme in solving elastoplastic problems is also demonstrated by numerical examples

accuracy and stability of integration algorithms for elastoplastic constitutive relations an analysis of accuracy and stability of algorithms for the integration of elastoplastic constitutive relations is carried out in this paper reference is made to a very general internal variable formulation of plasticity and to two families of algorithms that generalize the well known trapezoidal and midpoint rules to fit the present context other integration schemes such as the radial return mean normal and closest point procedures are particular cases of this general formulation the meaning of first and second order accuracy in the presence of the plastic consistency condition is examined in detail and the criteria derived are used to identify two second order accurate members of the proposed algorithms a general methodology is also derived whereby the numerical stability properties of integration schemes can be systematically assessed with the aid of this methodology the generalized midpoint rule is seen to have far better stability properties than the generalized trapezoidal rule finally numerical examples are presented that illustrate the performance of the algorithms

a generalized finite element method for solving the helmholtz equation in two dimensions with minimal pollution when using the galerkin fem for solving the helmholtz equation in two dimensions the error of the corresponding solution differs substantially from the error of the best approximation and this effect increases with higher wave number k in this paper we will design a generalized finite element method gfem for the helmholtz equation such that the pollution effect is minimal

an iterative substructuring method for coupled fluid solid acoustic problems a fast parallel iterative method is proposed for the solution of linear equations arising from finite element discretization of the time harmonic coupled fluid solid systems in fluid pressure and solid displacement formulation the fluid and the solid domains are decomposed into nonoverlapping subdomains continuity of the solution is enforced by lagrange multipliers the system is augmented by duplicating the degrees of freedom on the wet interface the original degrees of freedom are then eliminated and the resulting system is solved by iterations preconditioned by a coarse space correction in each iteration the method requires the solution of one independent local acoustic problem per subdomain and the solution of a global problem with several degrees of freedom per subdomain computational results show that the method is scalable with the problem size frequency and the number of subdomains the method generalizes the feti h method for the helmholtz equation to coupled fluid elastic scattering the number of iterations is about same as for the feti h method for the related helmholtz problem with neumann boundary condition instead of an elastic scatterer if enough coarse space functions are used convergence behavior is explained from the spectrum of the iteration operator and from numerical near decoupling of the equations in the fluid and in the solid regions

a fast method for the solution of the helmholtz equation in this paper we consider the numerical solution of the helmholtz equation arising from the study of the wave equation in the frequency domain the approach proposed here differs from those recently considered in the literature in that it is based on a decomposition that is exact when considered analytically so the only degradation in computational performance is due to discretization and roundoff errors in particular we make use of a multiplicative decomposition of the solution of the helmholtz equation into an analytical plane wave and a multiplier which is the solution of a complex valued advection diffusion reaction equation the use of fast multigrid methods for the solution of this equation is investigated numerical results show that this is an efficient solution algorithm for a reasonable range of frequencies

hyperspectral image segmentation using a new spectral unmixing based binary partition tree representation the binary partition tree bpt is a hierarchical region based representation of an image in a tree structure the bpt allows users to explore the image at different segmentation scales often the tree is pruned to get a more compact representation and so the remaining nodes conform an optimal partition for some given task here we propose a novel bpt construction approach and pruning strategy for hyperspectral images based on spectral unmixing concepts linear spectral unmixing consists of finding the spectral signatures of the materials present in the image endmembers and their fractional abundances within each pixel the proposed methodology exploits the local unmixing of the regions to find the partition achieving a global minimum reconstruction error results are presented on real hyperspectral data sets with different contexts and resolutions

elasto plastic finite element method based on incremental deformation theory and continuum based shell elements for planar anisotropic sheet materials abstract an implicit approach for the incremental analysis of planar anisotropic sheet forming processes is developed based on the incremental deformation theory the incremental deformation theory based on the minimum plastic work path enables convenient decoupling of deformation and rotation by the polar decomposition the mathematical description of a constitutive law for the incremental deformation theory is obtained from the flow theory along the minimum plastic work path the resulting constitutive law is then incorporated in an elasto plastic finite element analysis code in the elasto plastic formulation continuum based resultant cbr shell element is employed the cbr shell allows large rotation and large membrane bending strain the laminar coordinate system is taken to coincide with planar anisotropic material axes then planar anisotropic axes during deformation are updated using a newly developed algorithm based on the polar decomposition an iterative solving method based on the incremental deformation theory is also developed for an accurate and stable stress integration the planar anisotropy is incorporated into the formulation for sheet forming by introducing non quadratic barlat s yield function for verification purposes two examples have been simulated and compared with experimental results the good verification results show that the present elasto plastic formulation for planar anisotropic sheet materials can provide a good theoretical basis for more extended analyses of sheet forming processes

a parallel multigrid based preconditioner for the 3d heterogeneous high frequency helmholtz equation we investigate the parallel performance of an iterative solver for 3d heterogeneous helmholtz problems related to applications in seismic wave propagation for large 3d problems the computation is no longer feasible on a single processor and the memory requirements increase rapidly therefore parallelization of the solver is needed we employ a complex shifted laplace preconditioner combined with the bi cgstab iterative method and use a multigrid method to approximate the inverse of the resulting preconditioning operator a 3d multigrid method with 2d semi coarsening is employed we show numerical results for large problems arising in geophysical applications

a modified generalized midpoint rule for the integration of rate dependent thermo elastic plastic constitutive equations the integration algorithm presented here is an extension of the widely used generalized midpoint rule a simple but very effective method is derived to optimize the location of the collocation point where plastic consistency is enforced in order to achieve high accuracy for virtually unlimited sizes of the time step these optimal locations are in the interval t2 t which automatically guarantees unconditional stability the optimal weighting parameter is estimated from two explicit formulas hence there is practically no increase in computational expense compared to applications of the conventional generalized midpoint rule furthermore the method features a special formulation of plastic consistency called a plastic predictor which minimizes the necessary iterations at gauss point level numerical examples demonstrate the efficiency and accuracy of the algorithm for rate dependent and rate independent plasticity including combined kinematic and isotropic hardening as well as thermal softening

wavenumber explicit analysis of a dpg method for the multidimensional helmholtz equation we study the properties of a novel discontinuous petrov galerkin dpg method for acoustic wave propagation the method yields hermitian positive definite matrices and has good pre asymptotic stability properties numerically we find that the method exhibits negligible phase errors otherwise known as pollution errors even in the lowest order case theoretically we are able to prove error estimates that explicitly show the dependencies with respect to the wavenumber the mesh size h and the polynomial degree p but the current state of the theory does not fully explain the remarkably good numerical phase errors theoretically comparisons are made with several other recent works that gave wave number explicit estimates numerically comparisons are made with the standard finite element method and its recent modification for wave propagation with clever quadratures the new dpg method is designed following the previously established principles of optimal test functions in addition to the nonstandard test functions in this work we also use a nonstandard wave number dependent norm on both the test and trial space to obtain our error estimates

algebraic multilevel preconditioner for the helmholtz equation in heterogeneous media an algebraic multilevel ml preconditioner is presented for the helmholtz equation in heterogeneous media it is based on a multilevel incomplete ldl t factorization and preserves the inherent complex symmetry of the helmholtz equation the ml preconditioner incorporates two key components for efficiency and numerical stability symmetric maximum weight matchings and an inverse based pivoting strategy the former increases the block diagonal dominance of the system whereas the latter controls l 1 for numerical stability when applied recursively their combined effect yields an algebraic coarsening strategy similar to algebraic multigrid methods even for highly indefinite matrices the ml preconditioner is combined with a krylov subspace method and applied as a black box solver to a series of challenging two and three dimensional test problems mainly from geophysical seismic imaging the numerical results demonstrate the robustness and efficiency of the ml preconditioner even at higher frequency regimes

fast vector quantization algorithms based on nearest partition set search a fast search method for vector quantization is proposed in this paper it makes use of the fact that in the generalized lloyd algorithm gla a vector in a training sequence is either placed in the same minimum distance partition mdp as in the previous iteration or in a partition within a very small subset of partitions the proposed method searches for the mdp for a training vector only in this subset of partitions plus the single previous mdp as the size of this subset is much smaller than the total number of codevectors the search process is speeded up significantly the creation of the subset is essential as it has a direct effect on the improvement in computation time of the proposed method the schemes that create the subset efficiently have been proposed the proposed method generates a codebook identical to that generated using the gla it is simple and requires only minor modification of the gla and a modest amount of additional memory the experimental results show that the computation time of codebook training was improved by factors from 6 6 to 50 7 and from 5 8 to 70 4 for two test data sets when codebooks of sizes from n 16 to 2048 were trained the proposed method was also combined with an earlier published method to further improve the computation time

mixed stabilized finite element methods in nonlinear solid mechanics part ii strain localization this paper deals with the question of strain localization associated with materials which exhibit softening due to tensile straining a standard local isotropic rankine damage model with strain softening is used as exemplary constitutive model both the irreducible and mixed forms of the problem are examined and stability and solvability conditions are discussed lack of uniqueness and convergence difficulties related to the strong material nonlinearities involved are also treated from this analysis the issue of local discretization error in the pre localization regime is deemed as the main difficulty to be overcome in the discrete problem focus is placed on low order finite elements with continuous strain and displacement fields triangular p1p1 and quadrilateral q1q1 although the presented approach is very general numerical examples show that the resulting procedure is remarkably robust it does not require the use of auxiliary tracking techniques and the results obtained do not suffer from spurious mesh bias dependence

a mixed method for approximating maxwell s equations a semidiscrete mixed finite element approximation to the time dependent maxwell s equations on a bounded smooth domain is analyzed a variational problem for the electric and magnetic fields in which the boundary conditions are enforced naturally is derived then a general convergence result for mixed methods is proven and it is shown how this result may be used to prove various error estimates when nedelec s curl conforming finite elements are used jz3 with connected boundary f and unit outward normal n let e x and 1 x denote respectively the dielectric constant and magnetic permeability of the medium occupying q let a x denote the conductivity of the medium then if e x t and h x t denote respectively the electric and magnetic fields maxwell s equations 10 state that

generalized midpoint finite element dynamic analysis of elastoplastic systems the application of a four parameter generalized midpoint integration method to small displacement elastoplastic dynamic problems is considered the integration of the governing relations over a time step is formulated as a non linear algebraic problem finite step problem by making use of generalized variables finite element modelling uniqueness and an extremum characterization of the solution of the finite step problem are discussed sufficient conditions for convergence of various iterative algorithms including newton raphson are given the b stability of the proposed procedure is assessed

a fast search algorithm for vector quantization using l sub 2 norm pyramid of codewords vector quantization for image compression requires expensive encoding time to find the closest codeword to the input vector this paper presents a fast algorithm to speed up the closest codeword search process in vector quantization encoding by using an appropriate topological structure of the codebook we first derive a condition to eliminate unnecessary matching operations from the search procedure then based on this elimination condition a fast search algorithm is suggested simulation results show that with little preprocessing and memory cost the proposed search algorithm significantly reduces the encoding complexity while maintaining the same encoding quality as that of the full search algorithm it is also found that the proposed algorithm outperforms the existing search algorithms

on the numerical integration of a class of pressure dependent plasticity models with mixed hardening radial return algorithms for both three dimensional and plane stress situations are developed for a class of pressure dependent plasticity models formulated in state variables with mixed hardening the consistent tangent matrix has been developed which among other advantages does not require numerical inversion the algorithms for gurson s mixed hardening model are incorporated in a finite element program to solve several simple uniaxial tension problems when compared with numerically integrated solutions the results from the finite element analysis show excellent agreement finally results of the axisymmetric necking problem using gurson s mixed hardening model are presented as an example of application

stress wave propagation in rods of elastic viscoplastic material abstract a number of uniaxial stress wave propagation problems are solved based on the unified multi dimensional elastic viscoplastic constitutive equations of bodner partom and a finite difference numerical procedure solutions are obtained for cases of a velocity imposed for a time period or indefinitely at the end of a semi infinite bar and for the condition of a finite bar subjected to a high velocity superimposed on an applied low velocity after a time interval work hardening is taken to be isotropic for stress of constant sign while an isochoric anisotropic work hardening formulation is employed for problems involving stresses of reversed sign due to unloading or reflections the numerical exercises are based on constants for a strongly strain rate sensitive material titanium and the results indicate good qualitative agreement with a wide range of experimental observations

on the computational significance of the strain space formulation of plasticity theory the strain space and traditional stress space formulations of plasticity theory are compared we show how plasticity theory has been implemented numerically to solve static and dynamic problems and conclude that the numerical loading criteria that have been used for two decades are identical to the strain space loading criteria proposed by naghdi and co workers

on electric and magnetic problems for vector fields in anisotropic nonhomogeneous media r 3 2 initiated by saranen 131 in the above n is the outward drawn unit normal to the boundary and a denotes the exterior product according to the simple models for static magnetic fields resp electric fields which are governed by 0 1 resp 0 2 we call 0 1 the magnetic type problem and 0 2 the electric type problem considering bounded smooth domains a c r3 we discussed in 131 by means of an appropriate hilbert space method the solvability and the representation of the solutions for both problems 0 1 and 0 2 such a new approach was necessary to cover the general nonhomogeneous cases where v and e are matrix valued functions here our aim is twofold first we will now include exterior domains in our consideration this will be achieved by using certain weighted spaces which slightly restrict the behavior of the fields at infinity to find the scalar potentials we have to solve the dirichlet and neumann problems in exterior domains consequently in order to define the vector potentials we solve appropriate auxiliary second order boundary problems for vector fields the other aspect of this paper is to point out that the dimension of the space of solutions for 0 1 or 0 2 with homogeneous right side is 254 0022 247x 83 010254 22 03 00 0

first order system least squares for elliptic problems with robin boundary conditions this paper studies a least squares approach to scalar second order elliptic partial differential equations with robin boundary conditions as in several earlier papers by bramble lazarov and pasciak math comp 66 1997 pp 935 955 cai et al siam j numer anal 31 1994 pp 1785 1799 cai manteuffel and mccormick siam j numer anal 34 1997 pp 425 454 1727 1741 chang siam j numer anal 29 1992 pp 452 461 and jiang and povinelli comput methods appl mech engrg 102 1993 pp 199 212 the scalar equation is first recast into a first order system by introducing velocity or flux variables where some norm is then applied to the residual of this system to create a least squares functional we show here that a least squares principle based on an l2 norm produces optimal discretization error estimates in the h1 norm for all variables in the system we further show that a least squares principle based on a combination of l2 and h 1 norms yields optimal discretization error in a corresponding combination of h1 and l2 norms for the variables finally a regularity result for the l2 least squares formulation and numerical examples for both formulations are given

on a numerical implementation of a formulation of anisotropic continuum elastoplasticity at finite strains in a recent theoretical study see c sansour i karsaj j soric a formulation of anisotropic continuum elastoplasticity at finite strains part i modelling international journal of plasticity 22 2006 2346 2365 a constitutive model for anisotropic elastoplasticity at finite strains has been developed the model is based on the multiplicative decomposition of the deformation gradient the stored energy function as well as the flow rule has been considered as quadratic functions of their arguments in both cases the list of arguments is extended to include structural tensors which describe the anisotropy of the material response at hand non linear isotropic hardening is considered as well in this paper the integration of the constitutive law is presented the associative flow rule is integrated using the exponential map which preserves the plastic incompressibility condition the numerical treatment of the problem is fully developed and expressions related to the local iteration and the consistent tangent operator are considered in detail it is shown that while the consistent linearisation of the model is quite complicated it still can be achieved if various intriguing implicit dependencies are identified and correctly dealt with various numerical examples of three dimensional deformations of whole structural components are presented the examples clearly illustrate the influence of anisotropy on finite elastoplastic deformations

an improvement of the minimum distortion encoding algorithm for vector quantization in this note we present a very simple method for improving the efficiency of minimum distortion encoding for vector quantization simulations indicates a reduction of up to 70 percent in the number of multiplications for a full search vector quantizer with a large number of codewords and about 25 40 percent for a tree search vector quantizer similar improvement can be achieved in other vector quantization systems

codewords distribution based optimal combination of equal average equal variance equal norm nearest neighbor fast search algorithm for vector quantization encoding vector quantization encoding requires expensive time to find the closest codeword through the codebook for each input vector a fast search algorithm for encoding is proposed in this paper the multilevel elimination criterion is still derived from the three features mean variance and norm inequalities constraints but the order of the three inequalities constraints instead of the predefined order like other conventional multilevel elimination criterion is optimized to speed up the encoding procedure in the proposed algorithm the elimination criterion at the first level is set to mean inequality constraint because of its narrower search width and the priority order at the second and or third level of variance and norm inequalities constraints is optimized based on the codewords distribution and the location of input vector in terms of the considered features the experimental results demonstrate the effectiveness of the proposed algorithm

first order system least squares for second order partial differential equations part i this paper develops a least squares functional that arises from recasting general second order uniformly elliptic partial differential equations in n 2 or 3 dimensions as a system of first order equations in part i z cai r d lazarov t manteuffel and s mccormick siam j numer anal 31 1994 pp 1785 1799 a similar functional was developed and shown to be elliptic in the h divv times h 1 norm and to yield optimal convergence for finite element subspaces of h divv times h 1 in this paper the functional is modified by adding a compatible constraint and imposing additional boundary conditions on the first order system the resulting functional is proved to be elliptic in the h 1 n 1 norm this immediately implies optimal error estimates for finite element approximation by standard subspaces of h 1 n 1 another direct consequence of this ellipticity is that multiplicative and additive multigrid algorithms applied to the resulting discrete functionals are optimally convergent as an alternative to perturbation based approaches the least squares approach developed here applies directly to convection diffusion reaction equations in a unified way and also admits a fast multigrid solver historically a missing ingredient in least squares methodology

a consistent formulation for the integration of combined plasticity and creep within the context of the consistent tangent update this paper outlines a stress update algorithm for combined creep and plasticity the algorithm is implicit providing unconditional stability and utilizes local newton iteration to solve scalar forms of the coupled constitutive equations for the creep and plastic strain increments the tangent for the local iteration is obtained accurately providing quadratic convergence at the gauss point level quadratic convergence of the global iteration procedure is also maintained using an explicitly derived consistent tangent for combined plasticity and creep further combination with an automatic time stepping scheme provides an efficient stable accurate and robust computational algorithm the algorithm has been implemented in the general purpose fe package lusas1

non linear b stability and symmetry preserving return mapping algorithms for plasticity and viscoplasticity a class of second order accurate return mapping algorithms is presented which lead to symmetric algorithmic tangent moduli and contain the classical backward euler return maps as a particular case more importantly it is shown that this class of return maps is contractive relative to the natural norm defined by the complementary helmholz free energy function b stability since the equations of classical plasticity and viscoplasticity are shown to be contractive relative to this natural norm the requirement of b stability furnishes the appropriate notion of unconditionally stable algorithms for plasticity and viscoplasticity the analysis that follows depends critically on the assumption of convexity in particular the models of plasticity and viscoplasticity considered obey the principle of maximum plastic dissipation the proposed algorithms obey the discrete counterpart of this classical principle

finite element method for the solution of maxwell s equations in multiple media this paper concerns a subdomain collocation finite element method which is applied to solve the electromagnetic equations with two or more media the solution is discontinuous both the implementation and the proof of convergence are discussed

is the helmholtz equation really sign indefinite the usual variational or weak formulations of the helmholtz equation are sign indefinite in the sense that the bilinear forms cannot be bounded below by a positive multiple of the appropriate norm squared this is often for a good reason since in bounded domains under certain boundary conditions the solution of the helmholtz equation is not unique at wavenumbers that correspond to eigenvalues of the laplacian and thus the variational problem cannot be sign definite however even in cases where the solution is unique for all wavenumbers the standard variational formulations of the helmholtz equation are still indefinite when the wavenumber is large this indefiniteness has implications for both the analysis and the practical implementation of finite element methods in this paper we introduce new sign definite also called coercive or elliptic formulations of the helmholtz equation posed in either the interior of a star shaped domain with impedance boundary conditions or the exterior of a star shape

a direct complementarity approach for the elastoplastic analysis of plane stress and plane strain structures this paper presents a direct complementarity approach for carrying out the elastoplastic analysis of plane stress and plane strain structures founded on a traditional finite step formulation our approach however avoids the typically cumbersome implementation of iterative predictorcorrector procedures associated with the ubiquitous return mapping algorithm instead at each predefined step the governing formulationcast in its most natural mathematical programming format known as a mixed complementarity problemis directly solved by using a complementarity solver run from within a mathematical modeling system we have chosen the industry standard general algebraic modeling system path mixed complementarity problem solver that is called from within the general algebraic modeling system environment we consider both von mises and tresca materials with perfect or hardening kinematic and isotropic behaviors our numerical tests five benchmark examples of which are presented in this paper have been carried out using models constructed from the mixed finite element of capsoni and corradi comput methods appl mech eng 1997 141 6793 which beneficially offers a locking free behavior and coarse mesh accuracy the results indicate in addition to an isochoric locking free behavior good accuracy and the ability to circumvent the difficult singularity problem associated with the corners of tresca yield surfaces

least square finite element method for electromagnetic fields in 2 d abstract a least squares finite element approximation scheme for electromagnetic fields in two dimensional domains is discussed considering the magnetic field strength lsh ls and the vector of the current density lsj ls as unknowns we describe maxwell s equation as a time dependent form in three dimensions then reduce it into two dimensional steady problems of two categories based on the first order system of partial differential equations the least squares method is applied to the finite element method the rates of convergence for both lsh ls and lsj ls achieve optimal order this method creates an easy way to develop computer software

iterative solution applied to the helmholtz equation complex deflation on unstructured grids abstract extensions of deflation techniques developed for the poisson and navier equations aubry et al 2008 mut et al 2010 lohner et al 2011 aubry et al 2011 1 2 3 4 are presented for the helmholtz equation numerous difficulties arise compared to the previous case after discretization the matrix is now indefinite without sommerfeld boundary conditions or complex with them it is generally symmetric complex but not hermitian discarding optimal short recurrences from an iterative solver viewpoint saad 2003 5 furthermore the kernel of the operator in an infinite space typically does not belong to the discrete space the choice of the deflation space is discussed as well as the relationship between dispersion error and solver convergence similarly to the symmetric definite positive spd case subdomain deflation accelerates convergence if the low frequency eigenmodes are well described however the analytic eigenvectors are well represented only if the dispersion error is low cpu savings are therefore restricted to a low to mid frequency regime compared to the mesh size which could be still relevant from an application viewpoint given the ease of implementation

dispersive and dissipative errors in the dpg method with scaled norms for helmholtz equation this paper studies the discontinuous petrov galerkin dpg method where the test space is normed by a modified graph norm the modification scales one of the terms in the graph norm by an arbitrary positive scaling parameter the main finding is that as the parameter approaches zero better results are obtained under some circumstances when the method is applied to the helmholtz equation the main tool used is a dispersion analysis on the multiple interacting stencils that form the dpg method the analysis shows that the discrete wavenumbers of the method are complex explaining the numerically observed artificial dissipation in the computed wave approximations since the dpg method is a nonstandard least squares galerkin method its performance is compared with a standard least squares method having a similar stencil

a new vector quantization clustering algorithm the pairwise nearest neighbor pnn algorithm is presented as an alternative to the linde buzo gray 1980 lbg generalized lloyd 1982 algorithm for vector quantization clustering the pnn algorithm derives a vector quantization codebook in a diminishingly small fraction of the time previously required without sacrificing performance in addition the time needed to generate a codebook grows only o n log n in training set size and is independent of the number of code words desired using this method one can either minimize the number of code words needed subject to a maximum rate the pnn algorithm can be used with squared error and weighted squared error distortion measure simulations on a variety of images encoded at 1 2 b pixel indicate that pnn codebooks can be developed in roughly 5 of the time required by the lbg algorithm

multilevel first order system least squares for elliptic grid generation a new fully variational approach is studied for elliptic grid generation egg it is based on a general algorithm developed in a companion paper a l codd t a manteuffel and s f mccormick siam j numer anal 41 2003 pp 2197 2209 that involves using newton s method to linearize an appropriate equivalent first order system first order system least squares fosls to formulate and discretize the newton step and algebraic multigrid amg to solve the resulting matrix equation the approach is coupled with nested iteration to provide an accurate initial guess for finer levels using coarse level computation the present paper verifies the assumptions of the companion work and confirms the overall efficiency of the scheme with numerical experiments

fast k dimensional tree algorithms for nearest neighbor search with application to vector quantization encoding fast search algorithms are proposed and studied for vector quantization encoding using the k dimensional k d tree structure here the emphasis is on the optimal design of the k d tree for efficient nearest neighbor search in multidimensional space under a bucket voronoi intersection search framework efficient optimization criteria and procedures are proposed for designing the k d tree for the case when the test data distribution is available as in vector quantization application in the form of training data as well as for the case when the test data distribution is not available and only the voronoi intersection information is to be used the criteria and bucket voronoi intersection search procedure are studied in the context of vector quantization encoding of speech waveform they are empirically observed to achieve constant search complexity for o log n tree depths and are found to be more efficient in reducing the search complexity a geometric interpretation is given for the maximum product criterion explaining reasons for its inefficiency with respect to the optimization criteria

a class of mixed assumed strain methods and the method of incompatible modes a three field mixed formulation in terms of displacements stresses and an enhanced strain field is presented which encompasses as a particular case the classical method of incompatible modes within this frame work incompatible elements arise as particular compatible mixed approximations of the enhanced strain field the conditions that the stress interpolation contain piece wise constant functions and be l2 ortho gonal to the enhanced strain interpolation ensure satisfaction of the patch test and allow the elimination of the stress field from the formulation the preceding conditions are formulated in a form particularly convenient for element design as an illustration of the methodology three new elements are developed and shown to exhibit good performance a plane 3d elastic plastic quad an axisymmetric element and a thick plate bending quad the formulation described herein is suitable for non linear analysis

second order accurate integration algorithms for von mises plasticity with a nonlinear kinematic hardening mechanism abstract two second order numerical schemes for von mises plasticity with a combination of linear isotropic and nonlinear kinematic hardening are presented the first scheme is the generalized midpoint integration procedure originally introduced by ortiz and popov in 1985 detailed and applied here to the case of armstrong frederick nonlinear kinematic hardening the second algorithm is based on the constitutive model exponential based reformulation and on the integration procedure previously introduced by the authors in the context of linearly hardening materials there are two main targets to the work firstly we wish to extensively test the generalized midpoint procedure since in the scientific literature no thorough numerical testing campaign has been carried out on this second order algorithm secondly we wish to extend the exponential based integration technique also to nonlinear hardening materials a wide numerical investigation is carried out in order to compare the performance of the two methods