mixed perfectly matched layers for direct transient analysis in 2d elastic heterogeneous media abstract we are concerned with elastic waves arising in plane strain problems in an elastic semi infinite arbitrarily heterogeneous medium specifically we discuss the development of a new mixed displacement stress formulation for forward elastic wave simulations in perfectly matched layer pml truncated heterogeneous media to date most pml formulations split the displacement and stress fields resulting in non physical components for each field in this work we favor unsplit schemes primarily for the relative ease by which the resulting forms can be incorporated into existing codes the ease by which the resulting semi discrete forms can be integrated in time and the ease by which they can be used in adjoint formulations arising in inverse problems contrary to most past and current developments we start by following classical lines and apply complex coordinate stretching to the governing equations in the frequency domain while retaining both displacements and stress quantities as unknowns with the aid of auxiliary variables the resulting mixed form is rendered second order in time thereby allowing the use of standard time integration schemes we report on numerical simulations demonstrating the stability and efficacy of the approach

second order power comparisons for a class of nonparametric likelihood based tests summary this paper compares the second order power properties of a broad class of nonparametric likelihood tests recently introduced by baggerly 1998 as a generalisation of owen s 1988 empirical likelihood it is shown that in a multi parameter setting identity of power up to first order does not imply identity up to second order unless one considers the average power criterion it is also shown that the empirical likelihood ratio enjoys an optimality property in terms of local maximinity

an efficient higher order pml in wlp fdtd method for time reversed wave simulation a higher order pml is proposed for the wlp fdtd method the parameter values in the higher order pml are optimized by moga the higher order pml is efficient in terms of absorbing performance the wlp fdtd method is employed to analyze the tr wave propagation problem derived from a stretched coordinate formulation a higher order complex frequency shifted cfs perfectly matched layer pml is proposed for the unconditionally stable finite difference time domain fdtd method based on weighted laguerre polynomials wlps the higher order pml is implemented with an auxiliary differential equation ade approach in order to further improve absorbing performance the parameter values of stretching functions in the higher order pml are optimized by the multi objective genetic algorithm moga the optimal solutions can be chosen from the pareto front for trading off between two independent objectives it is shown in a numerical test that the higher order pml is efficient in terms of attenuating propagating waves and reducing late time reflections moreover the higher order pml can be placed very close to the wall when analyzing the channel characteristics of time reversal tr waves in a multipath indoor environment numerical examples of tr wave propagation demonstrate the availability of the proposed method

a note on convergence of the multigrid v cycle several recent papers have discussed the convergence of the multigrid v cycle in particular there are several results for the symmetric case where the numbers of smoothings before the fine to coarse transfer and after the coarse to fine transfer are the same in most instances the smoother h i e 1a has been limited to the case where e is positive definite and the eigenvalues h of h satisfy 0

a pml using a convolutional curl operator and a numerical reflection coefficient for general linear media a general time domain representation of the chew and weedon 1994 stretched coordinate perfectly matched layer pml absorbing boundary condition is described this new approach mathematically operates on the spatial field derivatives and allows the pml update equations to be trivially derived from any set of general linear medium update equations a method for calculating the frequency dependent reflection coefficient for this form of the pml is derived for general linear media two and three dimensional numerical test results which validate the calculation of the reflection coefficient are presented the range of numerical tests include the pml matching of free space a magnetoplasma and a free space waveguide improving the reflection coefficient is examined

second order pml the n th order pmls based on the unsplit field formulations and the z transform methods are proposed to truncate the finite difference time domain fdtd domains which will be validated through numerical simulations whether the higher order pml with more than two poles such as n 3 will hold better absorption performance as compared with the conventional complex frequency shifted cfs second order perfectly matched layer pmls the advantages and disadvantages of different pmls are demonstrated it has shown that the higher order pmls have the advantages of both the conventional and the cfs pmls in terms of absorption performance since the conventional pml is ineffective at absorbing the evanescent waves and the cfs pml is incapable of absorbing low frequency propagating waves it is clearly shown that the second order pml is overall the optimal choice for truncating arbitrary fdtd domains since it not only requires less computational time and memory but holds almost the same absorption performance as compared with the third order pml three numerical simulations have been carried out in three dimensional 3d problems to confirm the analysis

empirical likelihood ratio confidence intervals for a single functional summary the empirical distribution function based on a sample is well known to be the maximum likelihood estimate of the distribution from which the sample was taken in this paper the likelihood function for distributions is used to define a likelihood ratio function for distributions it is shown that this empirical likelihood ratio function can be used to construct confidence intervals for the sample mean for a class of m estimates that includes quantiles and for differentiable statistical functionals the results are nonparametric extensions of wilks s 1938 theorem for parametric likelihood ratios the intervals are illustrated on some real data and compared in a simulation to some bootstrap confidence intervals and to intervals based on student s t statistic a hybrid method that uses the bootstrap to determine critical values of the likelihood ratio is introduced

on the use of inexact subdomain solvers for bddc algorithms the standard bddc balancing domain decomposition by constraints preconditioner is shown to be equivalent to a preconditioner built from a partially subassembled finite element model this results in a system of linear algebraic equations which is much easier to solve in parallel than the fully assembled model the cost is then often dominated by that of the problems on the subdomains an important role is also played both in theory and practice by an averaging operator and in addition exact dirichlet solvers are used on the subdomains in order to eliminate the residual in the interior of the subdomains the use of inexact solvers for these problems and even the replacement of the dirichlet solvers by a trivial extension are considered it is established that one of the resulting algorithms has the same eigenvalues as the standard bddc algorithm and the connection of another with the feti dp algorithm with a lumped preconditioner is also considered multigrid methods are used in the experimental work and under certain assumptions it is established that the iteration count essentially remains the same as when exact solvers are used while considerable gains in the speed of the algorithm can be realized since the cost of the exact solvers grows superlinearly with the size of the subdomain problems while the multigrid methods are linear

unconditionally stable higher order cnad pml for left handed materials an unconditionally stable and efficient higher order complex frequency shifted perfectly matched layer cfs pml based on the crank nicolson approximate decoupling cnad algorithm is proposed for truncating the finite difference time domain fdtd computational domain filled with the left handed materials lhms the proposed higher order cfs pml is implemented by the bilinear transform bt approach and the lhms are solved by the trapezoidal recursive convolution trc method a numerical example is provided to validate the effectiveness of the proposed implementation the results show that the proposed cfs pml not only has better absorbing performance compared with the first order cnad cfs pml and the alternating direction implicit adi cfs pml but also takes advantage of the unconditional stability of the original crank nicolson algorithm

the analysis of multigrid algorithms for pseudodifferential operators of order minus one multigrid algorithms are developed to solve the discrete systems approximating the solutions of operator equations involving pseudodifferential operators of order minus one classical multigrid theory deals with the case of differential operators of positive order the pseudodifferential operator gives rise to a coercive form on h sup minus 1 2 omega effective multigrid algorithms are developed for this problem these algorithms are novel in that they use the inner product on h sup minus 1 omega as a base inner product for the multigrid development the authors show that the resulting rate of iterative convergence can at worst depend linearly on the number of levels in these novel multigrid algorithms in addition it is shown that the convergence rate is independent of the number of levels and unknowns in the case of a pseudodifferential operator defined by a single layer potential finally the results of numerical experiments illustrating the theory are presented 19 refs 1 fig 2 tabs

two level hierarchical fem method for modeling passive microwave devices in recent years multigrid methods have been proven to be very efficient for solving large systems of linear equations resulting from the discretization of positive definite differential equations by either the finite difference method or theh version of the finite element method in this paper an iterative method of the multiple level type is proposed for solving systems of algebraic equations which arise from thep version of the finite element analysis applied to indefinite problems a two levelv cycle algorithm has been implemented and studied with a gauss seidel iterative scheme used as a smoother the convergence of the method has been investigated and numerical results for a number of numerical examples are presented

an optimized hybrid convolutional perfectly matched layer for efficient absorption of electromagnetic waves abstract a hybrid technique is studied in order to improve the performance of convolutional perfectly matched layer cpml in the finite difference time domain fdtd medium this technique combines the first order of higdon s annihilation equation as absorbing boundary condition abc with cpml to vanish the perfect electric conductor pec effects at the end of the cpml region an optimization algorithm is required to find optimum parameters of the proposed absorber in this investigation the particle swarm optimization pso is utilized with two separate objective functions in order to minimize the average and peak value of relative error using a standard test the overall performance of the proposed absorber is compared to the original cpml the results clearly illustrate this method provides approximately 10 db enhancements in cpml absorption error the performance memory and time requirement of the novel absorber hybrid cpml h cpml was analyzed during 2d and 3d tests and compared to most reported pmls the h cpml requirement of computer resources is similar to cpml and can simply be implemented to truncate fdtd domains furthermore an optimized set of parameters are provided to generalize the hybrid method

a multi grid method with a priori and a posteriori level choice for the regularization of nonlinear ill posed problems in this paper we study a multi grid method for the numerical solution of nonlinear systems of equations arising from the discretization of ill posed problems where the special eigensystem structure of the underlying operator equation makes it necessary to use special smoothers we provide uniform contraction factor estimates and show that a nested multigrid iteration together with an a priori or a posteriori chosen stopping index defines a regularization method for the ill posed problem i e a stable solution method that converges to an exact solution of the underlying infinite dimensional problem as the data noise level goes to zero with optimal rates under additional regularity conditions

convergence estimates for multigrid algorithms without regularity assumptions a new technique for proving rate of convergence estimates of multi grid algorithms for symmetric positive definite problems will be given in this paper the standard multigrid theory requires a regularity and approxima tion assumption in contrast the new theory requires only an easily verified approximation assumption this leads to convergence results for multigrid re finement applications problems with irregular coefficients and problems whose coefficients have large jumps in addition the new theory shows why it suffices to smooth only in the regions where new nodes are being added in multigrid refinement applications

empirical type likelihoods allowing posterior credible sets with frequentist validity higher order asymptotics summary with reference to a general class of empirical type likelihoods we develop higher order asymptotics for the frequentist coverage of bayesian credible sets based on posterior quantiles and highest posterior density these asymptotics in turn characterise members of the class that allow approximate frequentist validity of such sets it is seen that the usual empirical likelihood does not enjoy this property up to the order of approximation considered here

an evaluation of the power and conditionality properties of empirical likelihood empirical and dual likelihood are two of a growing array of artificial or approximate likelihoods currently in use in statistics a question of major interest focuses on the performance of these new constructs relative to ordinary parametric likelihoods we consider here two criteria local power and conditional properties looking at tests of a scalar parameter we show that there is no loss of efficiency in using a dual or empirical likelihood model to second order to third order either the artificial likelihood or the true likelihood test could be more efficient this is determined by the fisher information the distance between the null and the alternative hypotheses and the statistical curvature of the models conditionality properties are assessed by comparing empirical likelihood with quasilikelihood if there is overdispersion present or more generally an unknown amount of dispersion then there is little difference in the ancillaries for conditional inference based on empirical likelihood or on other possible likelihoods such as a quasilikelihood if the amount of dispersion is known however it is correct to base inference on the quasilikelihood

optimal order multigrid methods for solving exterior boundary value problems the coupling of boundary elements and finite elements combines the advantage of boundary elements for treating domains extended to infinity and that of finite elements in treating the nonhomogeneity of equations and the complexity of domains in the case of the laplacian by taking a circle or a sphere as the artificial coupling boundary it is shown that the corresponding boundary integral equation can be solved without any cost and the coupled system is reduced to a simple finite element system two multigrid methods are proposed to solve this finite element linear system both methods are of optimal order and can be used to solve such finite element equations as efficiently as to solve those arising from interior boundary value problems numerical experiments are included to show the efficiency and advantages of the methods an apparent significance of the methods is that the boundary elements appear neither in the discretization nor in the coding

a posteriori boundary element error estimation an a posteriori error estimator is presented for the boundary element method in a general framework it is obtained by solving local residual problems for which a local concept is introduced to accommodate the fact that integral operators are nonlocal operators the estimator is shown to have an upper and a lower bound by the constant multiples of the exact error in the energy norm for symm s and hypersingular integral equations numerical results are also given to demonstrate the eectiveness of the estimator for these equations it can be used for adaptive h p and hp methods c 1999 elsevier science b v all rights reserved msc 65n35 65n15 65r20 65d07 45l10

an efficient complex frequency shifted perfectly matched layer for second order acoustic wave equation summary in the context of simulations of wave propagations in unbounded domain absorbing boundary conditions are often used to truncate the simulation domain to a finite space perfectly matched layer pml has proven to be an excellent absorbing boundary conditions however as this technique was primarily designed for the first order equation system it cannot be applied to the second order equation system directly in this paper based on a complex coordinate stretching technique we developed a novel efficient auxiliary differential equation form of the complex frequency shifted pml for the second order equation system this facilitates the use of complex frequency shifted pml in acoustic simulations based upon wave equations of second order form compared with previous state of the art methods the proposed one has the advantage of simpler implementation it is an unsplit field scheme that can be extended to higher order discretization schemes conveniently numerical results from both homogeneous and heterogeneous computational domains are provided to illustrate the validity of the method copyright 2013 john wiley sons ltd

unsplit implementation of higher order pmls an unsplit implementation of higher order perfectly matched layers pmls using a recursive integration approach is presented the formulation which is based on the complex coordinate stretching of space is developed for a general complex frequency shifted stretching function but is applicable to pmls employing the standard stretching function or a mixture of either types the approach results in the development of two general formulae that could be used to easily generate pml correction equations for any pml order numerical results from finite difference time domain models are presented to illustrate the validity of the approach

weak solvability of interior transmission problems via mixed finite elements and dirichlet to neumann mappings we study the weak solvability of an interior linear nonlinear transmission problem arising in steady heat transfer and potential theory for the variational formulation we use a dirichlet to neumann mapping on the interface which is obtained from the application of the boundary integral method to the linear domain and we utilize a mixed finite element method in the nonlinear region existence and uniqueness of solution for the continuous formulation are provided and general approximation results for a fully discrete galerkin method are derived in particular a compatibility condition between the mesh sizes involved is deduced in order to conclude the solvability and stability of this galerkin scheme

an auxiliary differential equation formulation for the complex frequency shifted pml an efficient auxiliary differential equation ade form of the complex frequency shifted perfectly matched layer cpml absorbing media derived from a stretched coordinate pml formulation is presented it is shown that a unit step response of the ade cpml equations leads to a discrete form that is identical to roden s convolutional pml method for fdtd implementations the derivation of discrete difference operators for the ade cpml equations for fdtd is also presented the ade cpml method is also extended in a compact form to a multiple pole pml formulation the advantage of the ade cpml method is that it provides a more flexible representation that can be extended to higher order methods in this paper it is applied to the discontinuous galerkin finite element time domain dgfetd method it is demonstrated that the ade cpml maintains the exponential convergence of the dgfetd method

multigrid convergence for nonsymmetric indefinite variational problems and one smoothing step we prove that the multigrid method for linear systems arising from nonsymmetric and indefinite elliptic variational problems converges for all sufficiently small h with one smoothing step only previous proofs required that the number of smoothing steps be within certain bounds which were quite difficult to compute our theory is based on sharp energy norm convergence estimates for the symmetric definite case and lower order terms are treated as perturbations the resulting estimates are so sharp that we obtain even the convergence of the v cycle

bayesian and frequentist confidence intervals arising from empirical type likelihoods summary for a general class of empirical type likelihoods for the population mean higher order asymp totics are developed with a view to characterizing its members which allow for any given prior the existence of a confidence interval that has approximately correct posterior as well as fre quentist coverage in particular it is seen that the usual empirical likelihood always allows such a confidence interval while many of its variants proposed in the literature do not enjoy this property an explicit form of the confidence interval is also given

nonconforming multigrid method for nonsymmetric and indefinite problems abstract the convergence of w cycle multigrid algorithms applied to nonsymmetric and indefinite elliptic boundary value problems using p 1 nonconforming finite elements is proved

preconditioning in h div and applications we consider the solution of the system of linear algebraic equations which arises from the finite element discretization of boundary value problems associated to the differential operator i grad div the natural setting for such problems is in the hilbert space h div and the variational formulation is based on the inner product in h div we show how to construct preconditioners for these equations using both domain decomposition and multigrid techniques these preconditioners are shown to be spectrally equivalent to the inverse of the operator as a consequence they may be used to precondition iterative methods so that any given error reduction may be achieved in a finite number of iterations with the number independent of the mesh discretization we describe applications of these results to the efficient solution of mixed and least squares finite element approximations of elliptic boundary value problems

expected lengths of confidence intervals based on empirical discrepancy statistics we consider a very general class of empirical discrepancy statistics that includes the cressie read discrepancy statistics and in particular the empirical likelihood ratio statistic higher order asymptotics for expected lengths of associated confidence intervals are investigated an explicit formula is worked out and its use for comparative purposes is discussed it is seen that the empirical likelihood ratio statistic which enjoys interesting second order power properties loses much of its edge under the present criterion

convergence of the multigrid v cycle algorithm for second order boundary value problems without full elliptic regularity the multigrid v cycle algorithm using the richardson relaxation scheme as the smoother is studied in this paper for second order elliptic boundary value problems the contraction number of the v cycle algorithm is shown to improve uniformly with the increase of the number of smoothing steps without assuming full elliptic regularity as a consequence the v cycle convergence result of braess and hackbusch is generalized to problems without full elliptic regularity

on the convergence of the multigrid method for a hypersingular integral equation of the first kind we present a multigrid method to solve linear systems arising from galerkin schemes for a hypersingular boundary integral equation governing three dimensional neumann problems for the laplacian our algorithm uses damped jacobi iteration gauss seidel iteration or sor as preand post smoothers if the integral equation holds on a closed lipschitz surface we prove convergence ofv andw cycles with any number of smoothing steps if the integral equation holds on an open lipschitz surface covering crack problems we show convergence of thew cycle numerical experiments are given which underline the theoretical results

multigrid convergence for a singular perturbation problem abstract so far there has been no analysis of multigrid methods applied to singularly perturbed dirichlet boundary value problems only for periodic boundary conditions does the fourier transformation mode analysis apply and it is not obvious that the convergence results carry over to the dirichlet case since the eigenfunctions are quite different in the two cases in this paper we prove a close relationship between multigrid convergence for the easily analysable case of periodic conditions and the convergence for the dirichlet case

the convergence rate of a multigrid method with gauss seidel relaxation for the poisson equation the numerical solution of the poisson equation is treated by a multigrid method for a uniform grid the convergence rate can be estimated even for the iteration with a v cycle independently of the shape of the domain as long as it is convex and polygonal the smoothing effect of the gaus seidel relaxation is described by a discrete seminorm which is weaker than the energy norm

a higher order perfectly matched layer formulation for finite difference time domain seismic wave modeling we have developed a higher order perfectly matched layer pml formulation to improve the absorption performance for finite difference time domain seismic modeling first we outlined a new unsplit correction approach which allowed for traditional first order pmls to be added directly to existing codes in a straightforward manner then using this framework we constructed a pml formulation that can be used to construct higher order pmls of arbitrary order the greater number of degrees of freedom associated with the higher order pml allow for enhanced flexibility of the pml stretching functions thus potentially facilitating enhanced absorption performance we found that the new approach can offer increased elastodynamic absorption particularly for evanescent waves we also discovered that the extra degrees of freedom associated with the higher order pml required careful optimization if enhanced absorption was to be achieved furthermore these extra degrees of freedom increased the computational requirements in comparison with first order schemes we reached our formulations using one compact equation thus increasing the ease of implementation additionally the formulations are based on a recursive integration approach that reduce pml memory requirements and do not require special consideration for corner regions we tested the new formulations to determine their ability to absorb body waves and surface waves we also tested standard staggered grid stencils and rotated staggered grid stencils

a dual dual mixed formulation for nonlinear exterior transmission problems we combine a dual mixed finite element method with a dirichletto neumann mapping derived by the boundary integral equation method to study the solvability and galerkin approximations of a class of exterior nonlinear transmission problems in the plane as a model problem we consider a nonlinear elliptic equation in divergence form coupled with the laplace equation in an unbounded region of the plane our combined approach leads to what we call a dual dual mixed variational formulation since the main operator involved has itself a dual type structure we establish existence and uniqueness of solution for the continuous and discrete formulations and provide the corresponding error analysis by using raviart thomas elements the main tool of our analysis is given by a generalization of the usual babuska brezzi theory to a class of nonlinear variational problems with constraints

an optimized higher order pml in domain decomposition wlp fdtd method for time reversal analysis in this paper an efficient higher order complex frequency shifted cfs perfectly matched layer pml derived from a stretched coordinate formulation is proposed for the unconditionally stable finite difference time domain method based on weighted laguerre polynomials the higher order cfs pml which is implemented with an auxiliary differential equation ade approach has apparent advantage in reducing late time reflections compared with the standard unsplit field pml and lower order cfs pml furthermore the parameter values of stretching functions in the higher order ade cfs pml are optimized with the multiobjective genetic algorithm to improve absorbing performance the optimal solutions can be chosen from the pareto front for trading off between two independent objectives the numerical formulation is derived and its absorbing ability is validated through three numerical tests moreover the proposed higher order pml can be placed very close to the objects and the simulation area can be further reduced accordingly numerical examples of time reversal wave propagation in a real indoor environment are included to validate the accuracy and efficiency of the proposed scheme

optimal order nonnested multigrid methods for solving finite element equations i on quasi uniform meshes we prove that the multigrid method works with optimal computational order even when the multiple meshes are not nested when a coarse mesh is not a submesh of the finer one the coarse level correction usually does not have the a projection property and does amplify the iterative error in some components nevertheless the low frequency components of the error can still be caught by the coarse level correction since the amplified highfrequency errors will be damped out by the fine level smoothing efficiently the optimal work order of the standard multigrid method can still be maintained however unlike the case of nested meshes a nonnested multigrid method with one smoothing does not converge in general no matter whether it is a v cycle or a w cycle method it is shown numerically that the convergence rates of nonnested multigrid methods are not necessarily worse than those of nested ones since nonnested multigrid methods accept quite arbitrarily related meshes we may then combine the efficiencies of adaptive refinements and of multigrid algorithms

an optimal iterative process for the johnson nedelec method of coupling boundary and finite elements we reformulate the discretization of the johnson nedelec method 11 of coupling boundary elements and finite elements for an exterior bidimensional laplacian this new formulation leads to optimal error estimates and allows the use of simple quadrature formulas for calculation of the boundary element matrix we show that if the parameter of discretization is sufficiently small the fully discrete scheme is well posed and the error estimates remain unaltered the rest of the paper is devoted to the study of an efficient algorithm for solving the resulting discrete linear systems

empirical likelihood as a goodness of fit measure summary the method of empirical likelihood can be viewed as one of allocating probabilities to an n cell contingency table so as to minimise a goodness of fit criterion it is shown that when the cressie read power divergence statistic is used as the criterion confidence regions enjoying the same convergence rates as those found for empirical likelihood can be obtained for the entire range of values of the cressie read parameter including 1 maximum entropy 0 empirical likelihood and 1 pearson s z2 it is noted that in the power divergence family empirical likelihood is the only member which is bartlettcorrectable however simulation results suggest that for the mean using a scaled f distribution yields more accurate coverage levels for moderate sample sizes

novel and efficient fdtd implementation of higher order perfectly matched layer based on ade method based on the stretched coordinate perfectly matched layer sc pml formulations and the auxiliary differential equation ade method an efficient and unsplit field implementation of the higher order pml scheme with more than one pole is proposed to truncate the finite difference time domain fdtd lattices the higher order pml has the advantages of both the conventional pml and the complex frequency shifted pml cfs pml in terms of absorbing performances the proposed algorithm is validated through two numerical tests carried out in three dimensional and two dimensional domains it is shown in the numerical simulations that the proposed pml formulations with the higher order scheme are efficient in terms of attenuating both the low frequency propagating waves and evanescent waves and reducing late time reflections and also hold much better absorbing performances than the conventional sc pml and the convolutional pml cpml with the cfs scheme

a conjugate gradient method and a multigrid algorithm for morley s finite element approximation of the biharmonic equation the numerical solution of the linear equations arising from morley s nonconforming displacement method is studied a suitable preconditioning for the conjugate gradient method is described furthermore the nonconformity of the discretization necessitates some non standard ingredients of multigrid algorithms

fem bem coupling methods for tokamak plasma axisymmetric free boundary equilibrium computations in unbounded domains abstract incorporating boundary conditions at infinity into simulations on bounded computational domains is a repeatedly occurring problem in scientific computing the combination of finite element methods fem and boundary element methods bem is the obvious instrument and we adapt here for the first time the two standard fem bem coupling approaches to the free boundary equilibrium problem the johnson nedelec coupling and the bielak maccamy coupling we recall also the classical approach for fusion applications dubbed according to its first appearance von hagenow lackner coupling and present the less used alternative introduced by albanese blum and de barbieri in 2 we show that the von hagenow lackner coupling suffers from undesirable non optimal convergence properties that suggest that other coupling schemes in particular johnson nedelec or albanese blum de barbieri are more appropriate for non linear equilibrium problems moreover we show that any of such coupling methods requires newton like iteration schemes for solving the corresponding non linear discrete algebraic systems

on the development of a higher order pml a higher order perfectly matched layer pml is proposed based on stretched coordinates to effectively attenuate both propagating and evanescent waves the new pml has multiple poles in contrast to the regular pml with a single pole the implementation is also derived and results are shown to be better than those of the regular pml and the recently proposed complex frequency shifted cfs pml with an insignificant increase in the computational cost

a multilevel algorithm for the biharmonic problem a finite element discretization of the mixed variable formulation of the biharmonic problem is considered a multilevel algorithm for the numerical solution of the discrete equations is described convergence is proved under the assumption ofh 3 regularity

multigrid in h div and h curl summary we consider the solution of systems of linear algebraic equations which arise from the finite element discretization of variational problems posed in the hilbert spaces bf h div and bf h curl in three dimensions we show that if appropriate finite element spaces and appropriate additive or multiplicative schwarz smoothers are used then the multigrid v cycle is an efficient solver and preconditioner for the discrete operator all results are uniform with respect to the mesh size the number of mesh levels and weights on the two terms in the inner products

a domain decomposition method based on bem and fem for linear exterior boundary value problems abstract we develop the finite dimensional analysis of a new domain decomposition method for linear exterior boundary value problems arising in potential theory and heat conductivity our approach uses a dirichlet to neumann mapping to transform the exterior problem into an equivalent boundary value problem on a bounded domain then the domain is decomposed into a finite number of annular subregions and the local steklov poincare operators are expressed conveniently either by bem or fem in order to obtain a symmetric interface problem the global steklov poincare problem is solved by using both a richardson type scheme and the preconditioned conjugate gradient method which yield iteration by subdomain algorithms well suited for parallel processing finally contractivity results and finite dimensional approximations are provided

variational formulations of transmission problems via fem bem and dtn mappings the purpose of this work is to review some of the main results on the weak solvability and galerkin approximations of interior and exterior transmission problems arising in potential theory and elastostatics both linear and nonlinear model problems are included in our presentation we consider variational formulations based on the combination of mixed finite elements with either boundary integral equations or dirichlet to neumann dtn mappings we provide existence and uniqueness of solution for the continuous formulations and give general approximation estimates for the associated galerkin schemes some open questions are also mentioned

iterative solution methods for plate bending problems multigrid and preconditioned cg algorithm the numerical solution of the linear equations arising from a discretization of the plate bending problem based on the zienkiewicz triangle is studied the finite element scheme proceeds from the mindlin reissner formulation with modified shear energy however the kirchhoff condition is imposed on discrete points a multigrid algorithm is analyzed and numerical examples are provided furthermore a suitable preconditioning is established for the use of conjugate gradients

a new convergence proof for the multigrid method including the v cycle for a positive definite finite element equation we describe a multigrid iteration and prove convergence under natural assumptions on the discretization and the elliptic problem hitherto existing convergence proofs require a sufficiently large number of smoothing iterations and exclude the v cycle the presented proof applies to procedures with any number of smoothing iterations and to the v cycle

an optimal order process for solving finite element equations a k level iterative procedure for solving the algebraic equations which arise from the finite element approximation of elliptic boundary value problems is presented and analyzed the work estimate for this procedure is proportional to the number of unknowns an optimal order result general geometry is permitted for the underlying domain but the shape plays a role in the rate of convergence through elliptic regularity finally a short discussion of the use of this method for parabolic problems is presented

overcoming corner singularities using multigrid methods we consider the poisson equation delta u f with homogeneous dirichlet boundary condition on a two dimensional polygonal domain o we develop a finite element multigrid method on quasi uniform grids that obtains cal o h m 1 epsilon convergence in the h 1 o norm for any positive epsilon when f in h m o the cost of the method is proportional to the number of elements in the triangulation the results of this paper can be generalized to other equations and other boundary conditions

multigrid computation of vector potentials in this paper we analyze the use of edge finite elements and the multigrid method to approximate the problem of computing a static magnetic field in a cavity we show how the mixed finite element discrete problem may be reformulated as a symmetric positive definite system this involves the proof of a discrete analogue of the second kind friedrichs inequality then we show how the multigrid method may be applied to compute the magnetic vector potential the difficulty here is that the bilinear forms on different meshes are not related in the standard way two different intergrid transfer operators are defined in the paper for the multigrid method the convergence theory and the numerical tests include both algorithms

finite element analysis of complex antennas and arrays various technical issues are addressed in the frequency and time domain finite element analysis of complex antennas and arrays that may consist of fine structures and composite materials the paper starts with the finite element formulation of a generic antenna problem formulation for the modeling of general electrically and magnetically dispersive lossy and anisotropic materials in the time domain finite element analysis is presented for the first time this is followed by discussion of three typical techniques for truncation of the finite element computational domain via the use of absorbing boundary conditions perfectly matched layers and boundary integral equations it then describes the modeling of antenna feeds using a current probe including an improved model a voltage gap and a waveguide port boundary condition after that numerical approaches to modeling infinite phased arrays large finite arrays and antenna platform interaction are presented including two novel domain decomposition algorithms in both the frequency and time domains numerical examples are given to demonstrate the capability and application of the finite element analysis of a variety of complex antennas and arrays