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

robust optimization for unconstrained simulation based problems in engineering design an optimized solution often turns out to be suboptimal when errors are encountered although the theory of robust convex optimization has taken significant strides over the past decade all approaches fail if the underlying cost function is not explicitly given it is even worse if the cost function is nonconvex in this work we present a robust optimization method that is suited for unconstrained problems with a nonconvex cost function as well as for problems based on simulations such as large partial differential equations pde solver response surface and kriging metamodels moreover this technique can be employed for most real world problems because it operates directly on the response surface and does not assume any specific structure of the problem we present this algorithm along with the application to an actual engineering problem in electromagnetic multiple scattering of aperiodically arranged dielectrics relevant to nanophotonic design the corresponding objective function is highly nonconvex and resides in a 100 dimensional design space starting from an optimized design we report a robust solution with a significantly lower worst case cost while maintaining optimality we further generalize this algorithm to address a nonconvex optimization problem under both implementation errors and parameter uncertainties

a pseudospectral method for time domain computation of electromagnetic scattering by bodies of revolution we present a multidomain pseudospectral method for the accurate and efficient time domain computation of scattering by body of revolution bor perfectly electrically conducting objects in the bor formulation of the maxwell equations the azimuthal dependence of the fields is accounted for analytically through a fourier series the numerical scheme in the r z plane is developed in general curvilinear coordinates and the method of characteristics is applied for patching field values in the individual subdomains to obtain the global solution a modified matched layer method is used for terminating the computational domain and special attention is given to proper treatment of the coordinate singularity in the scattered field formulation and correct time domain boundary conditions along edges numerical results for monochromatic plane wave scattering by smooth and nonsmooth axis symmetric objects including spheres cone spheres and finite cylinders is compared with results from the literature illustrating the accuracy and computational efficiency associated with the use of properly constructed spectral methods to emphasize the versatility of the presented framework we compute plane wave scattering by a missile and find satisfactory agreement with method of moment mom computations

on the stability of boundary conditions for molecular dynamics we study the stability of boundary conditions for molecular dynamics simulations a general stability criterion is established we first consider a one dimensional model with nearest neighbor interaction and multiple neighbor interactions we then generalize the results to more realistic models in 3d with nonlinear atomic interaction

plane wave analysis and comparison of split field biaxial and uniaxial pml methods as abcs for pseudospectral electromagnetic wave simulations in curvilinear coordinates in this paper we discuss and compare split field biaxial and uniaxial perfectly matched layer pml methods for absorbing outgoing vector waves in cylindrical and spherical coordinates we first extend berenger s split field formulation into spherical and cylindrical coordinates in such a way that it maintains all the desirable properties it exhibits in rectangular coordinates then we discuss the biaxial and the uniaxial medium pml methods in cartesian coordinates and extend them to spherical and cylindrical coordinates properties of plane wave solutions of the pml methods are analyzed in particular the decay and boundness properties of the solutions are considered in order to provide further insight into the different formulations presented herein moreover we propose a set of symmetric hyperbolic equations for both the biaxial and the uniaxial pml methods in the time domain which is fine tuned in numerical experiments and very suitable for time domain problems all three types of spherical and cylindrical pml methods are applied in simulations of plane wave scattering as well as radiating dipole problems we use a multidomain pseudospectral chebyshev numerical scheme and the effectiveness of the pml methods is demonstrated through the accurate numerical results obtained the order of outer boundary reflection is as low as 0 1 of the exact solution

a nondiffusive finite volume scheme for the three dimensional maxwell s equations on unstructured meshes we prove a sufficient cfl like condition for the l2 stability of the second order accurate finite volume scheme proposed by remaki for the time domain solution of maxwell s equations in heterogeneous media with metallic and absorbing boundary conditions we yield a very general sufficient condition valid for any finite volume partition in two and three space dimensions numerical tests show the potential of this original finite volume scheme in one two and three space dimensions for the numerical solution of maxwell s equations in the time domain

an absorbing matched layer implementation for the transmission line matrix method abstract an absorbing matched layer for the transmission line matrix method in acoustics is proposed so far existing formulations of absorbing layers for tlm have been obtained from empirical considerations in the present study a formulation is proposed on the basis of acoustic equations the approach is based on the discretization of the propagation wave equation for a dissipative and non homogeneous medium and from the perfectly match layer formalism of berenger two solutions are proposed that both give a specific scattering matrix for the transmission line matrix method one is equivalent to an artificial purely dissipative medium and the other to a non homogeneous and dissipative artificial medium the proposed solutions are compared to an existing empirical formulation of absorbing layer it is shown that the non homogenous and dissipative solution is less interesting than the purely dissipative one because its efficiency can strongly depend on the receiver location the purely dissipative solution can outperform the empirical matched connexion law formulation for a large range of incidence angle if an optimized value of the damping factor is used for the frequency 100 hz significant efficiencies better than 28 db for normal to grazing incidence and between 30 db and 50 db for normal incidence to oblique incidence can be reached with an absorbing layer thickness of only one wavelength

a new family of mixed finite elements for the linear elastodynamic problem we construct and analyze a new family of quadrangular in two dimensions or cubic in three dimensions mixed finite elements for the approximation of elastic wave equations our elements lead to explicit schemes via mass lumping after time discretization including in the case of anisotropic media error estimates are given for these new elements

reliability based syndrome decoding of linear block codes in this correspondence various aspects of reliability based syndrome decoding of binary codes are investigated first it is shown that the least reliable basis lrb and the most reliable basis mrb are dual of each other by exploiting this duality an algorithm performing maximum likelihood ml soft decision syndrome decoding based on the lrb is presented contrarily to previous lrb based ml syndrome decoding algorithms this algorithm is more conveniently implementable for codes whose codimension is not small new sufficient conditions for optimality are derived these conditions exploit both the ordering associated with the lrb and the structure of the code considered with respect to mrr based sufficient conditions they present the advantage of requiring no soft information and thus can be preprocessed and stored based on these conditions low complexity soft decision syndrome decoding algorithms for particular classes of codes are proposed finally a simple algorithm is analyzed after the construction of the lrb this algorithm computes the syndrome of smallest hamming weight among o k sup i candidates where k is the dimension of the code for an order i of reprocessing at practical bit error rates for codes of length n spl les 128 this algorithm always outperforms any algebraic decoding algorithm capable of correcting up to t 1 errors with an order of reprocessing of at most 2 where t is the error correcting capability of the code considered

continuous galerkin methods for solving the time dependent maxwell equations in 3d geometries a few years ago costabel and dauge proposed a variational setting which allows one to solve numerically the time harmonic maxwell equations in 3d geometries with the help of a continuous approximation of the electromagnetic field in this paper we investigate how their framework can be adapted to compute the solution to the time dependent maxwell equations in addition we propose some extensions such as the introduction of a mixed variational setting and its discretization to handle the constraint on the divergence of the field 2007 elsevier inc all rights reserved

finite difference modeling of the electroseismic logging in a fluid saturated porous formation in a fluid saturated porous medium an electromagnetic em wavefield induces an acoustic wavefield due to the electrokinetic effect a potential geophysical application of this effect is electroseismic es logging in which the converted acoustic wavefield is received in a fluid filled borehole to evaluate the parameters of the porous formation around the borehole in this paper a finite difference scheme is proposed to model the es logging responses to a vertical low frequency electric dipole along the borehole axis the em field excited by the electric dipole is calculated separately by finite difference first and is considered as a distributed exciting source term in a set of extended biot s equations for the converted acoustic wavefield in the formation this set of equations is solved by a modified finite difference time domain fdtd algorithm that allows for the calculation of dynamic permeability so that it is not restricted to low frequency poroelastic wave problems the perfectly matched layer pml technique without splitting the fields is applied to truncate the computational region the simulated es logging waveforms approximately agree with those obtained by the analytical method the fdtd algorithm applies also to acoustic logging simulation in porous formations

adaptive finite element method for the sound wave problems in two kinds of media abstract in this paper we consider the adaptive finite element method for sound wave propagation problems in two kinds of media which are the linear anisotropic acoustic materials the cloak metamaterials and penetrable media and the nonlinear acoustic materials a posteriori error estimator based on the new flux recovery technique and a residual type posteriori error estimator are proposed based on our a posteriori error estimators the adaptive finite element algorithm is given for numerical simulations of the helmholtz equations in different media extensive numerical results demonstrate the effectiveness of the adaptive algorithm

fast direct solution of the helmholtz equation with a perfectly matched layer or an absorbing boundary condition we consider the efficient numerical solution of the helmholtz equation in a rectangular domain with a perfectly matched layer pml or an absorbing boundary condition abc standard bilinear trilinear finite element discretization on an orthogonal mesh leads to a separable system of linear equations for which we describe a cyclic reduction type fast direct solver we present numerical studies to estimate the reflection of waves caused by an absorbing boundary and a pml and we optimize certain parameters of the layer to minimize the reflection copyright 2003 john wiley sons ltd

3 d thin wire fdtd approach for resistively loaded cylindrical antennas fed by coaxial lines for the efficient finite difference time domain fdtd analysis of electrically thin and resistively loaded cylindrical antennas the 2 d cylindrical thin wire approach with circular symmetry is extended to the 3 d cartesian fdtd with non cubic cells for asymmetric cases the axial geometry of the antenna is represented as a set of piecewise linear lumped resistors and the near fields around the antenna and the coaxial feed aperture are approximated to the quasi static fields with the cylindrical behavior from the cylindrical to cartesian coordinate transformation of the quasi static fields and the contour path integration along fdtd unit cells in the vicinity of the antenna and its feed the 3 d cartesian fdtd equations are derived these equations may correspond to a full coarse grid fdtd approach with the equivalent corrections for some numerical examples the proposed approach provides comparable accuracy to the reference data with fine grid resolution effects of the cell size and the resistive loading profile are investigated numerically

recursive evaluation of space time lattice green s functions up to a multiplicative constant the lattice green s function lgf as defined in condensed matter physics and lattice statistical mechanics is equivalent to the z domain counterpart of the finite difference time domain green s function gf on a lattice expansion of a well known integral representation for the lgf on a dimensional hyper cubic lattice in powers of z 1 and application of the chu vandermonde identity results in 1 nested finite sum representations for discrete space time gfs due to severe numerical cancellations these nested finite sums are of little practical use for 2 the finite sum may be evaluated in closed form in terms of a generalized hypergeometric function for special lattice points that representation simplifies considerably while on the other hand the finite difference stencil may be used to derive single lattice point second order recurrence schemes for generating 2d discrete space time gf time sequences on the fly for arbitrary symbolic lattice points zeilberger s algorithm produces a third order recurrence operator with polynomial coefficients of the sixth degree the corresponding recurrence scheme constitutes the most efficient numerical method for the majority of lattice points in spite of the fact that for explicit numeric lattice points the associated third order recurrence operator is not the minimum recurrence operator as regards the asymptotic bounds for the possible solutions to the recurrence scheme perron s theorem precludes factorial or exponential growth along horizontal lattices directions rapid initial growth does occur but poses no problems in augmented dynamic range fixed precision arithmetic by analysing long distance wave propagation along a horizontal lattice direction we have concluded that the chirp up oscillations of the discrete space time gf are the root cause of grid dispersion anisotropy with each factor of ten increase in the lattice distance one would have to roughly double the pulse width of the source signature to keep pulse distortion at bay the gf time sequences can also be used for an efficient computation of discrete space frequency lgfs especially if one employs aitken s 2 process for the acceleration of the convergence of the consecutive partial sums

signal processing techniques to reduce the sinusoidal steady state error in the fdtd method techniques to improve the accuracy of the finite difference time domain fdtd solutions employing sinusoidal excitations are developed the fdtd computational domain is considered as a sampled system and analyzed with respect to the aliasing error using the nyquist sampling theorem after a careful examination of how the high frequency components in the excitation cause sinusoidal steady state errors in the fdtd solutions the use of smoothing windows and digital low pass filters is suggested to reduce the error the reduction in the error is demonstrated for various cases

an adaptive edge element method with perfectly matched absorbing layers for wave scattering by biperiodic structures an edge element adaptive strategy with error control is developed for wave scattering by biperiodic structures the unbounded computational domain is truncated to a bounded one by a perfectly matched layer pml technique the pml parameters such as the thickness of the layer and the medium properties are determined through sharp a posteriori error estimates numerical experiments are presented to illustrate the competitive behavior of the proposed adaptive method

perfectly matched layers for the heat and advection diffusion equations we design a perfectly matched layer for the advection diffusion equation we show that the reflection coefficient is exponentially small with respect to the damping parameter and the width of the pml and this independently of the advection and of the viscosity numerical tests assess the efficiency of the approach

discretized boundary equation method for two dimensional scattering problems a unified approach named discretized boundary equation dbe method is introduced for two dimensional 2 d scattering problems it is based on the discretization of field expressions for one or two components of the scattered field the dbes can be used either on the object surface to obtain the solution directly or on the truncation boundary of a finite difference fd or finite element fe mesh as termination conditions this paper describes the general theory of the dbe method and key points or limitations for its implementation a new on surface formulation for the solution of scattering by perfectly conducting cylinders is presented as an application of the two component version of the dbe method and validated through numerical examples mesh termination conditions for the fd or fe method are derived based on the one component formulation of the dbe method and their equivalence and difference to the measured equation of invariance are discussed in particular the dbe obtained with the minimum norm least squares solution is investigated thoroughly and its validity and features are demonstrated through numerical results generated together with the fd method for scattering by cylinders with various material properties

some experiences from fdtd analysis of infinite and finite multi octave phased arrays some experiences from finite differences time domain fdtd analysis of infinite and finite multi octave phased arrays are presented first a more unified derivation of equations suitable for unit cell analysis of phased arrays or other types of periodic structures using fdtd is presented second results from fdtd calculations of small to very large multi octave finite arrays are summarized in order to answer the question of how large an array model must be in order to capture the characteristics of both the interior and the edge elements of a large multi octave phased array it is found that a considerably larger number of elements is required in the broad band case than in the normal narrow band case and it is also found that fdtd is well suited for such calculations third simple methods to save computer memory using locally fine grids in an otherwise coarse fdtd grid to model finite phased arrays are explored the two local grid methods tested were found in our application to suffer from numerical instabilities

the computation of resonances in open systems using a perfectly matched layer in this paper we consider the problem of computing resonances in open systems we first characterize resonances in terms of improper eigen functions of the helmholtz operator on an unbounded domain the perfectly matched layer pml technique has been successfully applied to the computation of scattering problems we shall see that the application of pml converts the resonance problem to a standard eigenvalue problem still on an infinite domain this new eigenvalue problem involves an operator which resembles the original helmholtz equation transformed by a complex shift in the coordinate system our goal will be to approximate the shifted operator first by replacing the infinite domain by a finite computational domain with a convenient boundary condition and second by applying finite elements on the computational domain we shall prove that the first of these steps leads to eigenvalue convergence to the desired resonance values which is free from spurious computational eigenvalues provided that the size of computational domain is sufficiently large the analysis of the second step is classical finally we illustrate the behavior of the method applied to numerical experiments in one and two spatial dimensions

evaluation of a spherical pml for vector fem applications the implementation and evaluation of a spherical perfectly matched layer pml within a cartesian finite element method context using standard curl conforming elements is presented in this paper results are compared to the long standing 1st order absorbing boundary condition abc and a new rigorous implementation of a 2nd order abc for curl conforming elements the 4 and 8 layer spherical pmls are shown to offer very attractive levels of absorption with reflections on the order of 60 to 70db demonstrated numerical tests show that the guidelines for cartesian pml absorbers in terms of maximum conductivity also carry over to the spherical pml the 2nd order abc is also shown to offer very good performance finally coding issues for both the spherical pml and the analytical abcs are briefly addressed

convergence analysis of the perfectly matched layer problems for time harmonic maxwell s equations this paper is concerned with convergence analysis of the perfectly matched layer pml problem in spherical coordinates for the three dimensional electromagnetic scattering under some simple assumptions on the pml medium parameter it is shown that the truncated pml problem attains a unique solution the main result of the paper is to establish an explicit error estimate between the solution of the scattering problem and that of the truncated pml problem the error estimate implies in particular that the pml solution converges exponentially to the scattering solution by increasing either the pml medium parameter or the pml layer thickness the convergence result is expected to be useful for determining the pml medium parameter in the computational electromagnetic scattering problems

replica time integrators this paper is concerned with the classical problem of wave propagation in discrete models of nonuniform spatial resolution we develop a new class of replica time integrators rtis that permit the two way transmission of thermal phonons across mesh interfaces this two way transmissibility is accomplished by representing the state of the coarse regions by means of replica ensembles consisting of collections of identical copies of the coarse regions in dimension d rtis afford an o n d speed up factor in sequential mode and o n d 1 in parallel over regions that are coarsened n fold in this work we restrict ourselves to the solution of the 3d continuous wave equation for both linear and non linear materials by a combination of phase error analysis and numerical testing we show that rtis are convergent and result in exact two way transmissibility at the courant friedrichs lewy limit for any angle of incidence in this limit rtis allow step waves and high frequency harmonics to cross mesh interfaces in both directions without internal reflections or appreciable loss or addition of energy the possible connections of rtis with discrete to continuum approaches and in particular with the transition between molecular dynamics and continuum thermodynamics are also pointed to by way of future outlook

compact high order schemes with gradient direction derivatives for absorbing boundary conditions we consider several compact high order absorbing boundary conditions abcs for the helmholtz equation in three dimensions a technique called the gradient method gm for abcs is also introduced and combined with the high order abcs gm is based on the principle of using directional derivatives in the direction of the wavefront propagation the new abcs are used together with the recently introduced compact sixth order finite difference scheme for variable wave numbers experiments on problems with known analytic solutions produced very accurate results demonstrating the efficacy of the high order schemes particularly when combined with gm the new abcs are then applied to the seg eage salt model showing the advantages of the new schemes

infinite phased array analysis using fdtd periodic boundary conditions pulse scanning in oblique directions unit cell analysis of infinite phased arrays in the finite difference time domain fdtd is performed by implementation of periodic boundary conditions the technique allows for pulse excitation and oblique scan directions in both the cardinal and intercardinal planes to our knowledge this is the first paper presenting fdtd computations for intercardinal pulse scanning in oblique directions the ordinary yee lattice is used which makes the algorithm easy to incorporate in an already existing fdtd code nonperiodic boundaries are truncated by berenger s see j comput phys vol 127 p 363 79 1996 perfectly matched layer pml active impedance of an infinite dipole array is calculated with the new method and validation is performed via the element by element approach i e by a conventional fdtd simulation of a corresponding large finite array excellent agreement is found and the technique has been numerically stable in all cases analyzed

a p adaptive method for electromagnetic wave propagation summary the discontinuous galerkin dg finite element method is used for the numerical solution of the three dimensional maxwell equations control of errors in the numerical level for the divergence free constraint of the magnetic field can be obtained through the use of divergence free vector bases in this work the so called perfectly hyperbolic ph formulation of the maxwell equations is employed to retain both divergence free magnetic field and in the presence of charges to satisfy the gauss constraint for the electric field at the numerical level for both approaches it is found that higher order approximations have favorable effect on the preservation of the divergence constraints and that the ph formulations retains these errors to a lower level it is shown that high order accuracy in space and time is achieved in unstructured meshes using implicit time marching for nonuniform meshes local resolution refinement is employed using p type adaptivity to ensure accurate electromagnetic wave propagation thus the potential of the method to reach the required higher resolution in anisotropic meshes and obtain accurate electromagnetic wave propagation with reduced computational effort is demonstrated this article is protected by copyright all rights reserved

a finite integration method for conformal structured grid electromagnetic simulation we describe a numerical scheme for solving maxwell s equations in the frequency domain on a conformal structured non orthogonal multi block mesh by considering maxwell s equations in a volume parameterized by dimensionless curvilinear coordinates we obtain a set of tensor equations that are a continuum analogue of common circuit equations and that separate the metrical and metric free parts of maxwell s equations and the material constitutive relations we discretize these equations using a new formulation that treats the electric field and magnetic induction using simple basis function representations to obtain a discrete form of faraday s law of induction but that uses finite integral representations for the displacement current and magnetic field to obtain a discrete form of ampere s law as in the finite integration technique t weiland a discretization method for the solution of maxwell s equations for six component fields electron commun ae u 31 1977 116 t weiland time domain electromagnetic field computation with finite difference methods int j numer model electron netw dev field 9 1996 295 319 we thereby derive new projection operators for the discrete tensor material equations and obtain a compact numerical scheme for the discrete differential operators this scheme is shown to exhibit significantly reduced numerical dispersion when compared to the standard linear finite element method we take advantage of the mesh structure on a block by block basis to implement these numerical operators efficiently and achieve computational speed with modest memory requirements when compared to explicit sparse matrix storage using the jacobi davidson g l g sleijpen h a van der vorst a jacobi davidson iteration method for linear eigenvalue problems siam j matrix anal appl 17 2 1996 401 425 s j cooke b levush eigenmode solution of 2 d and 3 d electromagnetic cavities containing absorbing materials using the jacobi davidson algorithm j comput phys 157 1 2000 350 370 and quasi minimal residual r w freund n m nachtigal qmr a quasi minimal residual method for non hermitian linear systems numer math 60 1991 315 339 iterative matrix solution algorithms we solve the resulting discrete matrix eigenvalue equations and demonstrate the convergence characteristics of the algorithm we validate the model for three dimensional electromagnetic problems both cavity eigenvalue solutions and a waveguide scattering matrix calculation

application of the perfectly matched absorbing layer model to the linear elastodynamic problem in anisotropic heterogeneous media we present and analyze a perfectly matched absorbing layer model for the velocity stress formulation of elastodynamics the principal idea of this method consists of introducing an absorbing layer in which we decompose each component of the unknown into two auxiliary components a component orthogonal to the boundary and a component parallel to it a system of equations governing these new unknowns then is constructed a damping term finally is introduced for the component orthogonal to the boundary this layer model has the property of generating no reflection at the interface between the free medium and the artificial absorbing medium in practice both the boundary condition introduced at the outer boundary of the layer and the dispersion resulting from the numerical scheme produce a small reflection which can be controlled even with very thin layers as we will show with several experiments this model gives very satisfactory results namely the reflection coefficient even in the case of heterogeneous anisotropic media is about 1 for a layer thickness of five space discretization steps

application of the nearly perfectly matched layer in acoustic wave modeling in this work we successfully applied an alternative formulation of the perfectly matched layer pml the so called nearly pml npml to acoustic wave propagation modeling the npml formulation shows great advantages over the standard complex stretched coordinate pml the npml formulation deviates from the standard pml through an inexact variable change but this fact only affects the wave behavior in the npml layer which is outside the region of interest the equivalence of the wave absorbing performance between these two pml formulations the standard complex stretched coordinate pml formulation and the npml formulation in 3d cartesian coordinates for acoustic wave propagation modeling is proved mathematically in this work in time domain methods the advantages of the npml over the standard pml were explained by both the analytical analysis and the numerical simulations in terms of implementation simplicity and computational efficiency the computation time saving is up to 17 for the 2d example used in this work for 3d problems this computational saving is more significant after theoretically analyzing the numerical reflections from the npml and the standard pml we concluded that these two pml formulations have exactly the same performance even after spatial discretization this conclusion is validated by numerical experiment finally we tested the npml in the marmousi velocity model and found its wave absorbing rate is high enough even for this realistic structure

well posed absorbing layer for hyperbolic problems the perfectly matched layer pml is an efficient tool to simulate propagation phenomena in free space on unbounded domain in this paper we consider a new type of absorbing layer for maxwell s equations and the linearized euler equations which is also valid for several classes of first order hyperbolic systems the definition of this layer appears as a slight modification of the pml technique we show that the associated cauchy problem is well posed in suitable spaces this theory is finally illustrated by some numerical results it must be underlined that the discretization of this layer leads to a new discretization of the classical pml formulation

three dimensional perfectly matched layer for the absorption of electromagnetic waves the perfectly matched layer is a technique of free space simulation developed for solving unbounded electromagnetic problems with the finite difference time domain method referred to as pml this technique has been described in a previous paper for two dimensional problems the present paper is devoted to the three dimensional case the theory of the perfectly matched layer is generalized to three dimensions and some numerical experiments are shown to illustrate the efficiency of this new method of free space simulation

an efficient surface impedance boundary condition for thin wires of finite conductivity to include dispersive loss into a sub cell thin wire model a new implementation of a surface impedance boundary condition sibc is proposed the surface impedance function is approximated in the frequency domain by a series of first order rational functions allowing straightforward transform into time domain the contribution of the wire radius is included in the surface impedance function extending the model to very thin or poorly conducting metal wires further the sibc includes the direct current dc resistance the approximation for the sibc is chosen such that the dependence on the wire radius and conductivity can be removed prior to the computation of the approximation coefficients consequently the wire radius and conductivity can be varied without re computing the coefficients the proposed model is compared with an existing sibc wire model based on the high frequency approximation and prony s method nec 2 generated reference data and analytical results the results indicate enhanced accuracy at a reduced computational cost as compared with an existing model

new absorbing layers conditions for short water waves we develop a new pml formulation for the linearized shallow water equations including the coriolis force the construction process is based on the uncoupling of the velocity components with the depth of water then the damping effect is only applied to the propagative modes just as was formerly done by nataf 1 to the linearized euler equations to enforce the long time stability we assess numerically the performance of the new absorbing condition and we illustrate in particular that it is stable for long time simulations

a finite element alternative to infinite elements abstract in this paper a simple idea based on midpoint integration rule is utilized to solve a particular class of mechanics problems namely static problems defined on unbounded domains where the solution is required to be accurate only in an interior and not in the far field by developing a finite element mesh that approximates the stiffness of an unbounded domain directly without approximating the far field displacement profile first the current formulation provides a superior alternative to infinite elements ies that have long been used to incorporate unbounded domains into the finite element method fem in contrast to most ies the present formulation a requires no new shape functions or special integration rules b is proved to be both accurate and efficient and c is versatile enough to handle a large variety of domains including those with anisotropic stratified media and convex polygonal corners in addition to this the proposed model leads to the derivation of a simple error expression that provides an explicit correlation between the mesh parameters and the accuracy achieved this error expression can be used to calculate the accuracy of a given mesh a priori this in turn allows one to generate the most efficient mesh capable of achieving a desired accuracy by solving a mesh optimization problem we formulate such an optimization problem solve it and use the results to develop a practical mesh generation methodology this methodology does not require any additional computation on the part of the user and can hence be used in practical situations to quickly generate an efficient and near optimal finite element mesh that models an unbounded domain to the required accuracy numerical examples involving practical problems are presented at the end to illustrate the effectiveness of this method

a perfectly matched layer for the helmholtz equation in a semi infinite strip the perfectly matched layer pml has become a widespread technique for preventing reflections from far field boundaries for wave propagation problems in both the time dependent and frequency domains we develop a discretization to solve the helmholtz equation in an infinite two dimensional strip we solve the interior equation using high order finite differences schemes the combined helmholtz pml problem is then analyzed for the parameters that give the best performance we show that the use of local high order methods in the physical domain coupled with a specific second order approximation in the pml yields global high order accuracy in the physical domain we discuss the impact of the parameters on the effectiveness of the pml numerical results are presented to support the analysis

energy dissipation splitting finite difference time domain method for maxwell equations with perfectly matched layers abstract in this paper we develop a novel kind of energy dissipation splitting finite difference time domain scheme for solving two dimensional maxwell equations with perfectly matched layers the discrete energy dissipation law convergence dispersion relation and stability are investigated for the scheme theoretical analysis shows that the scheme is unconditionally stable and of second order accuracy both in time and space numerical experiments confirm the theoretical results

boundary conditions for simulations of oscillating bubbles using the non linear acoustic approximation we have developed a new boundary condition for finite volume simulations of oscillating bubbles our method uses an approximation to the motion outside the domain based on the solution at the domain boundary we then use this approximation to apply boundary conditions by defining incoming characteristic waves at the domain boundary our boundary condition is applicable in regions where the motion is close to spherically symmetric we have tested our method on a range of one and two dimensional test cases results show good agreement with previous studies the method allows simulations of oscillating bubbles for long run times 5 10 5 time steps with a cfl number of 0 8 on highly truncated domains in which the boundary condition may be applied within 0 1 of the maximum bubble radius conservation errors due to the boundary conditions are found to be of the order of 0 1 after 105 time steps the method significantly reduces the computational cost of fixed grid finite volume simulations of oscillating bubbles two dimensional results demonstrate that highly asymmetric bubble features such as surface instabilities and the formation of jets may be captured on a small domain using this boundary condition

an improved new implementation of complex frequency shifted pml for the fdtd method a new implementation of the perfectly matched layer absorbing boundary for finite difference time domain grids is presented the approach which is based on the complex co ordinate stretching perfectly matched layer pml formulation uses the complex frequency shifted stretching function and is based on the simple concept of the recursive evaluation of an integral avoiding the calculation of time derivatives this recursive integration pml is simple to implement efficient and exhibits a modest gain in performance over the convolutional pml without requiring any extra computational resources or an increase in the algorithmic complexity of the pml implementation

the optimal force gradient symplectic finite difference time domain scheme for electromagnetic wave propagation in this communication we design an optimal force gradient symplectic finite difference time domain sfdtd scheme for numerically solving maxwell s equations based on the additional constraint of the minimized norm of fourth order truncation errors the numerical dissipation can be minimized and the optimal time coefficients for the third order force gradient symplectic method can be obtained due to the second order accurate adopted in space domain in general the proposed optimal sfdtd method is still second order accurate the numerical stability and numerical dispersion analysis indicate that the optimal force gradient sfdtd method has higher accuracy and stability compared with the nonoptimal force gradient sfdtd method moreover in order to verify the validity of the presented method the scattering parameters of a line fed rectangular microstrip antenna are calculated

fdtd modeling of electromagnetic wave scattering from a wedge with perfectly reflecting boundaries comparisons against analytical models and calibration a classical canonical problem of electromagnetic wave scattering from a nonpenetrable wedge is modeled with the finite difference time domain fdtd method and results are calibrated against the analytical reference solution a novel numerical multistep diffraction coefficient calculation model is introduced comparisons against analytical exact solutions as well as high frequency asymptotic hfa techniques such as the uniform theory of diffraction utd and parabolic equation pe method are also given

improved pml for the fdtd solution of wave structure interaction problems in a previous paper an optimum perfectly matched layer has been designed for the finite difference time domain fdtd solution of wave structure interaction problems the present paper shows the results of subsequent investigations that were done with the intention of reducing the thickness of this optimum pml four improvements to the pml are presented the resulting reductions of the thickness are discussed

numerical solution of the nonlinear helmholtz equation using nonorthogonal expansions in j comput phys 171 2001 632 677 we developed a fourth order numerical method for solving the nonlinear helmholtz equation which governs the propagation of time harmonic laser beams in media with a kerr type nonlinearity a key element of the algorithm was a new nonlocal two way artificial boundary condition abc set in the direction of beam propagation this two way abc provided for reflectionless propagation of the outgoing waves while also fully transmitting the given incoming beam at the boundaries of the computational domain altogether the algorithm of j comput phys 171 2001 632 677 has allowed for a direct simulation of nonlinear self focusing without neglecting nonparaxial effects and backscattering to the best of our knowledge this capacity has never been achieved previously in nonlinear optics in the current paper we propose an improved version of the algorithm the principal innovation is that instead of using the dirichlet boundary conditions in the direction orthogonal to that of the laser beam propagation we now introduce sommerfeld type local radiation boundary conditions which are constructed directly in the discrete framework numerically implementation of the sommerfeld conditions requires evaluation of eigenvalues and eigenvectors for a non hermitian matrix subsequently the separation of variables which is a key building block of the aforementioned nonlocal abc is implemented through an expansion with respect to the nonorthogonal basis of the eigenvectors numerical simulations show that the new algorithm offers a considerable improvement in its numerical performance as well as in the range of physical phenomena that it is capable of simulating

the focusing energy critical hartree equation abstract we consider the focusing energy critical nonlinear hartree equation i u t u x 4 u 2 u we proved that if a maximal lifespan solution u i r d c satisfies sup t i u t 2 w 2 where w is the static solution of the equation then the maximal lifespan i r moreover the solution scatters in both time directions for spherically symmetric initial data similar result has been obtained in c miao g xu l zhao global wellposedness scattering and blowup for the energy critical focusing hartree equation in the radial case colloq math in press the argument is an adaptation of the recent work of r killip and m visan r killip m visan the focusing energy critical nonlinear schrodinger equation in dimensions five and higher preprint on energy critical nonlinear schrodinger equations

dirichlet to neumann map for domains with corners and approximate boundary conditions we present in this paper the dirichlet to neumann operator for the wave equation on a straight wedge in r 2 using fourier integral operators as a consequence we recover the classical approximate boundary conditions of orders 1 and 2

development of a godunov method for maxwell s equations with adaptive mesh refinement in this paper we present a second order 3d method for maxwell s equations based on a godunov scheme with adaptive mesh refinement amr in order to achieve it we apply a limiter which better preserves extrema and boundary conditions based on a characteristic fields decomposition despite being more complex simplifications in the boundary conditions make the resulting method competitive in computer time consumption and accuracy compared to fdtd amr allows us to simulate systems with a sharp step in material properties with negligible rebounds and also large domains with accuracy in small wavelengths a godunov method is used to solve a conservative law s form of maxwell s equations suitable interpolation schemes and limiters allow solving maxwell s equations with amr a new numerical method for boundary conditions allows to simulate unbounded domains using amr allows solving big domain simulations in reasonable computational time

analysis of the convected helmholtz equation with a uniform mean flow in a waveguide with complete radiation boundary conditions abstract in this paper we propose complete radiation boundary conditions crbcs for solutions of the convected helmholtz equation with a uniform mean flow in a waveguide we first study crbcs for the helmholtz equation in a waveguide noting that the convected helmholtz equation is associated with the helmholtz equation via the prandtl glauert transformation crbcs for the convected helmholtz equation is derived from crbcs for the helmholtz equation we analyse well posedness and convergence of approximate solutions satisfying crbcs for the convected helmholtz equation in addition simple numerical experiments will be presented to confirm the theoretical results

application of the symplectic finite difference time domain scheme to electromagnetic simulation an explicit fourth order finite difference time domain fdtd scheme using the symplectic integrator is applied to electromagnetic simulation a feasible numerical implementation of the symplectic fdtd sfdtd scheme is specified in particular new strategies for the air dielectric interface treatment and the near to far field nff transformation are presented by using the sfdtd scheme both the radiation and the scattering of three dimensional objects are computed furthermore the energy conserving characteristic hold for the sfdtd scheme is verified under long term simulation numerical results suggest that the sfdtd scheme is more efficient than the traditional fdtd method and other high order methods and can save computational resources

a comparison of fdtd pml with tdie presented in this paper is a comparison of two popular numerical techniques viz the finite difference time domain method and the time domain integral equation method for electromagnetic scattering problems the comparison is made via standard canonical shapes a cube and a sphere to address the factors affecting accuracy efficiency and the required computer resources

a mapped finite and infinite partition of unity method for convected acoustic radiation in axisymmetric domains a mapped infinite partition of unity method is developed to solve frequency domain acoustic applications for convected radiation in axisymmetric domains the paper presents the formulation and the discretization technique the partition of unity method is coupled with infinite elements based on the astley leis conjugated formulation the performances of the method are analysed on two applications convected propagation in an uniform duct and dipole radiation the aim of such a method compared to the classical finite element method is to solve shortwave applications with a respectable level of accuracy

fast 3d frequency domain full waveform inversion with a parallel block low rank multifrontal direct solver application to obc data from the north sea wide azimuth long offset obc obn surveys provide a suitable framework to perform computationally efficient frequency domain full waveform inversion fwi with a few discrete frequencies frequency domain seismic modeling is performed efficiently with moderate computational resources for a large number of sources with a sparse multifrontal direct solver gauss elimination techniques for sparse matrices approximate solutions of the time harmonic wave equation are computed using a block low rank blr approximation leading to a significant reduction in the operation count and in the volume of communication during the lu factorization as well as offering a great potential for reduction in the memory demand moreover the sparsity of the seismic source vectors is exploited to speed up the forward elimination step during the computation of the monochromatic wavefields the relevance and the computational efficiency of the frequency domain fwi performed in the visco acoustic vti approximation is shown with a real 3d obc case study from the north sea the fwi subsurface models show a dramatic resolution improvement relative to the initial model built by reflection traveltime tomography the amplitude errors introduced in the modeled wavefields by the blr approximation for different low rank thresholds have a negligible footprint in the fwi results with respect to a standard multifrontal sparse direct factorization and without compromise on the accuracy of the imaging the blr approximation can bring a reduction of the lu factor size by a factor up to three this reduction is not yet exploited to reduce the effective memory usage ongoing work the flop reduction can be larger than a factor of 10 and can bring a factor of time reduction of around three moreover this reduction factor tends to increase with frequency namely with the matrix size frequency domain visco acoustic vti fwi can be viewed as an efficient tool to build an initial model for elastic fwi of 4 c obc data

microwave biomedical data inversion using the finite difference contrast source inversion method we present a contrast source inversion csi technique which is based on a finite difference fd solver for use in microwave biomedical imaging the algorithm is capable of inverting complex permittivity biomedical data sets without the explicit use of a forward solver at each iteration the fd solver is based in the frequency domain utilizes perfectly matched layer pml boundary conditions and the stiffness matrix is solved via an lu decomposition and gaussian elimination an important feature of the fd csi algorithm is that the stiffness matrix associated with the fd solver depends only upon the background medium and frequency and thus the lu decomposition is only performed once before the iterative inversion process unlike the usual integral equation ie based inversion techniques the fd csi algorithm is readily capable of utilizing an arbitrary backarbitrary backgroundground medium for the inversion process

analysis of a cartesian pml approximation to acoustic scattering problems in r2 abstract in this paper we consider a cartesian pml approximation to solutions of acoustic scattering problems on an unbounded domain in r 2 the perfectly matched layer pml technique in a curvilinear coordinate system has been researched for acoustic scattering applications both in theory and computation our goal will be to extend the results of spherical cylindrical pml to pml in cartesian coordinates that is the well posedness of cartesian pml approximation on both the unbounded and truncated domains the exponential convergence of approximate solutions as a function of domain size is also shown we note that once the stability and convergence of the continuous truncated problem has been achieved the analysis of the resulting finite element approximations is then classical finally the results of numerical computations illustrating the theory and efficiency of the cartesian pml approach will be given

finite element computation of absorbing boundary conditions for time harmonic wave problems this paper proposes a new method in the frequency domain to define absorbing boundary conditions for general two dimensional problems the main feature of the method is that it can obtain boundary conditions from the discretized equations without much knowledge of the analytical behavior of the solutions and is thus very general it is based on the computation of waves in periodic structures and needs the dynamic stiffness matrix of only one period in the medium which can be obtained by standard finite element software boundary conditions at various orders of accuracy can be obtained in a simple way this is then applied to study some examples for which analytical or numerical results are available good agreements between the present results and analytical solutions allow to check the efficiency and the accuracy of the proposed method