energy conserving explicit local time stepping for second order wave equations locally refined meshes impose severe stability constraints on explicit time stepping methods for the numerical simulation of time dependent wave phenomena to overcome that stability restriction local time stepping methods are developed which allow arbitrarily small time steps precisely where small elements in the mesh are located when combined with a symmetric finite element discretization in space with an essentially diagonal mass matrix the resulting discrete numerical scheme is explicit is inherently parallel and exactly conserves a discrete energy starting from the standard second order leap frog scheme time stepping methods of arbitrary order of accuracy are derived numerical experiments illustrate the efficiency and usefulness of these methods and validate the theory

randomized and distributed self configuration of wireless networks two layer markov random fields and near optimality this work studies the near optimality versus the complexity of distributed configuration management for wireless networks we first develop a global probabilistic graphical model for a network configuration which characterizes jointly the statistical spatial dependence of a physical and a logical configuration the global model is a gibbs distribution that results from the internal network properties on node positions wireless channel and interference and the external management constraints on physical connectivity and signal quality a local model is a two layer markov random field i e a random bond model that approximates the global model with the local spatial dependence of neighbors the complexity of the local model is defined through the communication range among nodes which corresponds to the number of neighbors in the two layer markov random field the local model is near optimal when the approximation error to the global model is within a given bound we analyze the tradeoff between approximation error and complexity we then derive sufficient conditions on the near optimality of the local model for a fast decaying wireless channel with power attenuation factor 4 a node only needs to communicate with o 1 neighbors for a local model to be near optimal for a slowly decaying channel with a power attenuation factor 2 4 a node may have to communicate with more than o n 4 4 neighbors to result in a bounded approximation error if the communication range is kept to be o 1 a bounded approximation error can also be achieved by reducing the density of active links to o n 4 4 for 4 the two layer markov random fields enable a class of randomized distributed algorithms such as the stochastic relaxation that allows a node to self configure based on information from neighbors we validate the model the analysis and the randomized distributed algorithms through simulation

metric driven mesh optimization using a local simulated annealing algorithm we report on results obtained with a metric driven mesh optimization procedure for simplicial meshes based on the simulated annealing sa method the use of sa improves the chances of removing pathological clusters of bad elements that have the tendency to lock into frozen configurations in difficult regions of the model such as corners and complex face intersections prejudicing the overall quality of the final grid a local version of the algorithm is developed that significantly lowers the computational cost numerical examples illustrate the effectiveness of the proposed methodology which is compared to a classical greedy gauss seidel optimization substantial improvement in the quality of the worst elements of the grid is observed for the local simulated annealing optimization furthermore the method appears to be robust to the choice of the algorithmic parameters copyright 2006 john wiley sons ltd

comparison of finite element techniques for solidification problems the accuracies of the computed temperatures of a liquid in a corner region under freezing conditions are compared for various fixed grid finite element techniques using the analytical solution for this problem as a reference in the finite element formulation of the problem different time stepping schemes are compared the implicit euler backward algorithm combined with an iterative scheme and two three time level methods the lees algorithm and a dupont algorithm which are both applied as non iterative schemes furthermore different methods for handling the evolution of latent heat are examined an approximation method suggested by lemmon and one suggested by del giudice both using the enthalpy formulation as well as a fictitious heat flow method presented by rolph and bathe results of calculations performed with the consistent heat capacity matrix are compared with those performed with a lumped heat capacity matrix

a conservative space time mesh refinement method for the 1 d wave equation part i construction we propose a new method for space time refinement for the 1 d wave equation this method is based on the conservation of a discrete energy through two different discretization grids which guarantees the stability of the scheme our approach results in a non interpolatory scheme whose stability condition is not affected by the transition between the two grids

fdtd local grid with material traverse often a finite difference time domain fdtd calculation requires a relatively higher mesh resolution in only small subvolumes of the total mesh space by locally applying finer grids local grids to these volumes the necessary resolution can be obtained computation time and memory requirements may be far less than for an fdtd space with the smaller mesh resolution throughout in many situations it is important that these local grids function when materials traverse the main grid local grid mg lg boundary surfaces since the volumes that require local grids may not be isolated in a homogeneous medium a local grid method which allows dielectric and or conducting materials to traverse the boundaries is developed three different fdtd problems that utilize the local grid method are used as validation tests results are compared with uniform mesh fdtd solutions

a high order non conforming discontinuous galerkin method for time domain electromagnetics in this paper we discuss the formulation stability and validation of a high order non dissipative discontinuous galerkin dg method for solving maxwell s equations on non conforming simplex meshes the proposed method combines a centered approximation for the numerical fluxes at inter element boundaries with either a second order or a fourth order leap frog time integration scheme moreover the interpolation degree is defined at the element level and the mesh is refined locally in a non conforming way resulting in arbitrary level hanging nodes the method is proved to be stable and conserves a discrete counterpart of the electromagnetic energy for metallic cavities numerical experiments with high order elements show the potential of the method

conservative and provably stable fdtd subgridding the finite difference time domain fdtd method is a common robust simulation technique for transient electromagnetic interactions with complicated structures however the standard fdtd method is limited to cartesian grids everywhere in the computational grid many practitioners have extended fdtd to handle multiresolution problems by using finer grids near structures with small geometrical features abutted to coarse grids in regions of empty space unfortunately subgridding implementations based on interpolation or extrapolation of neighboring field values can exhibit late time instabilities herein a subgridding method based on multigrid finite element principles will be developed and its stability proven numerical results will assess its performance in 2 d and 3 d

an explicit fourth order orthogonal curvilinear staggered grid fdtd method for maxwell s equations the explicit fourth order staggered finite difference time domain scheme previously proposed for a cartesian grid is extended to maxwell s equations in an orthogonal curvilinear coordinate system and applied to electromagnetic wave problems a simple technique is also presented for generating orthogonal curvilinear grids that conform to the material boundaries and interfaces of the problem numerical experiments are presented to illustrate the efficiency and accuracy of the method

nodal high order methods on unstructured grids we present a convergent high order accurate scheme for the solution of linear conservation laws in geometrically complex domains as our main example we include a detailed development and analysis of a scheme for the time domain solution of maxwell s equations in a three dimensional domain the fully unstructured spatial discretization is made possible by the use of a high order nodal basis employing multivariate lagrange polynomials defined on the triangles and tetrahedra while the equations themselves are satisfied in a discontinuous galerkin form with the boundary conditions being enforced weakly through a penalty term accuracy stability and convergence of the semidiscrete approximation to maxwell s equations is established rigorously and bounds on the growth of the global divergence error are provided concerns related to efficient implementations are discussed in detail this sets the stage for the presentation of examples verifying the theoretical results and illustrating the versatility flexibility and robustness when solving two and three dimensional benchmark problems in computational electromagnetics pure scattering as well as penetration is discussed and high parallel performance of the scheme is demonstrated

locally implicit discontinuous galerkin method for time domain electromagnetics in the recent years there has been an increasing interest in discontinuous galerkin time domain dgtd methods for the solution of the unsteady maxwell equations modeling electromagnetic wave propagation one of the main features of dgtd methods is their ability to deal with unstructured meshes which are particularly well suited to the discretization of the geometrical details and heterogeneous media that characterize realistic propagation problems such dgtd methods most often rely on explicit time integration schemes and lead to block diagonal mass matrices however explicit dgtd methods are also constrained by a stability condition that can be very restrictive on highly refined meshes and when the local approximation relies on high order polynomial interpolation an implicit time integration scheme is a natural way to obtain a time domain method which is unconditionally stable but at the expense of the inversion of a global linear system at each time step a more viable approach consists of applying an implicit time integration scheme locally in the refined regions of the mesh while preserving an explicit time scheme in the complementary part resulting in an hybrid explicit implicit or locally implicit time integration strategy in this paper we report on our recent efforts towards the development of such a hybrid explicit implicit dgtd method for solving the time domain maxwell equations on unstructured simplicial meshes numerical experiments for 3d propagation problems in homogeneous and heterogeneous media illustrate the possibilities of the method for simulations involving locally refined meshes

reduction methods for nonlinear steady state thermal analysis hybrid analysis techniques based on the combined use of finite elements and the classical bubnov galerkin approximation are presented for predicting nonlinear steady state temperature distributions in structures and solids in these hybrid techniques the modelling versatility of the finite element method is preserved and a substantial reduction in the number of degrees of freedom is achieved by expressing the vector of nodal temperatures as a linear combination of a small number of global temperature modes or basis vectors the bubnov galerkin technique is then used to compute the coefficients of the linear combination i e the amplitudes of the global temperature modes the basis vectors chosen are the path derivatives commonly used in perturbation techniques namely the derivatives of the nodal temperature vector with respect to a preselected control or path parameter s the vectors are generated by using the finite element model of the initial discretization also the performance of alternate sets of basis vectors is investigated in the alternate sets only a few path derivatives are generated and they are augmented by a constant vector representing a uniform temperature rise or drop and by reciprocal vectors with nonzero components equal to the reciprocals of the nonzero components of the path derivatives a problem adaptive computational algorithm is presented for efficient evaluation of global approximation vectors and generation of the reduced system of equations and for monitoring the accuracy of the reduced system of equations the potential of the proposed reduction methods for the solution of large scale nonlinear steady state thermal problems is also discussed the effectiveness of these methods is demonstrated by means of four numerical examples including conduction convection and radiation modes of heat transfer this study shows that the use of the uniform temperature mode and the path derivatives as global approximation vectors significantly increases the accuracy of the solutions obtained by reduction methods thereby enhancing the effectiveness of these methods for the solution of large scale nonlinear thermal problems

extension of the fdtd huygens subgridding algorithm to two dimensions this paper extends to two dimensions the finite difference time domain huygens subgridding algorithm previously published in the one dimensional case the algorithm is described in detail and several numerical experiments are provided to illustrate its possibilities and to demonstrate its effectiveness

parallel multilevel series k way partitioning scheme for irregular graphs in this paper we present a parallel formulation of a multilevel k way graph partitioning algorithm a key feature of this parallel formulation is that it is able to achieve a high degree of concurrency while maintaining the high quality of the partitions produced by the serial multilevel k way partitioning algorithm in particular the time taken by our parallel graph partitioning algorithm is only slightly longer than the time taken for re arrangement of the graph among processors according to the new partition experiments with a variety of finite element graphs show that our parallel formulation produces high quality partitionings in a short amount of time for example a 128 way partitioning of graphs with one million vertices can be computed in a little over two seconds on a 128 processor cray t3d furthermore the quality of the partitions produced is comparable edge cuts within 5 to those produced by the serial multilevel k way algorithm thus our parallel algorithm makes it feasible to perform frequent repartitioning of graphs in dynamic computations without compromising the partitioning quality

comment on a unique formal system for binary decompositions of database relations probability distributions and graphs abstract it is shown that the formal system for binary decompositions of database relations applies successfully to binary decompositions of probability distributions and graphs too as an application the problem of determining the binary decompositions of a given information system no matter if a relation a probability distribution or a graph is discussed and a number of search procedures using the derivation rules of the proposed formal system are presented and compared on a sample relation

a framework for linear information inequalities we present a framework for information inequalities namely inequalities involving only shannon s information measures for discrete random variables a region in ir 2 sup n 1 denoted by spl gamma is identified to be the origin of all information inequalities involving n random variables in the sense that all such inequalities are partial characterizations of spl gamma a product from this framework is a simple calculus for verifying all unconstrained and constrained linear information identities and inequalities which can be proved by conventional techniques these include all information identities and inequalities of such types in the literature as a consequence of this work most identities and inequalities involving a definite number of random variables can now be verified by a software called itip which is available on the world wide web our work suggests the possibility of the existence of information inequalities which cannot be proved by conventional techniques we also point out the relation between spl gamma and some important problems in probability theory and information theory

conservative space time mesh refinement methods for the fdtd solution of maxwell s equations a new variational space time mesh refinement method is proposed for the fdtd solution of maxwell s equations the main advantage of this method is to guarantee the conservation of a discrete energy that implies that the scheme remains l 2 stable under the usual cfl condition the only additional cost induced by the mesh refinement is the inversion at each time step of a sparse symmetric positive definite linear system restricted to the unknowns located on the interface between coarse and fine grid the method is presented in a rather general way and its stability is analyzed an implementation is proposed for the yee scheme in this case various numerical results in 3 d are presented in order to validate the approach and illustrate the practical interest of space time mesh refinement methods

a staggered fourth order accurate explicit finite difference scheme for the time domain maxwell s equations abstract we consider a model explicit fourth order staggered finite difference method for the hyperbolic maxwell s equations appropriate fourth order accurate extrapolation and one sided difference operators are derived in order to complete the scheme near metal boundaries and dielectric interfaces an eigenvalue analysis of the overall scheme provides a necessary but not sufficient stability condition and indicates long time stability numerical results verify both the stability analysis and the scheme s fourth order convergence rate over complex domains that include dielectric interfaces and perfectly conducting surfaces for a fixed error level we find the fourth order scheme is computationally cheaper in comparison to the yee scheme by more than an order of magnitude some open problems encountered in the application of such high order schemes are also discussed

on information theoretic characterizations of markov random fields and subfields let x i i in v form a markov random field mrf represented by an undirected graph g v e and v be a subset of v we determine the smallest graph that can always represent the subfield x i i in v as an mrf based on this result we obtain a necessary and sufficient condition for a subfield of a markov tree to be also a markov tree when g is a path so that x i i in v form a markov chain it is known that the i measure is always nonnegative kawabata and yeung in 1992 we prove that markov chain is essentially the only mrf such that the i measure is always nonnegative by applying our characterization of the smallest graph representation of a subfield of an mrf we develop a recursive approach for constructing information diagrams for mrfs our work is built on the set theoretic characterization of an mrf yeung et al in 2002

computational algorithms for transient analysis the burden of weight and consequences towards formalizing discrete numerically assigned dna algorithmic markers wp family abstract different from the way we have been looking in the past at developments encompassing modal type and a wide class of step by step time stepping approaches for transient and dynamic field problems and significantly different from the way these have been developed and described in standard text books over the years this paper outlines the theoretical ideas and basis towards providing a generalized methodology and formulations leading to integral and a wide class of integration operators for the resulting solution of these transient equation systems it is herein postulated that integral operators and a wide class of integration operators pertain to and emanate from the same family with the burden which is being carried by a virtual field or weighted function field specifically introduced for the time discretization is strictly enacted in a mathematically consistent manner so as to first permit obtaining the adjoint operator of the original semi discretized equation system subsequently the selection or burden carried by the virtual or weighted function fields originally introduced to facilitate the time discretization process determines the formal development and outcome of exact integral operators approximate integral operators and a wide class of integration operators thus the present developments not only serve as a prelude towards the formal developments for exact integral operators but also demonstrate that the resulting approximate integral operators and a wide class of integration operators and known methods are simply subsets of the generalizations of a standardized w p family and emanate from the principles presented herein the burden of weight and the resulting consequences towards subsequently enabling a formal basis for the selection of discrete numerically assigned dna algorimmic markers to particularly identitfy a wide class of algorithms is described for transient field problems and dynamic field problems respectively

the mortar finite element method with lagrange multipliers the present paper deals with a variant of a non conforming domain decomposition technique the mortar finite element method in the opposition to the original method this variant is never conforming because of the relaxation of the matching constraints at the vertices and the edges in 3d of subdomains it is shown that written under primal hybrid formulation the approximation problem issued from a discretization of a second order elliptic equation in 2d is nonetheless well posed and provides a discrete solution that satisfies optimal error estimates with respect to natural norms finally the parallelization advantages consequence of this variant are also addressed

generation of curvilinear coordinates on multiply connected regions with boundary singularities a new algorithm to generate smooth two dimensional boundary conforming coordinates with grid lines control on multiply connected regions including boundary singularities is devised the technique fits into the category of elliptic grid generators since it is based on the numerical solution of poisson equations the physical domain d is transformed into a topologically equivalent connected rectangular domain d by defining a branch cut inside d control of the grid line spacing over the multiply connected regions is established by appropriately distributing nodal points on the branch cut and on other boundary curves simple and computationally convenient expressions for the control functions present in the poisson system are obtained from this initial distribution of points thus a natural link between clustering properties and the control functions is created fixing the nodal points on the branch cut causes the convergence of the numerical method about the singular boundary points an iterative smoothing process relocating the branch cut is described as a result smooth grids are obtained grid quality analysis shows that coordinate line orthogonality in the new meshes is superior than in similar grids obtained from a well known commercial software the algorithm is successfully tested over a variety of multiply connected domains the computational advantage of this novel grids is revealed by using them to numerically model the vibrations of complexly shaped annular membranes

runge kutta based explicit local time stepping methods for wave propagation locally refined meshes severely impede the efficiency of explicit runge kutta rk methods for the simulation of time dependent wave phenomena by taking smaller time steps precisely where the smallest elements are located local time stepping lts methods overcome the bottleneck caused by the stringent stability constraint of but a few small elements in the mesh starting from classical or low storage explicit rk methods explicit lts methods of arbitrarily high accuracy are derived when combined with an essentially diagonal finite element mass matrix the resulting time marching schemes retain the high accuracy stability and efficiency of the original rk methods while circumventing the geometry induced stiffness numerical experiments with continuous and discontinuous galerkin finite element discretizations corroborate the expected rates of convergence and illustrate the usefulness of these lts rk methods

a domain decomposition method for the acoustic wave equation with discontinuous coefficients and grid change a domain decomposition technique is proposed for the computation of the acoustic wave equation in which the bulk modulus and density fields are allowed to be discontinuous at the interfaces inside each subdomain the method presented coincides with the second order finite difference schemes traditionally used in geophysical modeling however the possibility of assigning to each subdomain its own space step makes numerical simulations much less expensive another interest of the method lies in the fact that its hybrid variational formulation naturally leads to exact equations for gridpoints on the interfaces transposing babuska brezzi s formalism on mixed and hybrid finite elements provides a suitable functional framework for this domain decomposition formulation and shows that the inf sup condition remains the basic requirement for convergence to occur

transfinite element methodology for non liner linear transient thermal modelling analysis progress and recent advances recent progress and advances in the development and applicability of a novel transfinite element computational methodology is presented for general non linear linear transient thermal problems the proposed methodology and concepts are new and unique and demonstrate the applicability to general transient non linear linear thermal analysis situations by combining classical galerkin schemes and transform approaches with contemporary finite element methods to preserve the modelling versatility and numerical features thereby a hybrid computational methodology is proposed characteristic features and pertinent details of the approach are described for non linear linear transient thermal problems wherein non linearities due temperature dependence of thermophysical properties and or general non linear bound ary conditions to include radiation effects due to phase change etc are considered in addition the use of high continuity formulations in conjuction with the proposed methodology to furnish accurate temperature distributions and temperature gradients making use of a relatively smaller number of degrees of freedom is also demonstrated numerical test cases are presented for a variety of problems to demonstrate the fundamental features and applicability of the proposed formulations the proposed hybrid transfinite element methodology and concepts offer significant potential for extension to several areas of mathematical physics and engineering and to interdisciplinary research areas

collapsibility and response variables in contingency tables summary various definitions of the collapsibility of a hierarchical log linear model for a multidimensional contingency table are considered and shown to be equivalent necessary and sufficient conditions for collapsibility are found in terms of the generating class it is shown that log linear models are appropriate for tables with response and explanatory variables if and only if they are collapsible onto the explanatory variables some key word8 collapsibility contingency table graphical model interaction graph log linear model response variable s sufficiency shown to be closely related some models have the property that relations between a set of the classifying factors may be studied by examination of the table of marginal totals formed by summing over the remaining factors such models are said to be collapsible onto the given set of factors collapsibility has important consequences for hypothesis testing and model selection and can be useful in data reduction we consider various definitions of collapsibility and show their equivalence furthermore necessary and sufficient conditions for collapsi bility are found in terms of the generating class many tables analysed in practice involve response variables simple examples one of which is given in 3 suffice to show the importance of distinguishing between response and explanatory variables first that inappropriate models may be avoided and second that natural and relevant models that are not log linear may be considered this paper characterizes appropriate and inappropriate log linear models for tables with response variables and some alternative approaches for the analysis of such tables are briefly considered we consider a multidimensional contingency table n based on a set of classifying factors f for a given subset a of f we are interested in the table of marginal totals na that is to say the table of cell counts summed over the remaining factors ac that is the complement of a in f we identify a hierarchical log linear model l that is the set of probabilities p e l with its generating class whose elements generators are given in square brackets thus for example the model ab bcd for a 4 way table corresponds

staircase free finite difference time domain formulation for general materials in complex geometries a stable cartesian grid staircase free finite difference time domain formulation for arbitrary material distributions in general geometries is introduced it is shown that the method exhibits higher accuracy than the classical yee 1966 scheme for complex geometries since the computational representation of physical structures is not of a staircased nature furthermore electromagnetic boundary conditions are correctly enforced the method significantly reduces simulation times as fewer points per wavelength are needed to accurately resolve the wave and the geometry both perfect electric conductors and dielectric structures have been investigated numerical results are presented and discussed

information theoretic characterizations of conditional mutual independence and markov random fields we take the point of view that a markov random field is a collection of so called full conditional mutual independencies using the theory of i measure we have obtained a number of fundamental characterizations related to conditional mutual independence and markov random fields we show that many aspects of conditional mutual independence and markov random fields have very simple set theoretic descriptions new insights into the structure of conditional mutual independence and markov random fields are obtained our results have immediate applications in the implication problem of probabilistic conditional independency and relational database we obtain a hypergraph characterization of a markov random field which makes it legitimate to view a markov random field as a hypergraph based on this result we naturally employ the graham reduction a tool from relational database theory to recognize a markov forest this connection between markov random fields and hypergraph sheds some light on the possible role of hypergraph theory in the study of markov random fields

a new family of mixed finite elements in ir 3 we introduce two families of mixed finite element on conforming inh div and one conforming inh curl these finite elements can be used to approximate the stokes system

the mortar finite element method for 3d maxwell equations first results in the framework of domain decomposition methods we extend the main ideas of the mortar element method to the numerical solution of maxwell s equations in wave form by h curl conforming finite elements the method we propose turns out to be a new nonconforming nonoverlapping domain decomposition method where nonmatching grids are allowed at the interfaces between subdomains a model problem is considered the convergence of the discrete approximation is analyzed and an error estimate is provided the method is proven to be slightly suboptimal with a loss of a factor scriptstyle sqrt rm ln h with respect to the degree of polynomials in order to achieve this convergence result we nevertheless need extra regularity assumptions on the solution of the continuous problem

convergent cartesian grid methods for maxwell s equations in complex geometries a convergent second order cartesian grid finite difference scheme for the solution of maxwell s equations is presented the scheme employs a staggered grid in space and represents the physical location of the material and metallic boundaries correctly hence eliminating problems caused by staircasing and contrary to the popular yee scheme enforces the correct jump conditions on the field components across material interfaces a detailed analysis of the accuracy of the new embedding scheme is presented confirming its second order global accuracy furthermore the scheme is proven to be a bounded error scheme and thus convergent conditions for fully discrete stability is furthermore established this enables the derivation of bounds for fully discrete stability with cfl restrictions being almost identical to those of the much simpler yee scheme the analysis exposes that the effects of staircasing as well as a lack of properly enforced jump conditions on the field components have significant consequences for the global accuracy it is among other things shown that for cases in which a field component is discontinuous along a grid line as happens at general two and three dimensional material interfaces the yee scheme may exhibit local divergence and loss of global convergence to validate the analysis several one and two dimensional test cases are presented showing an improvement of typically 1 to 2 orders of accuracy at little or no additional computational cost over the yee scheme which in most cases exhibits first order accuracy c 2001 academic press

solution of non linear thermal transient problems by a reduction method a new algorithm for solving transient thermal problems in a reduced subspace of the original space of discretization is described the basis of the subspace is formed by using the system response at the first time step or an approximation to it and a set of orthogonal vectors obtained by the algorithm of lanczos derivatives of these vectors are included when treating non linear cases the method allows one to handle the sharp gradients that appear in thermally loaded structures and the response is accurately predicted by using only a small number of degrees of freedom in the reduced system the algorithm is specially well suited for treating large scale problems examples dealing with one two and three dimensional cases of linear and non linear conduction problems are presented

explicit local time stepping methods for maxwell s equations explicit local time stepping methods are derived for time dependent maxwell equations in conducting and non conducting media by using smaller time steps precisely where smaller elements in the mesh are located these methods overcome the bottleneck caused by local mesh refinement in explicit time integrators when combined with a finite element discretisation in space with an essentially diagonal mass matrix the resulting discrete time marching schemes are fully explicit and thus inherently parallel in a non conducting source free medium they also conserve a discrete energy which provides a rigorous criterion for stability starting from the standard leap frog scheme local time stepping methods of arbitrarily high accuracy are derived for non conducting media numerical experiments with a discontinuous galerkin discretisation in space validate the theory and illustrate the usefulness of the proposed time integration schemes

a staggered upwind embedded boundary sueb method to eliminate the fdtd staircasing error in spite of its flexibility and second order accuracy in a homogeneous medium yee s finite difference time domain fdtd method suffers from serious degradation when treating material interfaces greatly reducing its accuracy in the presence of inhomogeneous media and perfect conductors indeed such so called staircasing approximation may lead to local zeroth order and global first order errors in this work an embedded fdtd scheme the staggered upwind embedded boundary sueb method is developed for the solution of oneand two dimensional maxwell s equations this simple embedded technique uses upwind conditions in the fdtd method to correctly represent the location and physical conditions of material and metallic boundaries hence eliminating problems caused by the staircasing approximation accuracy analysis has been made to show that the sueb method maintains a second order accuracy globally since the entire problem has been embedded into the simple staggered grid similar to that employed by the yee s scheme extra effort is only needed when treating the grid points close to the interfaces therefore little additional computational cost is needed over yee s scheme the sueb method has been validated by analytical solutions for plane wave normally incident to a planar boundary and for the tm wave propagation in the presence of a dielectric cylinder and a perfectly electrically conducting cylinder

a spatial high order hexahedral discontinuous galerkin method to solve maxwell s equations in time domain in this paper we present a non dissipative spatial high order discontinuous galerkin method to solve the maxwell equations in the time domain the non intuitive choice of the space of approximation and the basis functions induce an important gain for mass stiffness and jump matrices in terms of memory this spatial approximation combined with a leapfrog scheme in time leads also to a fast explicit and accurate method a study of the dispersive error is carried out and a stability condition for the proposed scheme is established some comparisons with other schemes are presented to validate the new scheme and to point out its advantages finally in order to improve the efficiency of the method in terms of cpu time on general unstructured meshes a strategy of local time stepping is proposed

space time mesh refinement for elastodynamics numerical results we propose here a generalization to the elastodynamic equations of the space time mesh refinement technique intro duced in raffinement de maillage spatio temporel pour les equations de maxwell ph d thesis universitede dau phine paris 2000 for the maxwells equations this method uses a discrete energy conservation to ensure the stability the method is presented in a variational way applicable to other type of hyperbolic systems several numerical experiments are provided to show the efficiency of this approach 2004 elsevier b v all rights reserved

a conservative space time mesh refinement method for the 1 d wave equation part ii analysis we introduced in 2 a new method for space time refinement for the 1 d wave equation this method is based on the conservation of a discrete energy through two different discretization grids which guarantees the stability of the scheme in this second part we analyse the accuracy of this scheme in a detailed way by means of a plane wave analysis and numerical experiments that permit us to point out spurious numerical phenomena and explain how to control them

calculation of the sar induced in head tissues using a high order dgtd method and triangulated geometrical models the great majority of numerical calculations of the specific absorption rate sar induced in human tissues exposed to microwaves are performed using the finite difference time domain fdtd method and voxel based geometrical models the straightforward implementation of the method and its computational efficiency are among the main reasons for fdtd being currently the leading method for numerical assessment of human exposure to electromagnetic waves however the rather difficult departure from the commonly used cartesian grid and cell size limitations regarding the discretization of very detailed structures of human tissues are often recognized as the main weaknesses of the method in this application context in particular interfaces between tissues where sharp gradients of the electromagnetic field may occur are hardly modeled rigorously in these studies we present here an alternative numerical dosimetry methodology which is based on a high order discontinuous galerkin time domain dgtd method and adapted geometrical models constructed from unstructured triangulations of tissue interfaces and discuss its application to the calculation of the sar induced in head tissues