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988
A 3D Perfectly Matched Medium from Modified Maxwell's Equations with Stretched Coordinates
 Microwave Opt. Tech. Lett
, 1994
"... A modified set of Maxwell's equations is presented that includes complex coordinate stretching along the three cartesian coordinates. The added degrees of freedom in the modified Maxwell's equations allow the specification of absorbing boundaries with zero reflection at all angles of incid ..."
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Cited by 253 (18 self)
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A modified set of Maxwell's equations is presented that includes complex coordinate stretching along the three cartesian coordinates. The added degrees of freedom in the modified Maxwell's equations allow the specification of absorbing boundaries with zero reflection at all angles of incidence and all frequencies. The modified equations are also related to the perfectly matched layer that was presented recently for 2D wave propagation. Absorbing material boundary conditions are of particular interest for finite difference time domain (FDTD) computations on a singleinstruction multipledata (SIMD) massively parallel supercomputer. A 3D FDTD algorithm has been developed on a Connection Machine CM5 based on the modified Maxwell's equations and simulation results are presented to validate the approach. 1. Introduction The finite difference time domain method [1, 2] is widely regarded as one of the most popular computational electromagnetics algorithms. Although FDTD is conceptually v...
On Nonreflecting Boundary Conditions
 J. COMPUT. PHYS
, 1995
"... Improvements are made in nonreflecting boundary conditions at artificial boundaries for use with the Helmholtz equation. First, it is shown how to remove the difficulties that arise when the exact DtN (DirichlettoNeumann) condition is truncated for use in computation, by modifying the truncated ..."
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Cited by 220 (3 self)
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Improvements are made in nonreflecting boundary conditions at artificial boundaries for use with the Helmholtz equation. First, it is shown how to remove the difficulties that arise when the exact DtN (DirichlettoNeumann) condition is truncated for use in computation, by modifying the truncated condition. Second, the exact DtN boundary condition is derived for elliptic and spheroidal coordinates. Third, approximate local boundary conditions are derived for these coordinates. Fourth, the truncated DtN condition in elliptic and spheroidal coordinates is modified to remove difficulties. Fifth, a sequence of new and more accurate local boundary conditions is derived for polar coordinates in two dimensions. Numerical results are presented to demonstrate the usefulness of these improvements.
Numerical methods for image registration
, 2004
"... In this paper we introduce a new framework for image registration. Our formulation is based on consistent discretization of the optimization problem coupled with a multigrid solution of the linear system which evolve in a GaussNewton iteration. We show that our discretization is helliptic independ ..."
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Cited by 207 (28 self)
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In this paper we introduce a new framework for image registration. Our formulation is based on consistent discretization of the optimization problem coupled with a multigrid solution of the linear system which evolve in a GaussNewton iteration. We show that our discretization is helliptic independent of parameter choice and therefore a simple multigrid implementation can be used. To overcome potential large nonlinearities and to further speed up computation, we use a multilevel continuation technique. We demonstrate the efficiency of our method on a realistic highly nonlinear registration problem. 1 Introduction and problem setup Image registration is one of today’s challenging image processing problems. Given a socalled reference R and a socalled template image T, the basic idea is to find a “reasonable ” transformation such that a transformed version of the template image becomes “similar ” to the reference image. Image registration
An overview of the trilinos project
 ACM Transactions on Mathematical Software
"... The Trilinos Project is an effort to facilitate the design, development, integration and ongoing support of mathematical software libraries within an objectoriented framework for the solution of largescale, complex multiphysics engineering and scientific problems. Trilinos addresses two fundament ..."
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Cited by 143 (17 self)
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The Trilinos Project is an effort to facilitate the design, development, integration and ongoing support of mathematical software libraries within an objectoriented framework for the solution of largescale, complex multiphysics engineering and scientific problems. Trilinos addresses two fundamental issues of developing software for these problems: (i) Providing a streamlined process and set of tools for development of new algorithmic implementations and (ii) promoting interoperability of independently developed software. Trilinos uses a twolevel software structure designed around collections of packages. A Trilinos package is an integral unit usually developed by a small team of experts in a particular algorithms area such as algebraic preconditioners, nonlinear solvers, etc. Packages exist underneath the Trilinos top level, which provides a common lookandfeel, including configuration, documentation, licensing, and bugtracking. Here we present the overall Trilinos design, describing our use of abstract interfaces and default concrete implementations. We discuss the services that Trilinos provides to a prospective package and how these services are used by various packages. We also illustrate how packages can be combined to rapidly develop new algorithms. Finally, we discuss how Trilinos facilitates highquality software engineering practices that are increasingly required from simulation software. Sandia is a multiprogram laboratory operated by Sandia Corporation, a LockheedMartin Company, for the United States Department of Energy under Contract DEAC0494AL85000. Permission to make digital/hard copy of all or part of this material without fee for personal or classroom use provided that the copies are not made or distributed for profit or commercial advantage, the ACM copyright/server notice, the title of the publication, and its date appear, and
Numerical Solution Of Problems On Unbounded Domains. A Review
 A review, Appl. Numer. Math
, 1998
"... While numerically solving a problem initially formulated on an unbounded domain, one typically truncates this domain, which necessitates setting the artificial boundary conditions (ABC's) at the newly formed external boundary. The issue of setting the ABC's appears most significant in many ..."
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Cited by 129 (18 self)
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While numerically solving a problem initially formulated on an unbounded domain, one typically truncates this domain, which necessitates setting the artificial boundary conditions (ABC's) at the newly formed external boundary. The issue of setting the ABC's appears most significant in many areas of scientific computing, for example, in problems originating from acoustics, electrodynamics, solid mechanics, and fluid dynamics. In particular, in computational fluid dynamics (where external problems represent a wide class of important formulations) the proper treatment of external boundaries may have a profound impact on the overall quality and performance of numerical algorithms and interpretation of the results. Most of the currently used techniques for setting the ABC's can basically be classified into two groups. The methods from the first group (global ABC's) usually provide high accuracy and robustness of the numerical procedure but often appear to be fairly cumbersome and (computa...
Mapping thin resistors and hydrocarbons with marine EMmethods: insights from 1Dmodeling,Geophysics
, 2006
"... All intext references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately. ..."
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Cited by 59 (7 self)
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All intext references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately.
Perfectly Matched Layers for Elastodynamics: A New Absorbing Boundary Condition
 J. Comp. Acoust
, 1996
"... The use of perfectly matched layers (PML) has recently been introduced by Berenger as a material absorbing boundary condition (ABC) for electromagnetic waves. In this paper, we will first prove that a fictitious elastodynamic material halfspace exists that will absorb an incident wave for all angle ..."
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Cited by 53 (5 self)
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The use of perfectly matched layers (PML) has recently been introduced by Berenger as a material absorbing boundary condition (ABC) for electromagnetic waves. In this paper, we will first prove that a fictitious elastodynamic material halfspace exists that will absorb an incident wave for all angles and all frequencies. Moreover, the wave is attenuative in the second halfspace. As a consequence, layers of such material could be designed at the edge of a computer simulation region to absorb outgoing waves. Since this is a material ABC, only one set of computer codes is needed to simulate an open region. Hence, it is easy to parallelize such codes on multiprocessor computers. For instance, it is easy to program massively parallel computers on the SIMD (single instruction multiple data) mode for such codes. We will show two and three dimensional computer simulations of the PML for the linearized equations of elastodyanmics. Comparison with Liao's ABC will be given. 1. Introduction Sim...
Mimetic Discretizations for Maxwell's Equations
 J. Comput. Phys
, 1999
"... This paper is a part of our attempt to develop a discrete analog of vector and tensor calculus that can be used to accurately approximate continuum models for a wide range of physical processes on logically rectangular, nonorthogonal, nonsmooth grids. These mimetic FDMs mimic fundamental properties ..."
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Cited by 44 (5 self)
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This paper is a part of our attempt to develop a discrete analog of vector and tensor calculus that can be used to accurately approximate continuum models for a wide range of physical processes on logically rectangular, nonorthogonal, nonsmooth grids. These mimetic FDMs mimic fundamental properties of the original continuum differential operators and allow the discrete approximations of partial differential equations (PDEs) to preserve critical properties including conservation laws and symmetries in the solution of the underlying physical problem. In particular, we have constructed discrete analogs of firstorder differential 881 00219991/99 operators, such as div, grad, and curl, that satisfy the discrete analogs of theorems of vector and tensor calculus [1013]. This approach has also been used to construct highquality mimetic FDMs for the divergence and gradient in approximating the diffusion equation [15, 38, 39]
Principles of mimetic discretizations of differential operators
 Compatible Spatial Discretizations, volume 142 of The IMA Volumes in Mathematics and its Applications
, 2006
"... Abstract. Compatible discretizations transform partial differential equations to discrete algebraic problems that mimic fundamental properties of the continuum equations. We provide a common framework for mimetic discretizations using algebraic topology to guide our analysis. The framework and all a ..."
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Cited by 41 (3 self)
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Abstract. Compatible discretizations transform partial differential equations to discrete algebraic problems that mimic fundamental properties of the continuum equations. We provide a common framework for mimetic discretizations using algebraic topology to guide our analysis. The framework and all attendant discrete structures are put together by using two basic mappings between differential forms and cochains. The key concept of the framework is a natural inner product on cochains which induces a combinatorial Hodge theory on the cochain complex. The framework supports mutually consistent operations of differentiation and integration, has a combinatorial Stokes theorem, and preserves the invariants of the De Rham cohomology groups. This allows, among other things, for an elementary calculation of the kernel of the discrete Laplacian. Our framework provides an abstraction that includes examples of compatible finite element, finite volume, and finite difference methods. We describe how these methods result from a choice of the reconstruction operator and explain when they are equivalent. We demonstrate how to apply the framework for compatible discretization for two scalar versions of the Hodge Laplacian. Key words. Mimetic discretizations, compatible spatial discretizations, finite element
Toward the development of a threedimensional unconditionally stable finitedifference timedomain method
 IEEE Trans. Microw. Theory Tech
, 2000
"... Abstract—In this paper, an unconditionally stable threedimensional (3D) finitedifference timemethod (FDTD) is presented where the time step used is no longer restricted by stability but by accuracy. The principle of the alternating direction implicit (ADI) technique that has been used in formul ..."
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Cited by 40 (0 self)
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Abstract—In this paper, an unconditionally stable threedimensional (3D) finitedifference timemethod (FDTD) is presented where the time step used is no longer restricted by stability but by accuracy. The principle of the alternating direction implicit (ADI) technique that has been used in formulating an unconditionally stable twodimensional FDTD is applied. Unlike the conventional ADI algorithms, however, the alternation is performed in respect to mixed coordinates rather than to each respective coordinate direction. Consequently, only two alternations in solution marching are required in the 3D formulations. Theoretical proof of the unconditional stability is shown and numerical results are presented to demonstrate the effectiveness and efficiency of the method. It is found that the number of iterations with the proposed FDTD can be at least four times less than that with the conventional FDTD at the same level of accuracy. Index Terms—Alternating direct implicit (ADI) technique, FDTD method, instability, unconditional stable. I.