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A 3-D Perfectly Matched Medium from Modified Maxwell's Equations with Stretched Coordinates

by Weng Cho Chew, William H. Weedon - 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 ..."
Abstract - Cited by 256 (18 self) - Add to MetaCart
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 2-D wave propagation. Absorbing material boundary conditions are of particular interest for finite difference time domain (FDTD) computations on a single-instruction multiple-data (SIMD) massively parallel supercomputer. A 3-D FDTD algorithm has been developed on a Connection Machine CM-5 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...
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On Nonreflecting Boundary Conditions

by Marcus Grote , Joseph B. Keller - 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 (Dirichlet-to-Neumann) condition is truncated for use in computation, by modifying the truncated ..."
Abstract - Cited by 219 (4 self) - Add to MetaCart
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 (Dirichlet-to-Neumann) 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

by Eldad Haber, Jan Modersitzki, Eldad Haber , 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 Gauss-Newton iteration. We show that our discretization is h-elliptic independ ..."
Abstract - Cited by 209 (29 self) - Add to MetaCart
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 Gauss-Newton iteration. We show that our discretization is h-elliptic 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 so-called reference R and a so-called 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
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An overview of the trilinos project

by Michael A. Heroux, Roscoe A. Bartlett, Vicki E. Howle, Robert J. Hoekstra, Jonathan J. Hu, Tamara G. Kolda, Richard B. Lehoucq, Kevin R. Long, Roger P. Pawlowski, Eric T. Phipps, Andrew G. Salinger, Heidi K. Thornquist, Ray S. Tuminaro, James M. Willenbring, Alan Williams, Kendall S. Stanley - 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 object-oriented framework for the solution of large-scale, complex multi-physics engineering and scientific problems. Trilinos addresses two fundament ..."
Abstract - Cited by 150 (20 self) - Add to MetaCart
The Trilinos Project is an effort to facilitate the design, development, integration and ongoing support of mathematical software libraries within an object-oriented framework for the solution of large-scale, complex multi-physics 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 two-level 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 look-and-feel, including configuration, documentation, licensing, and bug-tracking. 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 Lockheed-Martin Company, for the United States Department of Energy under Contract DE-AC04-94AL85000. 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

by Semyon V. Tsynkov - 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 ..."
Abstract - Cited by 126 (19 self) - Add to MetaCart
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

by Chester J Weiss, See Profile, Steven Constable, Chester J. Weiss , 2006
"... All in-text references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately. ..."
Abstract - Cited by 60 (7 self) - Add to MetaCart
All in-text references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately.

An unsplit convolutional perfectly matched layer technique improved at . . .

by Roland Martin, Dimitri Komatitsch , 2009
"... ..."
Abstract - Cited by 53 (7 self) - Add to MetaCart
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Perfectly Matched Layers for Elastodynamics: A New Absorbing Boundary Condition

by W. C. Chew, Q. H. Liu - 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 half-space exists that will absorb an incident wave for all angle ..."
Abstract - Cited by 50 (4 self) - Add to MetaCart
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 half-space exists that will absorb an incident wave for all angles and all frequencies. Moreover, the wave is attenuative in the second half-space. 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...

Locally divergence-free discontinuous Galerkin methods for the Maxwell Equations

by Bernardo Cockburn , Fengyan Li , Chi-Wang Shu - J. Comput. Phys
"... Abstract In this paper, we develop the locally divergence-free discontinuous Galerkin method for numerically solving the Maxwell equations. The distinctive feature of the method is the use of approximate solutions that are exactly divergence-free inside each element. As a consequence, this method h ..."
Abstract - Cited by 47 (4 self) - Add to MetaCart
Abstract In this paper, we develop the locally divergence-free discontinuous Galerkin method for numerically solving the Maxwell equations. The distinctive feature of the method is the use of approximate solutions that are exactly divergence-free inside each element. As a consequence, this method has a smaller computational cost than that of the discontinuous Galerkin method with standard piecewise polynomial spaces. We show that, in spite of this fact, it produces approximations of the same accuracy. We also show that this method is more efficient than the discontinuous Galerkin method using globally divergence-free piecewise polynomial bases. Finally, a post-processing technique is used to recover (2k þ 1)th order of accuracy when piecewise polynomials of degree k are used.
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Mimetic Discretizations for Maxwell's Equations

by James M. Hyman, Mikhail Shashkov - 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 ..."
Abstract - Cited by 44 (5 self) - Add to MetaCart
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 first-order differential 881 0021-9991/99 operators, such as div, grad, and curl, that satisfy the discrete analogs of theorems of vector and tensor calculus [10--13]. This approach has also been used to construct high-quality mimetic FDMs for the divergence and gradient in approximating the diffusion equation [15, 38, 39]
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