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Title: Detailed analysis of the effects of stencil spatial variations with arbitrary high-order finite-difference Maxwell solver

Abstract

Due to discretization effects and truncation to finite domains, many electromagnetic simulations present non-physical modifications of Maxwell's equations in space that may generate spurious signals affecting the overall accuracy of the result. Such modifications for instance occur when Perfectly Matched Layers (PMLs) are used at simulation domain boundaries to simulate open media. Another example is the use of arbitrary order Maxwell solver with domain decomposition technique that may under some condition involve stencil truncations at subdomain boundaries, resulting in small spurious errors that do eventually build up. In each case, a careful evaluation of the characteristics and magnitude of the errors resulting from these approximations, and their impact at any frequency and angle, requires detailed analytical and numerical studies. To this end, we present a general analytical approach that enables the evaluation of numerical discretization errors of fully three-dimensional arbitrary order finite-difference Maxwell solver, with arbitrary modification of the local stencil in the simulation domain. The analytical model is validated against simulations of domain decomposition technique and PMLs, when these are used with very high-order Maxwell solver, as well as in the infinite order limit of pseudo-spectral solvers. Results confirm that the new analytical approach enables exact predictions in eachmore » case. It also confirms that the domain decomposition technique can be used with very high-order Maxwell solver and a reasonably low number of guard cells with negligible effects on the whole accuracy of the simulation.« less

Authors:
 [1];  [2]
  1. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Commissariat a l'Energie Atomique et aux Energies Alternatives (CEA-Saclay), Gif-sur-Yvette (France)
  2. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
OSTI Identifier:
1379112
Alternate Identifier(s):
OSTI ID: 1246505
Grant/Contract Number:
AC02-05CH11231
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Computer Physics Communications
Additional Journal Information:
Journal Volume: 200; Journal Issue: C; Journal ID: ISSN 0010-4655
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Citation Formats

Vincenti, H., and Vay, J. -L.. Detailed analysis of the effects of stencil spatial variations with arbitrary high-order finite-difference Maxwell solver. United States: N. p., 2015. Web. doi:10.1016/j.cpc.2015.11.009.
Vincenti, H., & Vay, J. -L.. Detailed analysis of the effects of stencil spatial variations with arbitrary high-order finite-difference Maxwell solver. United States. doi:10.1016/j.cpc.2015.11.009.
Vincenti, H., and Vay, J. -L.. Sun . "Detailed analysis of the effects of stencil spatial variations with arbitrary high-order finite-difference Maxwell solver". United States. doi:10.1016/j.cpc.2015.11.009. https://www.osti.gov/servlets/purl/1379112.
@article{osti_1379112,
title = {Detailed analysis of the effects of stencil spatial variations with arbitrary high-order finite-difference Maxwell solver},
author = {Vincenti, H. and Vay, J. -L.},
abstractNote = {Due to discretization effects and truncation to finite domains, many electromagnetic simulations present non-physical modifications of Maxwell's equations in space that may generate spurious signals affecting the overall accuracy of the result. Such modifications for instance occur when Perfectly Matched Layers (PMLs) are used at simulation domain boundaries to simulate open media. Another example is the use of arbitrary order Maxwell solver with domain decomposition technique that may under some condition involve stencil truncations at subdomain boundaries, resulting in small spurious errors that do eventually build up. In each case, a careful evaluation of the characteristics and magnitude of the errors resulting from these approximations, and their impact at any frequency and angle, requires detailed analytical and numerical studies. To this end, we present a general analytical approach that enables the evaluation of numerical discretization errors of fully three-dimensional arbitrary order finite-difference Maxwell solver, with arbitrary modification of the local stencil in the simulation domain. The analytical model is validated against simulations of domain decomposition technique and PMLs, when these are used with very high-order Maxwell solver, as well as in the infinite order limit of pseudo-spectral solvers. Results confirm that the new analytical approach enables exact predictions in each case. It also confirms that the domain decomposition technique can be used with very high-order Maxwell solver and a reasonably low number of guard cells with negligible effects on the whole accuracy of the simulation.},
doi = {10.1016/j.cpc.2015.11.009},
journal = {Computer Physics Communications},
number = C,
volume = 200,
place = {United States},
year = {Sun Nov 22 00:00:00 EST 2015},
month = {Sun Nov 22 00:00:00 EST 2015}
}

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