Detailed analysis of the effects of stencil spatial variations with arbitrary highorder finitedifference Maxwell solver
Abstract
Due to discretization effects and truncation to finite domains, many electromagnetic simulations present nonphysical 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 threedimensional arbitrary order finitedifference 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 highorder Maxwell solver, as well as in the infinite order limit of pseudospectral solvers. Results confirm that the new analytical approach enables exact predictions in eachmore »
 Authors:
 Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Commissariat a l'Energie Atomique et aux Energies Alternatives (CEASaclay), GifsurYvette (France)
 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) (SC25)
 OSTI Identifier:
 1379112
 Alternate Identifier(s):
 OSTI ID: 1246505
 Grant/Contract Number:
 AC0205CH11231
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Computer Physics Communications
 Additional Journal Information:
 Journal Volume: 200; Journal Issue: C; Journal ID: ISSN 00104655
 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 highorder finitedifference 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 highorder finitedifference 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 highorder finitedifference 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 highorder finitedifference Maxwell solver},
author = {Vincenti, H. and Vay, J. L.},
abstractNote = {Due to discretization effects and truncation to finite domains, many electromagnetic simulations present nonphysical 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 threedimensional arbitrary order finitedifference 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 highorder Maxwell solver, as well as in the infinite order limit of pseudospectral 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 highorder 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}
}
Web of Science

Controlling the numerical Cerenkov instability in PIC simulations using a customized finite difference Maxwell solver and a local FFT based current correction
In this study we present a customized finitedifferencetimedomain (FDTD) Maxwell solver for the particleincell (PIC) algorithm. The solver is customized to effectively eliminate the numerical Cerenkov instability (NCI) which arises when a plasma (neutral or nonneutral) relativistically drifts on a grid when using the PIC algorithm. We control the EM dispersion curve in the direction of the plasma drift of a FDTD Maxwell solver by using a customized higher order finite difference operator for the spatial derivative along the direction of the drift (1ˆ direction). We show that this eliminates the main NCI modes with moderate k _{1}, while keepsmore »Cited by 3