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 »
- Authors:
-
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Commissariat a l'Energie Atomique et aux Energies Alternatives (CEA-Saclay), Gif-sur-Yvette (France)
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
- Publication Date:
- Research Org.:
- Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP)
- OSTI Identifier:
- 1379112
- Alternate Identifier(s):
- OSTI ID: 1246505
- Grant/Contract Number:
- AC02-05CH11231
- Resource Type:
- 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. https://doi.org/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. https://doi.org/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}
}
Web of Science
Works referenced in this record:
Plasma mirrors for ultrahigh-intensity optics
journal, April 2007
- Thaury, C.; Quéré, F.; Geindre, J. -P.
- Nature Physics, Vol. 3, Issue 6
Optical properties of relativistic plasma mirrors
journal, March 2014
- Vincenti, H.; Monchocé, S.; Kahaly, S.
- Nature Communications, Vol. 5, Issue 1
Numerical Cherenkov instabilities in electromagnetic particle codes
journal, August 1974
- Godfrey, Brendan B.
- Journal of Computational Physics, Vol. 15, Issue 4
On the elimination of numerical Cerenkov radiation in PIC simulations
journal, December 2004
- Greenwood, Andrew D.; Cartwright, Keith L.; Luginsland, John W.
- Journal of Computational Physics, Vol. 201, Issue 2
Numerical stability analysis of the pseudo-spectral analytical time-domain PIC algorithm
journal, February 2014
- Godfrey, Brendan B.; Vay, Jean-Luc; Haber, Irving
- Journal of Computational Physics, Vol. 258
A domain decomposition method for pseudo-spectral electromagnetic simulations of plasmas
journal, June 2013
- Vay, Jean-Luc; Haber, Irving; Godfrey, Brendan B.
- Journal of Computational Physics, Vol. 243
Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media
journal, May 1966
- Kane Yee,
- IEEE Transactions on Antennas and Propagation, Vol. 14, Issue 3
The PSTD algorithm: A time-domain method requiring only two cells per wavelength
journal, June 1997
- Liu, Q. H.
- Microwave and Optical Technology Letters, Vol. 15, Issue 3
Asymmetric Perfectly Matched Layer for the Absorption of Waves
journal, December 2002
- Vay, Jean-Luc
- Journal of Computational Physics, Vol. 183, Issue 2
Efficiency of the Perfectly Matched Layer with high-order finite difference and pseudo-spectral Maxwell solvers
journal, September 2015
- Lee, P.; Vay, J. -L.
- Computer Physics Communications, Vol. 194
High-Order Finite Differences and the Pseudospectral Method on Staggered Grids
journal, August 1990
- Fornberg, Bengt
- SIAM Journal on Numerical Analysis, Vol. 27, Issue 4
Closed-form expressions for the finite difference approximations of first and higher derivatives based on Taylor series
journal, July 1999
- Khan, Ishtiaq Rasool; Ohba, Ryoji
- Journal of Computational and Applied Mathematics, Vol. 107, Issue 2
Mathematical proof of closed form expressions for finite difference approximations based on Taylor series
journal, January 2003
- Khan, Ishtiaq Rasool; Ohba, Ryoji; Hozumi, Noriyuki
- Journal of Computational and Applied Mathematics, Vol. 150, Issue 2
A perfectly matched layer for the absorption of electromagnetic waves
journal, October 1994
- Berenger, Jean-Pierre
- Journal of Computational Physics, Vol. 114, Issue 2
A perfectly matched layer for the absorption of electromagnetic waves
journal, October 1994
- Berenger, Jean-Pierre
- Journal of Computational Physics, Vol. 114, Issue 2
Asymmetric Perfectly Matched Layer for the Absorption of Waves
journal, December 2002
- Vay, Jean-Luc
- Journal of Computational Physics, Vol. 183, Issue 2
High-Order Finite Differences and the Pseudospectral Method on Staggered Grids
journal, August 1990
- Fornberg, Bengt
- SIAM Journal on Numerical Analysis, Vol. 27, Issue 4
Works referencing / citing this record:
Identification of Coupling Mechanisms between Ultraintense Laser Light and Dense Plasmas
journal, March 2019
- Chopineau, L.; Leblanc, A.; Blaclard, G.
- Physical Review X, Vol. 9, Issue 1
Accurate modeling of plasma acceleration with arbitrary order pseudo-spectral particle-in-cell methods
journal, March 2017
- Jalas, S.; Dornmair, I.; Lehe, R.
- Physics of Plasmas, Vol. 24, Issue 3
Few-cycle laser wakefield acceleration on solid targets with controlled plasma scale length
journal, March 2019
- Zaïm, N.; Böhle, F.; Bocoum, M.
- Physics of Plasmas, Vol. 26, Issue 3
Spatial Properties of High-Order Harmonic Beams from Plasma Mirrors: A Ptychographic Study
journal, October 2017
- Leblanc, A.; Monchocé, S.; Vincenti, H.
- Physical Review Letters, Vol. 119, Issue 15
Achieving Extreme Light Intensities using Optically Curved Relativistic Plasma Mirrors
journal, September 2019
- Vincenti, Henri
- Physical Review Letters, Vol. 123, Issue 10
Identification of coupling mechanisms between ultraintense laser light and dense plasmas
text, January 2018
- Chopineau, L.; Leblanc, A.; Blaclard, G.
- arXiv
Porting WarpX to GPU-accelerated platforms
journal, December 2021
- Myers, A.; Almgren, A.; Amorim, L. D.
- Parallel Computing, Vol. 108
Interaction of Ultraintense Radially-Polarized Laser Pulses with Plasma Mirrors
journal, December 2020
- Zaïm, N.; Guénot, D.; Chopineau, L.
- Physical Review X, Vol. 10, Issue 4
Identification of Coupling Mechanisms between Ultraintense Laser Light and Dense Plasmas
journal, March 2019
- Chopineau, L.; Leblanc, A.; Blaclard, G.
- Physical Review X, Vol. 9, Issue 1