Highorder upwind schemes for the wave equation on overlapping grids: Maxwell's equations in secondorder form
Abstract
Highorder accurate upwind approximations for the wave equation in secondorder form on overlapping grids are developed. Although upwind schemes are well established for firstorder hyperbolic systems, it was only recently shown by Banks and Henshaw how upwinding could be incorporated into the secondorder form of the wave equation. This new upwind approach is extended here to solve the timedomain Maxwell's equations in secondorder form; schemes of arbitrary order of accuracy are formulated for general curvilinear grids. Taylor timestepping is used to develop singlestep spacetime schemes, and the upwind dissipation is incorporated by embedding the exact solution of a local Riemann problem into the discretization. Secondorder and fourthorder accurate schemes are implemented for problems in two and three space dimensions, and overlapping grids are used to treat complex geometry and problems with multiple materials. Stability analysis of the upwindscheme on overlapping grids is performed using normal mode theory. The stability analysis and computations confirm that the upwind scheme remains stable on overlapping grids, including the difficult case of thin boundary grids when the traditional nondissipative scheme becomes unstable. The accuracy properties of the scheme are carefully evaluated on a series of classical scattering problems for both perfect conductors and dielectric materialsmore »
 Authors:

 Rensselaer Polytechnic Inst., Troy, NY (United States). Dept. of Mathematical Sciences
 Publication Date:
 Research Org.:
 Rensselaer Polytechnic Inst., Troy, NY (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
 OSTI Identifier:
 1393833
 Alternate Identifier(s):
 OSTI ID: 1549294
 Grant/Contract Number:
 AC5207NA27344
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Journal of Computational Physics
 Additional Journal Information:
 Journal Volume: 352; Journal ID: ISSN 00219991
 Publisher:
 Elsevier
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; wave equations; electromagnetics; upwind methods; overlapping grids
Citation Formats
Angel, Jordan B., Banks, Jeffrey W., and Henshaw, William D. Highorder upwind schemes for the wave equation on overlapping grids: Maxwell's equations in secondorder form. United States: N. p., 2017.
Web. doi:10.1016/j.jcp.2017.09.037.
Angel, Jordan B., Banks, Jeffrey W., & Henshaw, William D. Highorder upwind schemes for the wave equation on overlapping grids: Maxwell's equations in secondorder form. United States. https://doi.org/10.1016/j.jcp.2017.09.037
Angel, Jordan B., Banks, Jeffrey W., and Henshaw, William D. Thu .
"Highorder upwind schemes for the wave equation on overlapping grids: Maxwell's equations in secondorder form". United States. https://doi.org/10.1016/j.jcp.2017.09.037. https://www.osti.gov/servlets/purl/1393833.
@article{osti_1393833,
title = {Highorder upwind schemes for the wave equation on overlapping grids: Maxwell's equations in secondorder form},
author = {Angel, Jordan B. and Banks, Jeffrey W. and Henshaw, William D.},
abstractNote = {Highorder accurate upwind approximations for the wave equation in secondorder form on overlapping grids are developed. Although upwind schemes are well established for firstorder hyperbolic systems, it was only recently shown by Banks and Henshaw how upwinding could be incorporated into the secondorder form of the wave equation. This new upwind approach is extended here to solve the timedomain Maxwell's equations in secondorder form; schemes of arbitrary order of accuracy are formulated for general curvilinear grids. Taylor timestepping is used to develop singlestep spacetime schemes, and the upwind dissipation is incorporated by embedding the exact solution of a local Riemann problem into the discretization. Secondorder and fourthorder accurate schemes are implemented for problems in two and three space dimensions, and overlapping grids are used to treat complex geometry and problems with multiple materials. Stability analysis of the upwindscheme on overlapping grids is performed using normal mode theory. The stability analysis and computations confirm that the upwind scheme remains stable on overlapping grids, including the difficult case of thin boundary grids when the traditional nondissipative scheme becomes unstable. The accuracy properties of the scheme are carefully evaluated on a series of classical scattering problems for both perfect conductors and dielectric materials in two and three space dimensions. Finally, the upwind scheme is shown to be robust and provide highorder accuracy.},
doi = {10.1016/j.jcp.2017.09.037},
journal = {Journal of Computational Physics},
number = ,
volume = 352,
place = {United States},
year = {2017},
month = {9}
}
Web of Science