Fourth order accurate compact scheme for first-order maxwell's equations

2023/06/29 by Versano, Idan, Turkel, Eli, Tsynkov, Semyon
#) 78M20 (Secondary) #65M06 (Primary #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2306.17263

Abstract

We construct a compact fourth-order scheme, in space and time, for the time-dependent Maxwell's equations given as a first-order system on a staggered (Yee) grid. At each time step, we update the fields by solving positive definite second-order elliptic equations. We face the challenge of finding compatible boundary conditions for these elliptic equations while maintaining a compact stencil. The proposed scheme is compared computationally with a non-compact scheme and data-driven approach.

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