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Fourth order accurate compact scheme for first-order maxwell's equations (2306.17263v2)
Published 29 Jun 2023 in math.NA and cs.NA
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.