Fourth-Order Accurate Compact Scheme for First-Order Maxwell’s Equations

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2024年6月15日

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I. Versano,
E. Turkel,
S. Tsynkov

摘要

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 develop compatible boundary conditions for these elliptic equations while maintaining a compact stencil. The proposed scheme is compared computationally with a non-compact scheme and with a convolutional dispersion relation preserving (DRP) scheme.