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arXiv · 2606.22754

Kreiss stability analysis of Hagstrom-Warburton nonreflecting boundary conditions for the first-order time-dependent Maxwell equations

Kaifang Liu·Matthias Schlottbom·J. J. W. van der Vegt·Yan Xu
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Abstract

We analyze the stability of the Hagstrom-Warburton nonreflecting boundary conditions (HW-NRBCs) for the first-order time-dependent Maxwell equations. The HW-NRBCs enjoy very small reflection coefficients and do not use high-order derivatives or nonlocal boundary operators, which makes them well-suited for high-order accurate numerical discretizations. The main result of this paper is an $L^2$ a-priori bound on the solution in terms of initial and boundary data and volume sources in a half-space. To obtain this result, we first derive a mapping that takes outgoing components to ingoing components of the solution of the Maxwell equations with HW-NRBCs, which shows that the Kreiss condition does not hold uniformly. Next, to prove stability, several symmetrizers are constructed, which establishes well-posedness in a generalized sense.

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Kaifang Liu, Matthias Schlottbom, J. J. W. van der Vegt, Yan Xu. 2026-08-08. Kreiss stability analysis of Hagstrom-Warburton nonreflecting boundary conditions for the first-order time-dependent Maxwell equations. https://arxiv.org/abs/2606.22754

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