Bérenger's PML on Rectangular Domains for Pauli's Equations

Laurence Halpern (1) , Jeffrey Rauch (2)

1 LAGA - Laboratoire Analyse, Géométrie et Applications
2 Department of Mathematics - University of Michigan

This article proves the well posedness of the boundary value problem that arises when Bérenger's PML agorithm is applied to Pauli's equations. As in standard practice, the computational domain is rectangular and the absorptions are positive near the boundary and zero in the interior so are always x-dependent. At the boundary of the rectangle , the natural absorbing boundary conditions are imposed. The estimates allow exponential growth in time, but have no loss of derivatives for the physical quantities. The analysis proceeds by Laplace transform. Existence is proved for a carefully constructed boundary value problems for a complex stretched Helmholtz equation. Uniqueness is reduced by an analyticity argument to a result in [15]. This is the first stability proof for Bérenger's algorithm with x-dependent absorptions on a domain whose boundary is not smooth.

Mots clés: trihedral corner; dissipative boundary conditions; Bérenger; Pauli system; Hyperbolic boundary value problem; PML

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Laurence Halpern, Jeffrey Rauch. Bérenger's PML on Rectangular Domains for Pauli's Equations. 2020. ⟨hal-02872141v1⟩