A preprocessing Galerkin discretization of the volume operator is used to construct a computable approximation to the boundary integral operator for strongly elliptic problems with variable coefficients.
Gr \"a le and S
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abstract
This paper considers the Helmholtz problem in the exterior of a ball with Dirichlet boundary conditions and radiation conditions imposed at infinity. The differential Helmholtz operator depends on the complex wavenumber with non-negative real part and is formulated for general spatial dimensions. We prove wavenumber explicit continuity estimates of the corresponding Dirichlet-to-Neumann (DtN) operator which do not deteriorate as the complex wavenumber tends to zero. The exterior Helmholtz problem can be equivalently reformulated on a bounded domain with DtN boundary conditions on the artificial boundary of a ball. We derive wavenumber independent trace and Friedrichs-type inequalities for the solution space in wavenumber-indexed norms.
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2026 2verdicts
UNVERDICTED 2representative citing papers
Establishes limiting absorption principle and well-posedness for the Helmholtz transmission problem in concentric multilayer spheres with sign-changing coefficients via T-coercivity and complex DtN, with uniqueness quantified by the optimal trace constant.
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BEM for variable coefficient second-order problems
A preprocessing Galerkin discretization of the volume operator is used to construct a computable approximation to the boundary integral operator for strongly elliptic problems with variable coefficients.
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Limiting Absorption Principle for the Helmholtz Equation with Sign-Changing Coefficients in Multilayer Spheres
Establishes limiting absorption principle and well-posedness for the Helmholtz transmission problem in concentric multilayer spheres with sign-changing coefficients via T-coercivity and complex DtN, with uniqueness quantified by the optimal trace constant.