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math.NA2025
Numerical analysis of the high-frequency Helmholtz equation using semiclassical analysis
Jeffrey Galkowski, Euan A. Spence
We consider the numerical solution of high-frequency scattering problems modeled by the Helmholtz equation with a bounded obstacle. Although the analysis of this problem dates back…
math.NA2025
Non-uniform finite-element meshes defined by ray dynamics for Helmholtz problems
Martin Averseng, Jeffrey Galkowski, Euan A. Spence
The -version of the finite-element method (-FEM) applied to the high-frequency Helmholtz equation has been a classic topic in numerical analysis since the 1990s. It is now ri…
math.NA2025★ 1 cited
Numerical evaluation of the Kirchhoff-Helmholtz integral outside a sphere
Michael J. Carley
A method is presented for the fast evaluation of the transient acoustic field generated outside a spherical surface using surface data on the sphere. The method employs Lebedev qua…