Year: 2026
Type: preprint
Abstract: Building on the null-infinity-layer construction, we develop an H1-conforming finite-element formulation of hyperboloidal compactification for the exterior Helmholtz equation. A change of coordinates maps infinity to a finite outer boundary, and a rescaling removes the leading oscillatory decay. We derive the transformed equation and a global sesquilinear weak formulation with bounded coefficients. The compactified boundary contributes an explicit boundary mass term, and its trace gives the far-field pattern up to a known normalization. We compare the resulting method with finite-element discretizations using perfectly matched layers (PML) and report benchmark results in two and three dimensions. Numerical experiments include scattering by a unit disk, resonance in a trapping geometry, a manufactured benchmark in three dimensions, and a submarine benchmark.
Source: arXiv (Cornell University)
Authors: Wess, Markus, Zenginoğlu, Anıl
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W7165874953
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