Work

Polynomial subspace operator preconditioning in 2-dimensional boundary element methods

Year: 2026

Type: article

Abstract: A less-known advantage of boundary element methods when compared to volume discretization techniques is that single-layer and hyper-singular operators have opposite-order mapping properties, which allows their mutual preconditioning. State-of-the-art methods rely on discretizations over a barycentric refinement, which is especially in 3 spatial dimensions (3d) computationally expensive. In this paper we propose and analyze a novel construction in 2d that exploits partition of unity of continuous piecewise quadratic basis functions to discretize the hyper-singular operator on the original grid. By elementary calculus we prove that the resulting hyper-singular operator forms an optimal preconditioner to the single-layer operator discretized by piecewise constants. The efficiency of our approach is documented by numerical experiments performed on a GPU.

Source: Computers & Mathematics with Applications

DOI: 10.1016/j.camwa.2026.08.014

Authors: Dalibor Lukáš, Zbyšek Machaczek

Language: English

Topic: Electromagnetic Scattering and Analysis

Subfield: Atomic and Molecular Physics, and Optics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,170

Funders: European Commission, Ministerstvo Životního Prostředí

Award: G1078609858