GCA-$\mathcal{H}^2$ matrix compression for electrostatic simulations

TL;DR

This paper introduces a novel matrix compression technique for electrostatic boundary element matrices that combines analytic and algebraic methods, optimized for GPU acceleration, enhancing efficiency and robustness in electrostatic simulations.

Contribution

The paper presents GCA-$\\mathcal{H}^2$ matrix compression, integrating Green's representation-based approximation with algebraic cross approximation, tailored for GPU acceleration.

Findings

Effective compression of boundary element matrices

Compatibility with GPU acceleration

Enhanced robustness and efficiency

Abstract

We consider a compression method for boundary element matrices arising in the context of the computation of electrostatic fields. Green cross approximation combines an analytic approximation of the kernel function based on Green's representation formula and quadrature with an algebraic cross approximation scheme in order to obtain both the robustness of analytic methods and the efficiency of algebraic ones. One particularly attractive property of the new method is that it is well-suited for acceleration via general-purpose graphics processors (GPUs).