A Robust GPU-Accelerated Kernel Compensation Solver with Novel Discretization for Photonic Crystals in Anisotropic Media

TL;DR

This paper introduces a GPU-accelerated solver for 3D photonic crystal eigenproblems in anisotropic media, featuring a novel discretization that guarantees matrix positive definiteness and improves robustness.

Contribution

It presents a new discretization method ensuring Hermitian positive definiteness and integrates kernel compensation with GPU acceleration for efficient eigenproblem solving.

Findings

The solver effectively eliminates null space issues.

Numerical experiments confirm robustness and accuracy.

The discretization guarantees matrix positive definiteness.

Abstract

This paper develops a robust solver for the Maxwell eigenproblem in 3D photonic crystals with anisotropic media. The solver employs the kernel compensation technique under the framework of Yee's scheme to eliminate null space and enable matrix-free, GPU-accelerated operations via 3D discrete Fourier transform. Furthermore, we propose a novel discretization for permittivity tensor containing off-diagonal entries and prove that the resulting matrix is Hermitian positive definite, which ensures the correctness of the kernel compensation technique. Numerical experiments on several benchmark examples are demonstrated to validate the robustness and accuracy of our scheme.