A robust GPU-accelerated kernel compensation solver with novel discretization for photonic crystals in anisotropic media

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.