New H-Matrix Solver Enhances Computational Efficiency for Scattering Problems

A new paper titled "H-Matrix Accelerated Direct Matrix Solver using Chebyshev-based Nyström Boundary Integral Equation Method" has been published by authors Jin Hu, Emrah Sever, Omid Babazadeh, Ian Jeffrey, Vladimir Okhmatovski, and Constantine Sideris. The paper presents an innovative approach to solving boundary integral equations, particularly for high contrast dielectric materials and large perfect electric conductor objects.

The authors have developed an H-matrix accelerated direct solver that utilizes a high-order Chebyshev-based Boundary Integral Equation (CBIE) method. This method has been formulated, tested, and profiled for performance, demonstrating significant improvements in matrix fill performance for small to moderately sized problems when compared to existing methods, such as the locally corrected Nyström (LCN) method. The CBIE method effectively handles singularities through a global change of variable method, which enhances its efficiency.

However, the study notes that for electrically large scattering problems, the matrix fill and factorization times can still dominate the overall solution time when using a direct solution approach. To address this limitation, the authors employ an H-Matrix framework, which helps to resolve challenges associated with poorly conditioned matrix equations, establishing the CBIE as a competitive high-order method for such problems.

The findings of this research could have significant implications for computational physics, particularly in fields that require efficient solutions to complex scattering problems. The full paper can be accessed at arXiv:2408.17116.