2022/01/18 by Daria Sushnikova, Sushnikova, Daria, Leslie Greengard +5 · 4 citations
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Computational Physics (physics.comp-ph) #Electromagnetic Scattering and Analysis #FOS: Mathematics #FOS: Physical sciences #Numerical Analysis (math.NA) #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.2201.07325
openalex publication_date 2022/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a fast direct solver for boundary integral equations on complex surfaces in three dimensions using an extension of the recently introduced recursive strong skeletonization scheme. For problems that are not highly oscillatory, our algorithm computes an LU-like hierarchical factorization of the dense system matrix, permitting application of the inverse in \mathcal O(n) time, where n is the number of unknowns on the surface. The factorization itself also scales linearly with the system size, albeit with a somewhat larger constant. The scheme is built on a level-restricted adaptive octree data structure, and therefore it is compatible with highly nonuniform discretizations. Furthermore, the scheme is coupled with high-order accurate locally-corrected Nyström quadrature methods to integrate the singular and weakly-singular Green's functions used in the integral representations. Our method has immediate applications to a variety of problems in computational physics. We concentrate here on studying its performance in acoustic scattering (governed by the Helmholtz equation) at low to moderate frequencies, and provide rigorous justification for compression of submatrices via proxy surfaces.