2013/08/29 by James Bremer, Adrianna Gillman, Bremer, James +3 · 1 citation
Engineering · Physics and Astronomy · #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.1308.6643
openalex publication_date 2013/08/29 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
We describe an accelerated direct solver for the integral equations which\nmodel acoustic scattering from curved surfaces. Surfaces are specified via a\ncollection of smooth parameterizations given on triangles, a setting which\ngeneralizes the typical one of triangulated surfaces, and the integral\nequations are discretized via a high-order Nystrom method. This allows for\nrapid convergence in cases in which high-order surface information is\navailable. The high-order discretization technique is coupled with a direct\nsolver based on the recursive construction of scattering matrices. The result\nis a solver which often attains O(N1.5) complexity in the number of\ndiscretization nodes N and which is resistant to many of the pathologies\nwhich stymie iterative solvers in the numerical simulation of scattering. The\nperformance of the algorithm is illustrated with numerical experiments which\ninvolve the simulation of scattering from a variety of domains, including one\nconsisting of a collection of 1000 ellipsoids with randomly oriented semiaxes\narranged in a grid, and a domain whose boundary has 12 curved edges and 8\ncorner points.\n