2019/02/22 by Oscar P. Bruno, Bruno, Oscar P., Liwei Xu +3 · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Computational Physics (physics.comp-ph) #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #FOS: Physical sciences #Numerical Analysis (math.NA) #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.1902.08687
openalex publication_date 2019/02/22 · openalex created_date 2022/07/29 · openalex updated_date 2026/08/01
We present a novel approach for the numerical solution of problems of elastic\nscattering by open arcs in two dimensions. Our methodology relies on the\ncomposition of weighted versions of the classical operators associated with\nDirichlet and Neumann boundary conditions in conjunction with a certain\n"open-arc elastic Calder 'on relation" whose validity is demonstrated in this\npaper on the basis of numerical experiments, but whose rigorous mathematical\nproof is left for future work. Using this Calder 'on relation in conjunction\nwith spectrally accurate quadrature rules and the Krylov-subspace linear\nalgebra solver GMRES, the proposed overall open-arc elastic solver produces\nresults of high accuracy in small number of iterations---for low and high\nfrequencies alike. A variety of numerical examples in this paper demonstrate\nthe accuracy and efficiency of the proposed methodology.\n