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Full-Text Articles in Mathematics
Well Conditioned Boundary Integral Equations For Two-Dimensional Sound-Hard Scattering Problems In Domains With Corners, Akash Anand, Jeffrey S. Ovall, Catalin Turc
Well Conditioned Boundary Integral Equations For Two-Dimensional Sound-Hard Scattering Problems In Domains With Corners, Akash Anand, Jeffrey S. Ovall, Catalin Turc
Mathematics and Statistics Faculty Publications and Presentations
We present several well-posed, well-conditioned direct and indirect integral equation formulations for the solution of two-dimensional acoustic scattering problems with Neumann boundary conditions in domains with corners. We focus mainly on Direct Regularized Combined Field Integral Equation (DCFIE-R) formulations whose name reflects that (1) they consist of combinations of direct boundary integral equations of the second-kind and first-kind integral equations which are preconditioned on the left by coercive boundary single-layer operators, and (2) their unknowns are physical quantities, i.e., the total field on the boundary of the scatterer. The DCFIE-R equations are shown to be uniquely solvable in appropriate function …