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This paper focuses on fast direct solvers for integral equations in thelow-to-moderate-frequency regime obtained by leveraging preconditioned firstkind or second kind operators regularized with Laplacian filters. The spectralerrors arising from boundary element discretizations are properly handled byfiltering that, in addition, allows for the use of low-rank representations forthe compact perturbations of all operators involved. Numerical results show theeffectiveness of the approaches and their effectiveness in the direct solutionof integral equations.

Fast Direct Solvers for Integral Equations at Low-Frequency Based on Operator Filtering