This manuscript presents a new extended linear system for integral equation based techniques for solving boundary value problems on locally perturbed geometries. The new extended  system is similar to the one presented by Greengard et al. (2009) for which a fast direct solver was constructed by Zhang and Gillman (2018) but the corresponding fast direct solver is more efficient than the one for the original extended system. Another important feature of the new extended system is that it can easily handle problems that require specialized quadrature for weakly singular kernels  . Numerical results illustrate the improved performance of the fast direct solver for the new extended system when compared to the fast direct solver for the original extended system.
This manuscript presents a new extended linear system for integral equation based techniques for solving boundary value problems on locally perturbed geometries. The new extended linear system is similar to a previously presented technique for which the authors have constructed a fast direct solver . The key features of the work presented in this paper are that the fast direct solver is more efficient for the new extended linear system and that problems involving specialized quadrature for weakly singular kernels can be easily handled . Numerical results illustrate the improved performance of the fast direct solver for the new extended system when compared to the fast direct solver for the original extended system.
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linear
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the one presented by Greengard et al. (2009) for which
a previously presented technique for which the authors have constructed
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was constructed by Zhang and Gillman (2018) but the corresponding
. The key features of the work presented in this paper are that the
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than the one for the original extended system. Another important feature of the new extended system is that it can easily handle problems that require
for the new extended linear system and that problems involving
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can be easily handled