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A discretization scheme for variable coefficient elliptic PDEs in the planeis presented. The scheme is based on high-order Gaussian quadratures and isdesigned for problems with smooth solutions, such as scattering problemsinvolving soft scatterers. The resulting system of linear equations is verywell suited to efficient direct solvers such as nested dissection and the morerecently proposed accelerated nested dissection schemes with O(N) complexity.

A high-order accurate discretization scheme for variable coefficient elliptic PDEs in the plane with smooth solutions