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

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