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

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

2011-01-18

arxiv.org/abs/1101.3383v1

Mathematics

Numerical Analysis

The report describes tentative work. No numerical examples are available at this point

Scientific paper

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.

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