SciCADE 2013
International Conference on Scientific Computation and Differential Equations
September 16-20, 2013, Valladolid (Spain)

Invited Talk

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A direct solver with O(N) complexity for a spectral multidomain method

P.G. Martinsson

Abstract
The talk describes a highly accurate technique for solving elliptic PDEs with variable coefficients and smooth solutions. The domain is tessellated into squares (or cubes), and the differential operator is discretized via high order (p=10 or 20) spectral differentiation on each square. A hierarchical direct solver is used to solve the resulting discrete system. The method is very efficient; e.g., a Helmholtz problem on a domain of size 200x200 wavelengths is solved to ten digits of accuracy in ten minutes on a standard laptop (using 6M degrees of freedom).

Organized by         Universidad de Valladolid     IMUVA