Abstract
We present a fast high-order Poisson solver for implementation on parallel computers. The method uses deferred correction, such that high-order accuracy is obtained by solving a sequence of systems with a narrow stencil on the left-hand side. These systems are solved by a domain decomposition method. The method is direct in the sense that for any given order of accuracy, the number of arithmetic operations is fixed. Numerical experiments show that these high-order solvers easily outperform standard second-order ones. The very fast algorithm in combination with the coarser grid allowed for by the high-order method, also makes it quite possible to compete with adaptive methods and irregular grids for problems with solutions containing widely different scales.
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Gustafsson, B., Hemmingsson-Frändén, L. A Fast Domain Decomposition High Order Poisson Solver. Journal of Scientific Computing 14, 223–243 (1999). https://doi.org/10.1023/A:1023265301820
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DOI: https://doi.org/10.1023/A:1023265301820