A fast domain decomposition high order Poisson solver
The authors present a fast high-order Poisson solver and give a theoretical foundation for the use of higher order approximations instead of lower order ones for elliptic boundary value problems. Estimates of computational complexity and memory requirements as well as error estimates are derived for one and two dimensional model problems. The 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 using a non-overlapping domain decomposition technique which give a possibility to use parallel computers both with shared and distributed memory in the solution. Finally, the authors present and discuss results from numerical experiments using a parallel computer with shared memory based on eight Alpha 21164 processors.
scientific article; zbMATH DE number 1455174