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Institutt for informatikk seminar: Wednesday 21 June, kl. 14:15

A tensor framework for preconditioners based on fast transforms

Kurt Otto

University of Uppsala

The framework is aimed at preconditioners for discretized multi-dimensional PDE problems, where the underlying grid is structured. Instead of embedding the discretized operator into a matrix, a tensor approach is advocated. Therefore, optimal approximations of complex tensors of even order are considered. By construction the ``blocks'' in the approximants are diagonalizable by fast transforms. Theorems describing efficient ways of computing the approximants are derived. As an application, effective preconditioners for the discretized Helmholtz equation with radiation boundary conditions are studied.

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