Powered by TCPDF (www.tcpdf.org) WAVELET-IN-TIME MULTIGRID-IN-SPACE PRECONDITIONING OF PARABOLIC EVOLUTION EQUATIONS

Abstract. Two different space-time variational formulations of linear parabolic evolution equa-tions are considered, one is symmetric and elliptic on the trial space while the other is not. In each case, space-time Petrov–Galerkin discretization using suitable tensor product trial and test functions leads to a large linear system of equations. Well-posedness of this system with respect to space-time norms induces a canonical preconditioner for the algebraic equations that arise after a choice of basis. For the iterative resolution of this algebraic system with parallelization in the temporal direc-tion we propose a sparse algebraic wavelet-in-time transformation on possibly nonuniform temporal meshes. This transformation block-diagonalizes the preconditioner, and the individual spatial blocks can then be inverted approximately by standard spatial multigrid methods in parallel. We document the performance of the preconditioner in a series of numerical experiments