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2015.64: An Efficient Reduced Basis Solver for Stochastic Galerkin Matrix Equations

2015.64: Catherine E. Powell, David Silvester and Valeria Simoncini (2015) An Efficient Reduced Basis Solver for Stochastic Galerkin Matrix Equations.

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Stochastic Galerkin finite element approximation of PDEs with random inputs leads to linear systems of equations with coefficient matrices that have a characteristic Kronecker product structure. By reformulating the systems as multi-term linear matrix equations, we develop an efficient solution algorithm which generalizes ideas from rational Krylov subspace approximation. The new approach determines a low-rank approximation to the solution matrix by performing a projection onto a low-dimensional space and provides an efficient solution strategy whose convergence rate is independent of the spatial approximation. Moreover, it requires far less memory than the standard preconditioned conjugate gradient method applied to the Kronecker formulation of the linear systems.

Item Type:MIMS Preprint
Uncontrolled Keywords:generalized matrix equations, PDEs with random data, stochastic finite elements, iterative solvers, rational Krylov subspace methods
Subjects:MSC 2000 > 35 Partial differential equations
MSC 2000 > 60 Probability theory and stochastic processes
MSC 2000 > 65 Numerical analysis
MIMS number:2015.64
Deposited By:Dr C.E. Powell
Deposited On:27 July 2015

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