Low-rank solutions to the stochastic Helmholtz equation

2023/02/16 by Kaya, Adem, Freitag, Melina A.
#35R60 #65F10 #65M60 #65N06 #65N22 #65N30 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2302.08393

Abstract

In this paper, we consider low-rank approximations for the solutions to the stochastic Helmholtz equation with random coefficients. A Stochastic Galerkin finite element method is used for the discretization of the Helmholtz problem. Existence theory for the low-rank approximation is established when the system matrix is indefinite. The low-rank algorithm does not require the construction of a large system matrix which results in an advantage in terms of CPU time and storage. Numerical results show that, when the operations in a low-rank method are performed efficiently, it is possible to obtain an advantage in terms of storage and CPU time compared to computations in full rank. We also propose a general approach to implement a preconditioner using the low-rank format efficiently.

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