TY - JOUR
T1 - Efficient Spectral Stochastic Finite Element Methods for Helmholtz Equations with Random Inputs
JO - East Asian Journal on Applied Mathematics
VL - 3
SP - 601
EP - 621
PY - 2019
DA - 2019/06
SN - 9
DO - http://doi.org/10.4208/eajam.140119.160219
UR - https://global-sci.org/intro/article_detail/eajam/13169.html
KW - Helmholtz equations, PDEs with random data, generalised polynomial chaos, stochastic
finite elements, iterative solvers.
AB - <p style="text-align: justify;">The implementation of spectral stochastic Galerkin finite element approximation methods for Helmholtz equations with random inputs is considered. The corresponding linear systems have matrices represented as Kronecker products. The sparsity of such matrices is analysed and a mean-based preconditioner is constructed. Numerical examples show the efficiency of the mean-based preconditioners for stochastic
Helmholtz problems, which are not too close to a resonant frequency.</p>