RT Journal Article
ID 0ddbb36a39a91067
A1 Feng, Xiaobing
A1 Lin, Junshan
A1 Lorton, Cody
T1 A MULTIMODES MONTE CARLO FINITE ELEMENT METHOD FOR ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS WITH RANDOM COEFFICIENTS
JF International Journal for Uncertainty Quantification
JO IJUQ
YR 2016
FD 2016-12-16
VO 6
IS 5
SP 429
OP 443
K1 random partial differential equations
K1 multimodes expansion
K1 LU decomposition
K1 Monte Carlo method
K1 finite element methods
AB This paper develops and analyzes an efficient numerical method for solving elliptic partial differential equations, where the diffusion coefficients are random perturbations of deterministic diffusion coefficients. The method is based upon a multimodes representation of the solution as a power series of the perturbation parameter, and the Monte Carlo technique for sampling the probability space. One key feature of the proposed method is that the governing equations for all the expanded mode functions share the same deterministic diffusion coefficient; thus an efficient direct solver by repeatedly using the LU decomposition of the discretized common deterministic diffusion operator can be employed for solving the finite element discretized linear systems. It is shown that the computational complexity of the algorithm is comparable to that of solving a few deterministic elliptic partial differential equations using the director solver. Error estimates are derived for the method, and numerical experiments are provided to test the efficiency of the algorithm and validate the theoretical results.
PB Begell House
LK http://dl.begellhouse.com/journals/52034eb04b657aea,4389a1c13f4fb473,0ddbb36a39a91067.html