A Monte Carlo approach to computing stiffness matrices arising in polynomial chaos approximations

Juan Galvis and O. Andrés Cuervo

Mathematics and Computers in Simulation (MATCOM), 2019, vol. 160, issue C, 72-81

Abstract: We use a Monte Carlo method to assemble finite element matrices for polynomial Chaos approximations of elliptic equations with random coefficients. In this approach, all expectations are approximated by a Monte Carlo method. The resulting methodology requires dealing with sparse block-diagonal matrices instead of block-full matrices. This leads to the solution of a coupled system of elliptic equations where the coupling is given by a Kronecker product matrix involving polynomial evaluation matrices. This generalizes the Classical Monte Carlo approximation and Collocation method for approximating functionals of solutions of these equations.

Keywords: Polynomial chaos; Random elliptic partial differential equations; Monte Carlo integration (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:160:y:2019:i:c:p:72-81

DOI: 10.1016/j.matcom.2018.11.008

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