Analysis and application of single level, multi-level Monte Carlo and quasi-Monte Carlo finite element methods for time-dependent Maxwell’s equations with random inputs. (English) Zbl 1473.65216
Summary: This article is devoted to three quadrature methods for the rapid solution of stochastic time-dependent Maxwell’s equations with uncertain permittivity, permeability and initial conditions. We develop the mathematical analysis of the error estimate for single level Monte Carlo method, multi-level Monte Carlo method, and the quasi-Monte Carlo method. The theoretical results are supplemented by numerical experiments.
MSC:
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 65C05 | Monte Carlo methods |
| 35L15 | Initial value problems for second-order hyperbolic equations |
| 35Q60 | PDEs in connection with optics and electromagnetic theory |
| 78M10 | Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory |
Software:
QMC4PDEReferences:
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