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Higher order QMC Galerkin discretization for parametric operator equations
(2013)SAM Research ReportWe construct quasi-Monte Carlo methods to approximate the expected values of linear functionals of Petrov-Galerkin discretizations of parametric operator equations which depend on a possibly infinite sequence of parameters. Such problems arise in the numerical solution of differential and integral equations with random field inputs. We analyze the regularity of the solutions with respect to the parameters in terms of the rate of decay of ...Report -
Multi-level higher order QMC Galerkin discretization for affine parametric operator equations
(2014)SAM Research ReportWe develop a convergence analysis of a multi-level algorithm combining higher order quasi-Monte Carlo (QMC) quadratures with general Petrov-Galerkin discretizations of countably affine parametric operator equations of elliptic and parabolic type, extending both the multi-Level first order analysis in [F.Y. Kuo, Ch. Schwab, and I.H. Sloan, Multi-level quasi-Monte Carlo finite element methods for a class of elliptic partial differential ...Report -
Higher order QMC Petrov-Galerkin discretization for affine parametric operator equations with random field inputs
(2013)SAM Research ReportWe construct quasi-Monte Carlo methods to approximate the expected values of linear functionals of Petrov-Galerkin discretizations of parametric operator equations which depend on a possibly infinite sequence of parameters. Such problems arise in the numerical solution of differential and integral equations with random field inputs. We analyze the regularity of the solutions with respect to the parameters in terms of the rate of decay of ...Report