Multilevel Designed Quadrature for Partial Differential Equations with Random Inputs

Probabilistic models, generic numerical methods in probability and statistics (65C20) Numerical solutions to stochastic differential and integral equations (65C30) Numerical quadrature and cubature formulas (65D32)

Uses Software

Matlab
Partial Differential Equation Toolbox
nwSpGr
top.m
top88.m

Cites Work

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Multi-index Monte Carlo: when sparsity meets sampling
Likelihood approximation by numerical integration on sparse grids
Further analysis of multilevel Monte Carlo methods for elliptic PDEs with random coefficients
Efficient topology optimization in MATLAB using 88 lines of code
Multilevel Monte Carlo methods and applications to elliptic PDEs with random coefficients
Optimization of mesh hierarchies in multilevel Monte Carlo samplers
Convergence rates of best \(N\)-term Galerkin approximations for a class of elliptic SPDEs
Multi-level Monte Carlo finite element method for elliptic PDEs with stochastic coefficients
A duality proof of Tchakaloff's theorem
Multilevel adaptive stochastic collocation with dimensionality reduction
Multi-index stochastic collocation for random PDEs
Multi-level quasi-Monte Carlo finite element methods for a class of elliptic PDEs with random coefficients
Multilevel Higher Order QMC Petrov--Galerkin Discretization for Affine Parametric Operator Equations
Strong and Weak Error Estimates for Elliptic Partial Differential Equations with Random Coefficients
Multilevel Monte Carlo Methods
Stochastic Spectral Galerkin and Collocation Methods for PDEs with Random Coefficients: A Numerical Comparison
ANALYTIC REGULARITY AND POLYNOMIAL APPROXIMATION OF PARAMETRIC AND STOCHASTIC ELLIPTIC PDE'S
ON THE OPTIMAL POLYNOMIAL APPROXIMATION OF STOCHASTIC PDES BY GALERKIN AND COLLOCATION METHODS
Numerical Integration in Multiple Dimensions with Designed Quadrature
A Multilevel Stochastic Collocation Method for Partial Differential Equations with Random Input Data
An Anisotropic Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data
Stochastic Finite Differences and Multilevel Monte Carlo for a Class of SPDEs in Finance
Quasi-Monte Carlo Finite Element Methods for a Class of Elliptic Partial Differential Equations with Random Coefficients
Finite Element Error Analysis of Elliptic PDEs with Random Coefficients and Its Application to Multilevel Monte Carlo Methods
Multilevel Quadrature for Elliptic Parametric Partial Differential Equations in Case of Polygonal Approximations of Curved Domains
Approximation of high-dimensional parametric PDEs

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