A quasi Monte Carlo-based model reduction method for solving Helmholtz equation in random media

Numerical optimization and variational techniques (65K10) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Pseudo-random numbers; Monte Carlo methods (11K45)

Cites Work

Unnamed Item
Quasi-Monte Carlo finite element methods for elliptic PDEs with lognormal random coefficients
Sparse operator compression of higher-order elliptic operators with rough coefficients
The Helmholtz equation in heterogeneous media: a priori bounds, well-posedness, and resonances
Modeling uncertainty in flow simulations via generalized polynomial chaos.
An efficient Monte Carlo interior penalty discontinuous Galerkin method for elastic wave scattering in random media
Multigrid with Rough Coefficients and Multiresolution Operator Decomposition from Hierarchical Information Games
Eliminating the pollution effect in Helmholtz problems by local subscale correction
Optimal Local Approximation Spaces for Generalized Finite Element Methods with Application to Multiscale Problems
Localization of elliptic multiscale problems
An Efficient Numerical Method for Acoustic Wave Scattering in Random Media
Mountain Waves and Gaussian Beams
Multiscale Finite Element Methods
A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data
Turbulence and the dynamics of coherent structures. I. Coherent structures
Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients
Is the Pollution Effect of the FEM Avoidable for the Helmholtz Equation Considering High Wave Numbers?
A Multiscale Reduced Basis Method for the Schrödinger Equation With Multiscale and Random Potentials
Computing Eigenvalues and Eigenfunctions of Schrödinger Equations Using a Model Reduction Approach
A Multiscale Finite Element Method for the Schrödinger Equation with Multiscale Potentials
Lecture Notes on Quantum Brownian Motion
High-dimensional integration: The quasi-Monte Carlo way

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