Adaptive sparse grid algorithms with applications to electromagnetic scattering under uncertainty

Authors:
Meilin Liu;Zhen Gao;Jan S. Hesthaven
Affiliations:
College of Information Science and Technology, Nanjing University of Aeronautics and Astronautics, China and Division of Applied Mathematics, Brown University, USA;Division of Applied Mathematics, Brown University, USA and Research Center for Applied Mathematics, Ocean University of China, China;Division of Applied Mathematics, Brown University, USA
Venue:
Applied Numerical Mathematics
Year:
2011

Citing 8
Cited 0

Testing multidimensional integration routines

Proc. of international conference on Tools, methods and languages for scientific and engineering computation
Large sample properties of simulations using latin hypercube sampling

Technometrics
Stochastic finite elements: a spectral approach

Stochastic finite elements: a spectral approach
The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations

SIAM Journal on Scientific Computing
Nodal high-order methods on unstructured grids

Journal of Computational Physics
High-Order Collocation Methods for Differential Equations with Random Inputs

SIAM Journal on Scientific Computing
Numerical integration formulas of degree two

Applied Numerical Mathematics
Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications

Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications

Quantified Score

Hi-index	0.01

Visualization

Abstract

We discuss adaptive sparse grid algorithms for stochastic differential equations with a particular focus on applications to electromagnetic scattering by structures with holes of uncertain size, location, and quantity. Stochastic collocation (SC) methods are used in combination with an adaptive sparse grid approach based on nested Gauss-Patterson grids. As an error estimator we demonstrate how the nested structure allows an effective error estimation through Richardson extrapolation. This is shown to allow excellent error estimation and it also provides an efficient means by which to estimate the solution at the next level of the refinement. We introduce an adaptive approach for the computation of problems with discrete random variables and demonstrate its efficiency for scattering problems with a random number of holes. The results are compared with results based on Monte Carlo methods and with Stroud based integration, confirming the accuracy and efficiency of the proposed techniques.