Stochastic spectral Galerkin and collocation methods for PDEs with random coefficients: a numerical comparison
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The modeling of a system composed by a gas phase and organic aerosol particles, and its numerical resolution are studied. The gas-aerosol system is modeled by ordinary differential equations coupled with a mixed-constrained optimization problem. This coupl ...
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We consider the problem of numerically approximating statistical moments of the solution of a time-dependent linear parabolic partial differential equation (PDE), whose coefficients and/or forcing terms are spatially correlated random fields. The stochasti ...
The numerical solution of linear systems with certain tensor product structures is considered. Such structures arise, for example, from the finite element discretization of a linear PDE on a d-dimensional hypercube. Linear systems with tensor product struc ...
Society for Industrial and Applied Mathematics2009
Numerical mathematics is the branch of mathematics that proposes, develops, analyzes and applies methods from scientific computing to several fields including analysis, linear algebra, geometry, approximation theory, functional equations, optimization and ...
In this work we first focus on the Stochastic Galerkin approximation of the solution u of an elliptic stochastic PDE. We rely on sharp estimates for the decay of the coefficients of the spectral expansion of u on orthogonal polynomials to build a sequence ...
We present a general method for numerical analysis of electrically large electromagnetic-field problems, which is based on merging diakoptic approach and surface integral-equation formulations. Compared with the classical approach, the proposed method prov ...