Block-diagonal preconditioning for spectral stochastic finite-element systems

Block-diagonal preconditioning for spectral stochastic finite-element systems

Deterministic models of fluid flow and the transport of chemicals in flows in heterogeneous porous media incorporate partial differential equations (PDEs) whose material parameters are assumed to be known exactly. To tackle more realistic stochastic flow problems, it is fitting to represent the permeability coefficients as random fields with prescribed statistics. Traditionally, large numbers o...

Finite-Element Preconditioning of G-NI Spectral Methods

Several old and new finite-element preconditioners for nodal-based spectral discretizations of −∆u = f in the domain Ω = (−1, 1) (d = 2 or 3), with Dirichlet or Neumann boundary conditions, are considered and compared in terms of both condition number and computational efficiency. The computational domain covers the case of classical single-domain spectral approximations (see [5]), as well as t...

Inverse Subspace Iteration for Spectral Stochastic Finite Element Methods

We study random eigenvalue problems in the context of spectral stochastic finite elements. In particular, given a parameter-dependent, symmetric positive-definite matrix operator, we explore the performance of algorithms for computing its eigenvalues and eigenvectors represented using polynomial chaos expansions. We formulate a version of stochastic inverse subspace iteration, which is based on...

Spectral Stochastic Finite-element Methods for Parametric Constrained Optimization Problems

We present a method to approximate the solution mapping of parametric constrained optimization problems. The approximation, which is of the spectral stochastic finite element type, is represented as a linear combination of orthogonal polynomials. Its coefficients are determined by solving an appropriate finite-dimensional constrained optimization problem. We show that, under certain conditions,...

Finite Element Preconditioning on Spectral Element Discretizations for Coupled Elliptic Equations