A FACTORIZATION OF THE SPECTRAL GALERKIN SYSTEM FOR PARAMETERIZED MATRIX EQUATIONS: DERIVATION AND APPLICATIONS

作者：Constantine Paul G^*; Gleich David F; Iaccarino Gianluca

来源：SIAM Journal on Scientific Computing, 2011, 33(5): 2995-3009.

• parameterized systems
• spectral methods
• stochastic Galerkin

Recent work has explored solver strategies for the linear system of equations arising from a spectral Galerkin approximation of the solution of PDEs with parameterized (or stochastic) inputs. We consider the related problem of a matrix equation whose matrix and right-hand side depend on a set of parameters (e.g., a PDE with stochastic inputs semidiscretized in space) and examine the linear system arising from a similar Galerkin approximation of the solution. We derive a useful factorization of this system of equations, which yields bounds on the eigenvalues, clues to preconditioning, and a flexible implementation method for a wide array of problems. We complement this analysis with (i) a numerical study of preconditioners on a standard elliptic PDE test problem and (ii) a fluids application using existing CFD codes; the MATLAB codes used in the numerical studies are available online.

• 出版日期2011