Computational Math Seminar: Delyan Kalchev
Adaptive Spectral Algebraic Multigrid for Finite Element Elliptic Equations with Stochastic Coefficients
Delyan Kalchev
Applied Mathematics,Ìý
Date and time:Ìý
Tuesday, September 30, 2014 - 10:30am
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Grandview Conference Room
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This is an adaptive extension of the smoothed aggregation element-based spectral algebraic multigrid proposed by Brezina and Vassilevski. The original method provides optimal (in terms of convergence) preconditioners for elliptic diffusion equations with highly heterogeneous coefficients, where under appropriate parameter choices the optimality is uniform with respect to the contrasts in the coefficient even in the case of aggressive coarsening. The purpose is to solve large number of equations with slowly changing coefficients. Since constructing coarse spaces by the original method is computationally expensive procedure, an adaptive approach is proposed which allows for reusing a previously constructed coarse space to efficiently build a two-level solver for a new, nearby problem. Adaptation allows for maintaining the approximation properties of the coarse space, and thus, the good convergence of the method as the coefficient changes. A particular problem targeted is solving sequences of linear systems arising through Monte Carlo Markov chain simulations with application in simulating subsurface flow with uncertainty in the permeability field.