Algebraic multiscale linear solver for heterogeneous elliptic problems

Conference paper (2012)

Authors

Y. Wang Stanford University
H. Hajibeygi Stanford University
H Tchelepi Stanford University
Affiliation
External organisation
More Info
expand_more

Published Date

2012

Language

English

Reuse Rights

Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.

Affiliation

External organisation

Abstract

An Algebraic Multiscale Solver (AMS) for the pressure system of equations arising from incompressible flow in heterogeneous porous media is developed. The algorithm allows for several independent preconditioning stages to deal with the full spectrum of errors. In addition to the fine-scale system of equations, AMS requires information about the superimposed (dual) coarse grid to construct a wirebasket reordered system. The primal coarse grid is used in the construction of a conservative coarse-scale operator and in the reconstruction of a conservative fine-scale velocity field. The convergence properties of AMS are studied for various combinations including (1) the MultiScale Finite-Element (MSFE) method, (2) the MultiScale Finite-Volume (MSFV) method, (3) Correction Functions (CF), (4) Block Incomplete LU factorization with zero fill-in (BILU), and (5) point-wise Incomplete LU factorization with zero fill-in (ILU). The reduced-problem boundary condition, which is used for localization, is investigated. For a wide range of test cases, the performance of the different preconditioning options is analyzed. It is found that the best overall performance is obtained by combining MSFE and ILU as the global and local preconditioners, respectively. Comparison between AMS and the widely used SAMG solver illustrates that they are comparable, especially for very large heterogeneous problems.