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ARTICLE IN PRESS APNUM:2172 Please cite this article in press as: B. Aksoylu, H. Klie, A family of physics-based preconditioners for solving elliptic equations on highly
 

Summary: ARTICLE IN PRESS APNUM:2172
Please cite this article in press as: B. Aksoylu, H. Klie, A family of physics-based preconditioners for solving elliptic equations on highly
heterogeneous media, Applied Numerical Mathematics (2008), doi:10.1016/j.apnum.2008.06.002
JID:APNUM AID:2172 /FLA [m3SC+; v 1.95; Prn:31/07/2008; 19:05] P.1 (1-28)
Applied Numerical Mathematics иии (ииии) иииГиии
www.elsevier.com/locate/apnum
A family of physics-based preconditioners for solving elliptic
equations on highly heterogeneous media
Burak Aksoylu a
, Hector Klie b,
a Department of Mathematics and Center for Computation and Technology, Louisiana State University, USA
b Center for Subsurface Modeling, Institute for Computational Science and Engineering, The University of Texas at Austin, USA
Abstract
Eigenvalues of smallest magnitude become a major bottleneck for iterative solvers especially when the underlying physical
properties have severe contrasts. These contrasts are commonly found in many applications such as composite materials, geological
rock properties and thermal and electrical conductivity. The main objective of this work is to construct a method as algebraic as
possible. However, the underlying physics is utilized to distinguish between high and low degrees of freedom which is central to
the construction of the proposed preconditioner. Namely, we propose an algebraic way of separating binary-like systems according
to a given threshold into high- and low-conductivity regimes of coefficient size O(m) and O(1), respectively where m 1. So,
the proposed preconditioner is essentially physics-based because without the utilization of underlying physics such an algebraic

  

Source: Aksoylu, Burak - Center for Computation and Technology & Department of Mathematics, Louisiana State University

 

Collections: Computer Technologies and Information Sciences