Solving elliptic finite element systems in near-linear time with support preconditioners.

Journal Article · Thu Jul 01 04:00:00 EDT 2004 · Proposed for publication in SIAM Journal of Matrix Analysis.

OSTI ID:961626

Vavasis, Stephen ^[1]; Hendrickson, Bruce Alan; Boman, Erik Gunnar

---

1. Cornell University, Ithaca, NY

We consider linear systems arising from the use of the finite element method for solving scalar linear elliptic problems. Our main result is that these linear systems, which are symmetric and positive semidefinite, are well approximated by symmetric diagonally dominant matrices. Our framework for defining matrix approximation is support theory. Significant graph theoretic work has already been developed in the support framework for preconditioners in the diagonally dominant case, and in particular it is known that such systems can be solved with iterative methods in nearly linear time. Thus, our approximation result implies that these graph theoretic techniques can also solve a class of finite element problems in nearly linear time. We show that the support number bounds, which control the number of iterations in the preconditioned iterative solver, depend on mesh quality measures but not on the problem size or shape of the domain.

• Research Organization: Sandia National Laboratories
• Sponsoring Organization: USDOE
• DOE Contract Number: AC04-94AL85000
• OSTI ID: 961626
• Report Number(s): SAND2004-3267J
• Journal Information: Proposed for publication in SIAM Journal of Matrix Analysis., Journal Name: Proposed for publication in SIAM Journal of Matrix Analysis.
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
99 GENERAL AND MISCELLANEOUS
APPROXIMATIONS
ELLIPTICAL CONFIGURATION
FINITE ELEMENT METHOD
ITERATIVE METHODS