A Three-level BDDC algorithm for saddle point problems

Journal Article · Wed Dec 10 04:00:00 EST 2008 · Numerical Mathmatics

OSTI ID:945050

Tu, X

BDDC algorithms have previously been extended to the saddle point problems arising from mixed formulations of elliptic and incompressible Stokes problems. In these two-level BDDC algorithms, all iterates are required to be in a benign space, a subspace in which the preconditioned operators are positive definite. This requirement can lead to large coarse problems, which have to be generated and factored by a direct solver at the beginning of the computation and they can ultimately become a bottleneck. An additional level is introduced in this paper to solve the coarse problem approximately and to remove this difficulty. This three-level BDDC algorithm keeps all iterates in the benign space and the conjugate gradient methods can therefore be used to accelerate the convergence. This work is an extension of the three-level BDDC methods for standard finite element discretization of elliptic problems and the same rate of convergence is obtained for the mixed formulation of the same problems. Estimate of the condition number for this three-level BDDC methods is provided and numerical experiments are discussed.

• Research Organization: Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, CA (US)
• Sponsoring Organization: Computational Research Division
• DOE Contract Number: AC02-05CH11231
• OSTI ID: 945050
• Report Number(s): LBNL-1319E
• Journal Information: Numerical Mathmatics, Journal Name: Numerical Mathmatics
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
ALGORITHMS
CONVERGENCE
LAWRENCE BERKELEY LABORATORY