BDDC and FETI-DP under minimalist assumptions

Authors:
J. Mandel;B. Sousedík
Affiliations:
University of Colorado Denver, Department of Mathematical Sciences, P.O. Box 173364, Campus Box 170, 80217, Denver, CO, USA;University of Colorado Denver, Dept. of Math. Sci., P.O. Box 173364, Campus Box 170, 80217, Denver, CO, USA and Czech Technical Univ., Dept. of Math., Faculty of Civil Eng.g, P.O. Box 173364, Camp ...
Venue:
Computing
Year:
2007

Citing 0
Cited 5

BDDC by a frontal solver and the stress computation in a hip joint replacement

Mathematics and Computers in Simulation
BDDC Preconditioners for Spectral Element Discretizations of Almost Incompressible Elasticity in Three Dimensions

SIAM Journal on Scientific Computing
Original article: Face-based selection of corners in 3D substructuring

Mathematics and Computers in Simulation
Original Article: Adaptive BDDC in three dimensions

Mathematics and Computers in Simulation
Adaptive-Multilevel BDDC and its parallel implementation

Computing

Quantified Score

Hi-index	0.00

Visualization

Abstract

The FETI-DP, BDDC and P-FETI-DP preconditioners are derived in a particulary simple abstract form. It is shown that their properties can be obtained from only a very small set of algebraic assumptions. The presentation is purely algebraic and it does not use any particular definition of method components, such as substructures and coarse degrees of freedom. It is then shown that P-FETI-DP and BDDC are in fact the same. The FETI-DP and the BDDC preconditioned operators are of the same algebraic form, and the standard condition number bound carries over to arbitrary abstract operators of this form. The equality of eigenvalues of BDDC and FETI-DP also holds in the minimalist abstract setting. The abstract framework is explained on a standard substructuring example.