BDDC and FETI-DP algorithms with adaptive coarse spaces for three-dimensional elliptic problems with oscillatory and high contrast coefficients

摘要

BDDC and FETI-DP algorithms are developed for three-dimensional ellipticproblems with adaptively enriched coarse components. It is known that theseenriched components are necessary in the development of robust preconditioners.To form the adaptive coarse components, carefully designed generalizedeigenvalue problems are introduced for each faces and edges, and the coarsecomponents are formed by using eigenvectors with their correspondingeigenvalues larger than a given tolerance $\lambda_{TOL}$. Upper bounds forcondition numbers of the preconditioned systems are shown to be $C\lambda_{TOL}$, with the constant $C$ depending only on the maximum number ofedges and faces per subdomain, and the maximum number of subdomains sharing anedge. Numerical results are presented to test the robustness of the proposedapproach.