Robust and efficient FETI domain decomposition algorithms for edge element approximations

Abstract

Purpose

A family of preconditioned dual‐primal FETI iterative algorithms for the solution of algebraic systems arising from edge element approximations in two dimensions is presented.

Design/methodology/approach

The primal constraints, which determine the size of the coarse problem to be solved at each iteration step, are here suitable averages over subdomain edges. The condition number of the corresponding methods is independent of the number of subdomains and possibly large jumps of the coefficients.

Findings

For h finite elements, it grows only polylogarithmically with the number of unknowns associated with individual substructures, while for hp approximations on geometrically refined meshes, it is independent of arbitrarily large aspect ratios.

Originality/value

Proposes an algorithm with a rate of convergence that is independent of possibly large jumps of the coefficients and mesh aspect ratios.

Citation

Toselli, A. and Vasseur, X. (2005), "Robust and efficient FETI domain decomposition algorithms for edge element approximations", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 24 No. 2, pp. 396-407. https://doi.org/10.1108/03321640510586033