Recycling of Solution Spaces in Multi-Preconditioned FETI Methods Applied to Structural Dynamics

This article presents a new method to recycle the solution space of an adaptive multi-preconditioned finite element tearing and interconnecting (AMP-FETI) algorithm in the case where the same operator is solved for multiple right-hand sides like in linear structural dynamics. It accelerates the computation from the second time step on by applying a coarse-space that is generated from Ritz approximations of local eigenproblems, using the solution space of the first time step. These eigenproblems are known to provide very efficient coarse-spaces but must usually be solved a priori at high computational cost. Their Ritz approximations are much smaller and less expensive to solve. Recycling methods based on Ritz approximations of global eigenproblems have been published for classical FETI algorithms but their efficient application to multi-preconditioned variants is not possible. The article also presents the application of a simpler recycling procedure, which reuses plain solution spaces, to AMP-FETI. Numerical results of the application of the presented methods to four test cases are shown. The new Ritz approximation method leads to coarse-spaces which turn out to be as efficient as those obtained from solving the unreduced eigenproblems. It is the most efficient recycling method currently available for multi-preconditioned dual domain decomposition techniques.