Deflated domain decomposition method for structural problems

Abstract

The paper presents a fast and stable solver algorithm for structural problems. The point is the distance between the eigenvector of the constrained stiffness matrix and the unconstrained matrix. The coarse motions are close to the kernel of the unconstrained matrix. We use lower-frequency deformation modes to construct an iterative solver algorithm through domain decomposition expressing near-rigid-body motions, deflation algorithms, and two-level algorithms. We remove the coarse space from the solution space and hand over the iteration space to the fine space. Our solver is parallelized, and the solver thus has two sets of domain decomposition. One decomposition generates the coarse space, and the other is for parallelization. The basic framework of the solver is the parallel conjugate gradient (CG) method on the fine space. We use the CG method for the basic framework instead of the (simplest) domain decomposition method. We conducted benchmark tests using elastic static analysis for thin plate models. A comparison with the standard CG solver results shows the new solver’s high-speed performance and remarkable stability.