Deflated Domain Decomposition Method for Structural Problems

Abstract

A fast and stable solver algorithm for structural problems is presented. The distance between the eigenvector of the constrained stiffness matrix and the unconstrained matrix is discussed. The coarse motions are close to the kernel of the unconstrained matrix. This relates to using 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 the iteration space is handed over to the fine space. Our solver is parallelized, and the solver thus has two sets of domain decomposition. One decomposition is for generating 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. The CG method and the simplest domain decomposition method are compared to explain the adoption of the CG method as the basic framework. Benchmark tests are conducted using elastic static analysis for thin plate models. A comparison with the standard CG solver results shows the high-speed performance and remarkable stability of the new solver.