Preconditioned Conjugate Gradient Method Enhanced by Deflation of Rigid Body Modes Applied to Composite Materials

摘要

The introduction of computed X-ray tomography allows for the construction of high quality, material-per-element based 3D meshes in the field of structural mechanics. The use of these meshes enables a shift from meso to micro scale analysis of composite materials like cement concrete, rocks and asphalt concrete. Unfortunately, because of the extremely long execution time, memory and storage space demands, the majority of commercially available finite element packages are not capable of handling efficiently the most computationally demanding operation of the finite element solution process, that is, the inversion of the structural stiffness matrix. To address this issue, an efficient iterative method based upon the preconditioned conjugate gradient method has been developed and is presented in this contribution. It is shown that enhancement of the preconditioned conjugate gradient method with information about the rigid body modes of the aggregates results in an aggregate independent convergence behavior. The resulting number of iterations is bounded by the material behavior of the matrix only.