Comparison of the deflated preconditioned conjugate gradient method and parallel direct solver for composite materials

Abstract

The demand for large FE meshes increases as parallel computing becomes the standard in FE simulations. Direct and iterative solution methods are used to solve the resulting linear systems. Many applications concern composite materials, which are characterized by large discontinuities in the material properties. An example of such a material is asphalt concrete, which is a mixture of components with large differences in material stiffness. Such discontinuities give rise to small eigenvalues that negatively affect the convergence of iterative solution methods such as the Preconditioned Conjugate Gradient (PCG) method. This paper considers the Deflated Preconditioned Conjugate Gradient (DPCG) method for solving such systems within reasonable time using the rigid body modes of sets of elements with homogeneous material properties. We compare the performance of the parallel direct solver MUMPS, the PCG method and the DPCG method for the FE mesh of a real asphalt core sample. The mesh is obtained using a CT scan. We show that the DPCG method is the method of choice for large linear systems with respect to the wall clock time, storage and accuracy of the solution.