Comparison of the deflated preconditioned conjugate gradient method and algebraic multigrid for composite materials

• Published in: Computational mechanics Vol. 50; no. 3; pp. 321 - 333
• Main Authors: Jönsthövel, T. B., van Gijzen, M. B., MacLachlan, S., Vuik, C., Scarpas, A.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 01.09.2012; Springer; Springer Nature B.V
• Subjects: Algebra; Algorithms; Asphalt; Classical and Continuum Physics; Comparative analysis; Composite materials; Composite materials industry; Computational Science and Engineering; Computed tomography; Computer simulation; Conjugate gradient method; Conjugates; Eigenvalues; Engineering; Finite element method; Iterative methods; Iterative solution; Linear systems; Material properties; Methods; Original Paper; Parallel computers; Rigid structures; Stiffness; Theoretical and Applied Mechanics; Vectors (mathematics); 65Z05; Structural mechanics; 65F10; Deflation; Conjugate gradients; Preconditioners; Rigid body modes; CT scan; 65F08; Algebraic multigrid
• ISSN: 0178-7675; 1432-0924; 1432-0924
• DOI: 10.1007/s00466-011-0661-y

Many applications in computational science and engineering concern composite materials, which are characterized by large discontinuities in the material properties. Such applications require fine-scale finite-element meshes, which lead to large linear systems that are challenging to solve with current direct and iterative solutions algorithms. In this paper, we consider the simulation of asphalt concrete, which is a mixture of components with large differences in material stiffness. The discontinuities in material stiffness give rise to many small eigenvalues that negatively affect the convergence of iterative solution algorithms such as the preconditioned conjugate gradient (PCG) method. This paper considers the deflated preconditioned conjugate gradient (DPCG) method in which the rigid body modes of sets of elements with homogeneous material properties are used as deflation vectors. As preconditioner we consider several variants of the algebraic multigrid smoothed aggregation method. We evaluate the performance of the DPCG method on a parallel computer using up to 64 processors. Our test problems are derived from real asphalt core samples, obtained using CT scans. We show that the DPCG method is an efficient and robust technique for solving these challenging linear systems.