Print Email Facebook Twitter Comparison of the deflated preconditioned conjugate gradient method and algebraic multigrid for composite materials Title Comparison of the deflated preconditioned conjugate gradient method and algebraic multigrid for composite materials Author Jönsthövel, T.B. Van Gijzen, M.B. MacLachlan, S. Vuik, C. Scarpas, A. Faculty Civil Engineering and Geosciences Department Structural Engineering Date 2012-09-01 Abstract 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. Subject DeflationAlgebraic multigridPreconditionersConjugate gradientsRigid body modesCT scanStructural mechanics65F1065F0865Z05 To reference this document use: http://resolver.tudelft.nl/uuid:cc01bde4-6f3a-4ed2-a628-91bbe0dc9df1 DOI https://doi.org/10.1007/s00466-011-0661-y Publisher Springer-Verlag ISSN 1432-0924 Source http://link.springer.com/article/10.1007/s00466-011-0661-y Source Computational mechanics, 50(3)2012 Part of collection Institutional Repository Document type journal article Rights (c)2012 The Authors and Springer Files PDF Jonsthovel.pdf 825.38 KB Close viewer /islandora/object/uuid:cc01bde4-6f3a-4ed2-a628-91bbe0dc9df1/datastream/OBJ/view