Print Email Facebook Twitter On the use of rigid body modes in the deflated preconditioned conjugate gradient method Title On the use of rigid body modes in the deflated preconditioned conjugate gradient method Author Jönsthövel, T.B. Van Gijzen, M.B. Vuik, C. Scarpas, A. Faculty Civil Engineering and Geosciences Department Structural Engineering Date 2013-02-11 Abstract Large discontinuities in material properties, such as those encountered in composite materials, lead to ill-conditioned systems of linear equations. These discontinuities give rise to small eigenvalues that may negatively affect the convergence of iterative solution methods such as the preconditioned conjugate gradient method. This paper considers the deflated preconditioned conjugate gradient method for solving such systems. Our deflation technique uses as the deflation space the rigid body modes of sets of elements with homogeneous material properties. We show that in the deflated spectrum the small eigenvalues are mapped to zero and no longer negatively affect the convergence. We justify our approach through mathematical analysis and show with numerical experiments on both academic and realistic test problems that the convergence of our DPCG method is independent of discontinuities in the material properties. Subject deflationpreconditionersconjugate gradientsrigid body modesCT scanstructural mechanics To reference this document use: http://resolver.tudelft.nl/uuid:bf9a8026-a83c-46f3-8185-06fd1c1094f5 DOI https://doi.org/10.1137/100803651 Publisher Society for Industrial and Applied Mathematics (SIAM) ISSN 1064-8275 Source https://doi.org/10.1137/100803651 Source SIAM Journal on Scientific Computing, 35 (1), 2013 Part of collection Institutional Repository Document type journal article Rights (c) 2013 SIAM Files PDF Jonsthovel_2013.pdf 1.03 MB Close viewer /islandora/object/uuid:bf9a8026-a83c-46f3-8185-06fd1c1094f5/datastream/OBJ/view