Scalable Algorithms for Contact Problems

Abstract

of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made.

Simulation of discrete cracks driven by nearly incompressible fluid via 2D combined finite‐discrete element method

“…A comprehensive compilation of the FDEM methodology was presented in the first book on the subject, which was published by Wiley in 2004. Key aspects of the algorithms used in this work to resolve contact detection and contact interaction can be found in Munjiza et al, which can also be complemented by Wriggers and Udo Nackenhorst and Dostál et al Furthermore, the description of the formulation implemented to resolve the stresses inside the finite elements can be found in Munjiza et al and Lei et al…”

“…A comprehensive compilation of the FDEM methodology was presented in the first book on the subject, which was published by Wiley 11 in 2004. Key aspects of the algorithms used in this work to resolve contact detection and contact interaction can be found in Munjiza et al, 32 which can also be complemented by Wriggers and Udo Nackenhorst 33 and Dostál et al 34 Furthermore, the description of the formulation implemented to resolve the stresses inside the finite elements can be found in Munjiza et al 35 and Lei et al 36,37 In the last decade, scientific application-driven developments of FDEM have taken place at Los Alamos National Laboratory, enabling researchers to shift the boundaries of FDEM solutions towards more advanced alternatives, see Figure 1. These developments have produced a whole range of cutting edge FDEM algorithms including the following:…”

On conditioning of Schur complements of H-TFETI clusters for 2D problems governed by Laplacian

“…The method was later adapted to the solution of variational inequalities [2], [4]. The dual problem reads…”

“…Here we are interested in the estimates that are necessary for the analysis of H-TFETI (hybrid total FETI, see e.g. [4]) without preconditioner. This method exploits the decomposition of domains into floating clusters, i.e.…”

“…The preconditioning transforms these constraints into more general constraints (see e.g. Dostál et al [4]). Let us mention that H-TFETI has been successfully applied to the solution of nonlinear elliptic problems discretized by some hundred billions of nodal variables [4].…”