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Sparsity pattern extraction for assembly of KKT‐like matrices in multibody dynamics
Author(s) -
Hofmeister Benedikt,
Gebhardt Cristian Guillermo,
Hente Christian,
Rolfes Raimund
Publication year - 2018
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201800105
Subject(s) - karush–kuhn–tucker conditions , solver , computer science , context (archaeology) , finite element method , matrix (chemical analysis) , iterative method , sparse matrix , constraint (computer aided design) , mathematical optimization , computational science , algorithm , mathematics , geometry , engineering , programming language , structural engineering , paleontology , materials science , physics , quantum mechanics , gaussian , composite material , biology
The implicit dynamic solution of multibody and finite element simulations with kinematic constraints requires the assembly of KKT‐like matrices, which are constant in structure, but unsymmetric in the most general case. Basically, the numerical solution is computed by means of a Newton‐Raphson iterative scheme and applying a direct sparse solver in this context demands a reordering step prior to the actual iterative solution procedure. This means that the sparsity pattern of the KKT structure has to be known in advance for all possible configurations and loading situations that are going to be employed along each stand along simulation step. In this contribution, we present a scheme, in which the sparsity pattern is extracted dynamically from the assembly code of KKT‐like matrices. The underlying sparse scheme is transparent to the element and constraint iteration matrix assembly. This is enabled by exploiting the structure and order of events during the element matrix assembly. The proposed strategy is implemented with an object‐oriented programming style in a modern Fortran 2008 environment.