Original title: Dynamic Contact Problems in Bone Neoplasm Analyses and the Primal-Dual Active Set (PDAS) Method
Authors: Nedoma, Jiří
Document type: Papers
Conference/Event: Applications of Mathematics 2015, Prague (CZ), 2015-11-18 / 2015-11-21
Year: 2015
Language: eng
Abstract: In the contribution growths of the neoplasms (benign and malignant tumors and cysts), located in a system of loaded bones, will be simulated. The main goal of the contribution is to present the useful methods and efficient algorithms for their solutions. Because the geometry of the system of loaded and possible fractured bones with enlarged neoplasms changes in time, the corresponding mathematical models of tumor’s and cyst’s evolutions lead to the coupled free boundary problems and the dynamic contact problems with or without friction. The discussed parts of these models will be based on the theory of dynamic contact problems without or with Tresca or Coulomb frictions in the visco-elastic rheology. The numerical solution of the problem with Coulomb friction is based on the semi-implicit scheme in time and the finite element method in space, where the Coulomb law of friction at every time level will be approximated by its value from the previous time level. The algorithm for the corresponding model of friction will be based on the discrete mortar formulation of the saddle point problem and the primal-dual active set algorithm. The algorithm for the Coulomb friction model will be based on the fixpoint algorithm, that will be an extension of the PDAS algorithm for the Tresca friction. In this algorithm the friction bound is iteratively modified using the normal component of the Lagrange multiplier. Thus the friction bound and the active and inactive sets are updated in every step of the iterative algorithm and at every time step corresponding to the semi-implicit scheme.
Keywords: Coulomb and Tresca frictions; dynamic contact problems; FEM; mathematical models of neoplasms - tumors and cysts; mortar approximation; PDAS algorithm; semi-implicit scheme; variational formulation
Host item entry: Applications of Mathematics 2015, ISBN 978-80-85823-65-3

Institution: Institute of Computer Science AS ČR (web)
Document availability information: Fulltext is available at external website.
External URL: http://am2015.math.cas.cz/proceedings/contributions/nedoma.pdf
Original record: http://hdl.handle.net/11104/0257300

Permalink: http://www.nusl.cz/ntk/nusl-202741


The record appears in these collections:
Research > Institutes ASCR > Institute of Computer Science
Conference materials > Papers