Computational Mathematics and Scientific Computing Seminar

Towards a Parallel Solver Environment for the Numerical Simulation of Arterial Wall Models

Speaker: Axel Klawonn, University of Duisburg-Essen

Location: Warren Weaver Hall 1302

Date: Oct. 15, 2010, 10 a.m.


The treatment of arteriosclerosis by a ballon angioplasty involves large deformations of the arterial walls. The numerical simulation of these large deformations is a challenging task which involves many computational state of the art techniques. In this talk, a computational framework for the numerical simulation of large elastic deformations is discussed. The mechanical behavior of arterial walls in the physiological range can be described by anisotropic, hyperelastic elasticity models. Different models can be considered. Each of them is represented by a polyconvex strain energy function in order to guarantee the existence of minimizers. Discretization of the three dimensional models by the finite element method usually results in a large number of equations which are solved using FETI domain decomposition methods suitable for parallel computing. A computational framework using a Newton-Krylov-FETI approach for the solution of the discretized models will be discussed and applied to different material wall models and geometries. The arterial geometries are obtained by intravascular ultrasound (IVUS) and virtual histology. Material parameters obtained by tension tests are considered. This presentation is based on joint work with Oliver Rheinbach, Faculty of Mathematics, University of Duisburg-Essen and Dominik Brands, Sarah Brinkhues, and J¨org Schr¨oder, Institute of Mechanics, Division of Civil Engineering, Faculty of Engineering, University of Duisburg-Essen.