Classical and all-floating FETI methods for the simulation of arterial tissues

TL;DR

This paper explores the application of classical and all-floating FETI methods to efficiently simulate the elastic behavior of arterial tissues with complex geometries and anisotropic properties, demonstrating improved convergence and implementation advantages.

Contribution

It introduces and compares classical and all-floating FETI methods for arterial tissue simulation, highlighting the benefits of the all-floating approach in convergence and implementation.

Findings

All-floating FETI shows better convergence in simulations.

FETI methods effectively handle nonlinear anisotropic tissue models.

Limitations depend on material parameters.

Abstract

High-resolution and anatomically realistic computer models of biological soft tissues play a significant role in the understanding of the function of cardiovascular components in health and disease. However, the computational effort to handle fine grids to resolve the geometries as well as sophisticated tissue models is very challenging. One possibility to derive a strongly scalable parallel solution algorithm is to consider finite element tearing and interconnecting (FETI) methods. In this study we propose and investigate the application of FETI methods to simulate the elastic behavior of biological soft tissues. As one particular example we choose the artery which is - as most other biological tissues - characterized by anisotropic and nonlinear material properties. We compare two specific approaches of FETI methods, classical and all-floating, and investigate the numerical behavior of different preconditioning techniques. In comparison to classical FETI, the all-floating approach has not only advantages concerning the implementation but in many cases also concerning the convergence of the global iterative solution method. This behavior is illustrated with numerical examples. We present results of linear elastic simulations to show convergence rates, as expected from the theory, and results from the more sophisticated nonlinear case where we apply a well-known anisotropic model to the realistic geometry of an artery. Although the FETI methods have a great applicability on artery simulations we will also discuss some limitations concerning the dependence on material parameters.