HAZniCS -- Software Components for Multiphysics Problems

TL;DR

This paper presents HAZniCS, a software toolbox that integrates finite element methods with advanced solvers to efficiently address complex interface-coupled multiphysics problems, demonstrated through brain biomechanics applications.

Contribution

The paper introduces a modular software suite combining FEniCS and HAZmath for robust multiphysics simulations with specialized solver algorithms.

Findings

Demonstrated robustness and efficiency in brain fluid flow simulations.

Successfully modeled electrodiffusion in brain tissue.

Validated solver performance with numerical examples.

Abstract

We introduce the software toolbox HAZniCS for solving interface-coupled multiphysics problems. HAZniCS is a suite of modules that combines the well-known FEniCS framework for finite element discretization with solver and graph library HAZmath. The focus of the paper is on the design and implementation of a pool of robust and efficient solver algorithms which tackle issues related to the complex interfacial coupling of the physical problems often encountered in applications in brain biomechanics. The robustness and efficiency of the numerical algorithms and methods is shown in several numerical examples, namely the Darcy-Stokes equations that model flow of cerebrospinal fluid in the human brain and the mixed-dimensional model of electrodiffusion in the brain tissue.