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 this article is on the design and implementation 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 the flow of cerebrospinal fluid in the human brain and the mixed-dimensional model of electrodiffusion in the brain tissue.

我们介绍了用于解决界面耦合多物理场问题的软件工具箱 HAZniCS。 HAZniCS 是一套模块，它将著名的有限元离散化 FEniCS 框架与求解器和图形库 HAZmath 相结合。本文的重点是设计和实现稳健且高效的求解器算法，该算法解决与大脑生物力学应用中经常遇到的物理问题的复杂界面耦合相关的问题。数值算法和方法的稳健性和效率在几个数值示例中得到了体现，即模拟人脑中脑脊液流动的达西-斯托克斯方程和脑组织中电扩散的混合维模型。