Solving the Partitioned Heat Equation Using FEniCS and preCICE

FEniCS is a general finite element library with high flexibili ty and very broad functionality. It can be used to solve a wide range of problems from science and engineering using the finite element method; corresponding examples can be found, for example, in the FEniCS documentation. We want to investigate how FEniCS-based solvers can be used to solve coupled problems in a partitioned approach. This talk explains how to solve the partitioned heat equation – a simple model problem for coupled problems. In our setup, two instances of FEniCS are used to solve the heat equation on two different domains that are non-overlapping. The two domains are only interacting with each other through a common coupling interface, where heat is exchanged. On the algorithmic level, the two domains are coupled at the interface via Dirichlet-Neumann coupling. The coupling and the communication between the two FEniCS-based solvers are realized with the coupling library preCICE. While the FEniCS-based heat equation solver and preCICE were already available, additional glue code (adapter) had to be developed to allow interfacing between FEniCS and preCICE. Note that all the software that is necessary for implementing the proposed setup is freely available as open-source. Beyond this study of a proof-of-concept kind, we plan to reuse components of this setup to perform more complex simulations - for example in the area of conjugate heat transfer. Here, the already existing FEniCS-based heat equation solver can be coupled with an appropriate flow solver using preCICE. Additionally, as FEniCS is a general finite element framework, other physical phenom ena may be simulated to solve different coupled problems.     «

FEniCS is a general finite element library with high flexibili ty and very broad functionality. It can be used to solve a wide range of problems from science and engineering using the finite element method; corresponding examples can be found, for example, in the FEniCS documentation. We want to investigate how FEniCS-based solvers can be used to solve coupled problems in a partitioned approach. This talk explains how to solve the partitioned heat equation – a simple model problem for coupled p...     »