GetFEM: Automated FE Modeling of Multiphysics Problems Based on a Generic Weak Form Language

This article presents the major mathematical and implementation features of a weak form language (GWFL) for an automated finite-element (FE) solution of partial differential equation systems. The language is implemented in the GetFEM framework and strategic modeling and software architecture choices both for the language and the framework are presented in detail. Moreover, conceptual similarities and differences to existing high-level FE frameworks are discussed. Special attention is given to the concept of a generic transformation mechanism that contributes to the high expressive power of GWFL, allowing to interconnect multiple computational domains or parts of the same domain. Finally, the capabilities of the language for expressing strongly coupled multiphysics problems in a compact and readable form are shown by means of modeling examples.

Automated summary

This article introduces a weak form language (GWFL) for an automated finite-element solution of partial differential equation systems, implemented in the GetFEM framework. It discusses strategic modeling and software architecture choices for the language and framework, as well as the conceptual similarities and differences to existing high-level FE frameworks. The article highlights the concept of a generic transformation mechanism and demonstrates the language's capabilities for expressing multiphysics problems in a compact and readable form.