FEniCS: Automated adaptive high-performance FEM solution of PDE in an open source domain specific software framework
Speaker: Johan Jansson, Assistant Professor, KTH
Title: FEniCS: Automated adaptive high-performance FEM solution of PDE in an open source domain-specific software framework
I started the FEniCS project in 2003 together with colleagues with the goal of Automation of Computational Mathematical Modeling (ACMM) as the modern manifestation of the basic principle of science: formulating mathematical equations (modeling) and solving equations (computation). The vision of FEniCS is to set a new standard towards the goals of generality, efficiency, and simplicity, concerning mathematical methodology, implementation, and application. ACMM includes the key steps of Automation of (a) discretization of partial differential equations (PDE), (b) solution of discrete systems, (c) error control of discrete solutions, (d) optimization and (e) modeling. FEniCS is based on adaptive finite element methods (FEM).
We have today to a large extent realized this ambitious vision. FEniCS defines a mathematical Python-based domain-specific language (DSL) for weak forms including automatic symbolic differentiation, which allows the automated formulation and solution of general PDE and FEM with goal-oriented adaptive error control. Sparse distributed-memory linear algebra via the highly scalable PETSc library is abstracted and allows scalable solution with tens of thousands of cores on supercomputers.
In FEniCS we have been able to provide a solution to one of the large open problems in science: prediction of aerodynamics and turbulent flow. I will show our mathematical Direct FEM Simulation (DFS) solution to the problem, the FEniCS realization and computational results in connection to the High Lift Prediction workshops organized by NASA and Boeing.
I am leading MOOC-HPFEM based on FEniCS, which is the largest MOOC at KTH with 10000+ participants from industry and universities. The basis is web-based mathematical programming in Jupyter and MSO4SC with FEniCS for effective learning of abstract concepts. Pervasive access to free computational resources allows easy access to open source FEniCS automated solution of PDE for anyone with a web browser.
I outline the future vision and suggest potential directions of collaboration.
Johan Jansson is an Assistant Professor in Scientific Computing at KTH and leads the CFD research line at BCAM – Basque Center for Applied Mathematics. His areas of expertise include automated computational mathematical modelling based on adaptive finite element methods: mathematical methods, algorithms and massively parallel software implementations with applications in computational mechanics, realized in FEniCS/FEniCS-HPC which he was part of starting. Based on high-profile national and international funding for research projects (Severo Ochoa, EU H2020, ELKARTEK, PRACE, etc.) he has been able to build up a large joint research environment between KTH-BCAM and attract both post-docs and PhD students from top institutions in the field: Stanford, Politecnico di Milano, Barcelona Supercomputing Center, Ecole Polytechnique and Texas A&M.