High Performance Finite Element Modeling I and II

Learn how to make cutting edge adaptive FEM simulations from top researchers at KTH. These two courses targets engineers in industry, or engineering students at masters and doctoral level/or towards the end of a bachelor study.

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Basic knowledge of linear algebra and calculus is a prerequisite to understand the content and therefore strongly recommended. Participants are advised to take part I before part II.

Engineering, Mathematics, Computer Science

​​High Performance Finite Element Modeling

Engineering simulations are rapidly becoming fundamental in virtually all industrial sectors, from medicine to energy, aerospace and beyond. In these courses you will learn the breakthrough general adaptive finite element methods (AFEM) and open source FEniCS software that will enable you to solve the grand challenges in science and engineering.

These courses targets engineers in industry, or engineering students at masters and doctoral level/or towards the end of a bachelor study. Learners that achieve top grades in the first course, in a series of two courses will be offered access to a supercomputer, and more advanced simulations of turbulent flow.

In the second course, you will carry out advanced, time-resolved parallel simulations of aerodynamics, allowing you to understand the mechanism of flight. You will also learn how to make cutting-edge adaptive FEM supercomputing simulations of aerodynamic principles from top researchers at KTH.

Part II is now open.

Sign up for High Performance Finite Element Modeling, part II

Part I of this course are now archived. None of the teachers participate actively in the classroom anymore but you can still access certain material.

Learning outcomes

After completing part I you will be able to:

  • derive AFEM for general PDE with relevance in industry: the Navier-Stokes equations for incompressible flow, the wave equation, linear elasticity, and multi-physics combinations of these equations.
  • derive fundamental properties of the methods, which are key for robustness and efficiency such as: energy conservation, stability, and a priori and a posteriori error estimates.
  • apply general FEM-algorithms such as assembly, adaptivity and local mesh refinement and have a basic understanding of their implementation in FEniCS-HPC.

After completing part II you will be able to:

  • How to describe the Direct FEM Simulation (DFS) methodology, including adaptive error control, slip boundary condition, and turbulent dissipation.
  • Methods for deriving stability estimates for the cG(1)cG(1) FEM applied to Navier-Stokes equations.
  • How to account for general FEM-algorithms such as assembly, adaptvity, and local mesh refinement and have a basic understanding of their implementation in FEniCS-HPC.
  • How to account for parallel data structures and algorithms for distributed memory architectures in a general FEM-framework and inspect their implementation in FEniCS-HPC: distributed computational mesh, ghost entities, distributed sparse linear and non-linear algebra, local mesh refinement by bisection for a distributed computational mesh, and general goal-oriented adaptive error control.
  • Ways to estimate the performance of different parallel algorithms.
  • How to use a general framework, such as FEniCS-HPC, to model and solve general PDE on a supercomputer, and specifically aerodynamics problems with DFS.

Faculty and research

Laura Saavedra.

Laura Saavedra, Teacher (Lecturer) (Universidad Politécnica de Madrid, UPM)
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Rahul Kumar

Rahul Kumar, Teacher (Postdoc) (Basque Center for Applied Mathematics, BCAM)
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Margarida Moragues,Teacher (Postdoc) (Basque Center for Applied Mathematics, BCAM)
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Aircraft simulation, FEniCS project and HPFEM

Sponsors
The courses in High Performance Finite Element Modeling are made possible with the support from:

  • The Swedish National Infrastructure for Computing (SNIC) with the SNIC Science Cloud (SSC) resource.
  • The EU Horizon 2020 project Mathematical Modelling, Simulation and Optimization for Societal Challenges with Scientific Computing (MSO4SC) with the Finis Terrae II supercomputing resource at CESGA - Centro de Supercomputación de Galicia.
  • PDC - Center for High-Performance Computing with the Beskow supercomputing resource.
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