The Infiniteness of Finite Elements – Explored through FEniCS
--Finite Element is an art to predict the future-- Klaus-Jurgen Bathe
Finite Element methods is one of the most widely used analysis techniques in engineering, technology and applied sciences and its popularity is expected to grow manifold in the coming years. This procedure which originated in the early 1940s as a method to solve complex elasticity and structural problems, is now used extensively to solve various problem of heat transfer and fluid flow with its reach extending well beyond electromagnetics. However, the development of finite element methods for solving practical engineering problems began with the advent of the digital computers. Finite element method, which is essentially a mathematical tool for solving Partial Differential Equations (generally referred as PDEs) has received widespread recognition for its effectiveness, capability and general applicability and employing Python further enhances it.
Python aids in the development of easy to use, intuitive, efficient and flexible softwares for solving the PDEs of the finite element methods and this talk will focus on one such software, named FEniCS. FEniCS is a powerful open-source package for solving PDEs. The FEniCS computing platform was created with the aim of automated solution to mathematical models through finite element methods allowing easy reproduction of mathematical formulation and rapid implementation of high performance solvers. Two case studies on the utlisation of the FeniCS package will be discussed subsequent to brief presentation on the concepts of finite elements methods and its implementation within the FeniCS Environment.
The talk will cover the following topics:
- Infiniteness of Finite Elements – 8 min
- Explored through FEniCS – 4 min
- Case Study #1 – 6 min
- Case Study #2 – 7 min
- Closing Remarks and Q & A session – 5 min
Elementary knowledge of Finite Element Theory with some experience in Python programming.
Gaurav Verma is a FEM enthiusiast and a passionate proponent of simulation sciences. He cultivated his love for python some years back and successfully employs the tools provided by the language to perform various numerical computations and engineering simulations. He is a Scientific Officer with Bhabha Atomic Research Centre, Mumbai and is presently a member of the Research Reactor Design and Projects Division. His field of interest is vibration of structures and Fluid-Structure Interaction.
- Github - https://github.com/gvverma
- LinkedIn - https://www.linkedin.com/in/gaurav-verma-3a236861/
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