Polyhedral FE

Implementation of Polyhedral Finite Elements: with application to heat transfer

Author

Zoltan Jozefik
Karthik Chittepu
Sheema Kooshapur

Supervisors:

David Franke,
Technische Universität München

Dr. Matthias Lambrecht,
P+Z Engineering GmbH

Abstract

Finite element procedures are now an important and frequently indispensable part of engineering analysis and design. Finite element computer programs are widely used in practically all branches of engineering. It is a flexible numeric procedure both for interpolation and approximation of the solution of partial differential equations. The PDE is approximated by a linear Galerkin finite element, which uses piecewise linear weight and basis functions. The resulting integral equation induces a system of linear equations, which needs to be solved with appropriate methods.

With the increase in the complexity on engineering problems the necessity for the extension of the standard elements has come into light. The arbitrary polyhedral finite elements lead to a greater flexibility in domain decomposition. A general simple local coordinate system, the natural element coordinates, was developed, which makes a formulation of interpolation functions on polyhedral elements possible that are independent of the dimension of the space, of the localization and vertex number.

The purpose of the project is to develop polyhedral finite elements, by implementing a numerical method to calculate the interpolation function at a particular point and integrating it with a finite element code for the calculating of unknowns. Reliability of these elements is tested by implementing them for heat transfer problems and visualizing the results and by comparing it with the analytical results.

Keywords

Finite element method, polyhedral elements, Voronoi decomposition, Heat transfer

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