A Geometrical Approach to 3D FEM Discretization of the Poisson Equation

A. Smirnov and H. Zhang (USA)


Finite element method, Poisson equation, unstructured meshes


A simple and lightweight 3D FEM solver was designed from general principles, and implemented in the multi physics modeling framework. The standard finite element method was applied for the discretization of the Poisson equation on tetrahedral meshes. Geometrical integration has lead to simple expressions of matrix coefficients in terms of easily computed local mesh variables. Numerical implementation of a simple Jacoby iterative scheme was demonstrated and validated on heat transfer problems.

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