Title :
MATHEMATICA notebook for computing tetrahedral finite element shape functions and matrices for the Helmholtz equation
Author :
Franco, Marcos A R ; Passaro, Angelo ; Machado, Jose M.
Author_Institution :
Inst. de Estudos Avancados, Contro Tecnico Aeroespacial, Brazil
fDate :
9/1/1998 12:00:00 AM
Abstract :
A MATHEMATICA notebook to compute the elements of the matrices which arise in the solution of the Helmholtz equation by the finite element method (nodal approximation) for tetrahedral elements of any approximation order is presented. The results of the notebook enable a fast computational implementation of finite element codes for high order simplex 3D elements reducing the overheads due to implementation and test of the complex mathematical expressions obtained from the analytical integrations. These matrices can be used in a large number of applications related to physical phenomena described by the Poisson, Laplace and Schrodinger equations with anisotropic physical properties
Keywords :
Helmholtz equations; engineering computing; finite element analysis; mathematics computing; matrix algebra; physics computing; software packages; FEM; Helmholtz equation; MATHEMATICA notebook; fast computational implementation; finite element codes; high order simplex 3D elements; matrices; nodal approximation; tetrahedral finite element shape functions; Anisotropic magnetoresistance; Application software; Finite element methods; Geometry; Laplace equations; Poisson equations; Schrodinger equation; Shape; Software tools; Testing;
Journal_Title :
Magnetics, IEEE Transactions on
