Finite Element Discretization of Piezothermoelastic Equations Using the Generalized Equation of Heat Conduction

2005 ◽  
Author(s):  
Zsolt Vi´zva´ry
Keyword(s):  
Finite Element ◽  
Heat Conduction ◽  
Generalized Equation ◽  
Finite Element Code ◽  
Spatial Discretization ◽  
Finite Element Discretization ◽  
Fourier’S Law ◽  
Galerkin’S Method ◽  
Element Discretization ◽  
Equation Of Heat Conduction

In this paper, the derivation of the finite element equations of piezothermoelasticity is presented using the classical and generalized Fourier’s law. Galerkin’s method is used to the spatial discretization of the equations. Based upon these equations, a finite element code is under development.

scholarly journals A PETSc-Based Parallel Implementation of Finite Element Method for Elasticity Problems

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Jianfei Zhang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Parallel Implementation ◽  
Good Choice ◽  
Finite Element Code ◽  
Finite Element Discretization ◽  
Element Analysis ◽  
Element Discretization ◽  
Elasticity Problems ◽  
Parallel Code

Starting a parallel code from scratch is not a good choice for parallel programming finite element analysis of elasticity problems because we cannot make full use of our existing serial code and the programming work is painful for developers. PETSc provides libraries for various numerical methods that can give us more flexibility in migrating our serial application code to a parallel implementation. We present the approach to parallelize the existing finite element code within the PETSc framework. Our approach permits users to easily implement the formation and solution of linear system arising from finite element discretization of elasticity problem. The main PETSc subroutines are given for the main parallelization step and the corresponding code fragments are listed. Cantilever examples are used to validate the code and test the performance.

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