scholarly journals A spectral element method for solving the Pennes bioheat transfer equation by using triangular and quadrilateral elements

2012 ◽  
Vol 36 (12) ◽  
pp. 6031-6049 ◽  
Author(s):  
Mehdi Dehghan ◽  
Mania Sabouri
Keyword(s):  
Transfer Equation ◽  
Spectral Element Method ◽  
Spectral Element ◽  
Bioheat Transfer ◽  
Quadrilateral Elements ◽  
Bioheat Transfer Equation ◽  
Element Method

Spectral Element Approach for Coupled Radiative and Conductive Heat Transfer in Semitransparent Medium

2007 ◽  
Vol 129 (10) ◽  
pp. 1417-1424 ◽  
Author(s):  
J. M. Zhao ◽  
L. H. Liu
Keyword(s):  
Heat Transfer ◽  
Transfer Equation ◽  
Spectral Element Method ◽  
Radiative Transfer Equation ◽  
Spectral Element ◽  
Conductive Heat Transfer ◽  
Conductive Heat ◽  
Element Approach ◽  
Semitransparent Medium ◽  
Element Method

A spectral element method is presented to solve coupled radiative and conductive heat transfer problems in multidimensional semitransparent medium. The solution of radiative energy source is based on a second order radiative transfer equation. Both the second order radiative transfer equation and the heat diffusion equation are discretized by spectral element approach. Four various test problems are taken as examples to verify the performance of the spectral element method. The h-and the p-convergence characteristics of the spectral element method are studied. The convergence rate of p refinement for different values of Planck number follows the exponential law and is superior to that of h refinement. The spectral element method has good property to tolerate skewed meshes. The predicted dimensionless temperature distributions determined by the spectral element method agree well with the results in references. The presented method is very effective to solve coupled radiative and conductive heat transfer in semitransparent medium with complex configurations and demands little on the quality of mesh.

scholarly journals The Implementation of Spectral Element Method in a CAE System for the Solution of Elasticity Problems on Hybrid Curvilinear Meshes

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Dmitriy Konovalov ◽  
Anatoly Vershinin ◽  
Konstantin Zingerman ◽  
Vladimir Levin
Keyword(s):  
Mathematical Simulation ◽  
High Performance ◽  
Spectral Element Method ◽  
New Technologies ◽  
Spectral Element ◽  
High Tech ◽  
Engineering Analysis ◽  
Elasticity Problems ◽  
Cae System ◽  
Element Method

Modern high-performance computing systems allow us to explore and implement new technologies and mathematical modeling algorithms into industrial software systems of engineering analysis. For a long time the finite element method (FEM) was considered as the basic approach to mathematical simulation of elasticity theory problems; it provided the problems solution within an engineering error. However, modern high-tech equipment allows us to implement design solutions with a high enough accuracy, which requires more sophisticated approaches within the mathematical simulation of elasticity problems in industrial packages of engineering analysis. One of such approaches is the spectral element method (SEM). The implementation of SEM in a CAE system for the solution of elasticity problems is considered. An important feature of the proposed variant of SEM implementation is a support of hybrid curvilinear meshes. The main advantages of SEM over the FEM are discussed. The shape functions for different classes of spectral elements are written. Some results of computations are given for model problems that have analytical solutions. The results show the better accuracy of SEM in comparison with FEM for the same meshes.

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