Finite element solution of transient heat conduction using iterative solvers

Mile R. Vujičić (School of Engineering, Materials Research Centre, University of Swansea, Swansea, UK)

Engineering Computations

ISSN: 0264-4401

Publication date: 1 June 2006

Abstract

Purpose

To provide an analysis of transient heat conduction, which is solved using different iterative solvers for graduate and postgraduate students (researchers) which can help them develop their own research.

Design/methodology/approach

Three‐dimensional transient heat conduction in homogeneous materials using different time‐stepping methods such as finite difference (Θ explicit, implicit and Crank‐Nicolson) and finite element (weighted residual and least squared) methods. Iterative solvers used in the paper are conjugate gradient (CG), preconditioned gradient, least square CG, conjugate gradient squared (CGS), preconditioned CGS, bi‐conjugate gradient (BCG), preconditioned BCG, bi‐conjugate gradient stabilized (BCGSTAB), reconditioned BCGSTAB and Gaussian elimination with incomplete Cholesky factorization.

Findings

Provides information on which time‐stepping method is the most accurate, which solver is the fastest to solve a symmetric and positive system of linear matrix equations of all those considered.

Practical implications

Fortran 90 code given as an abstract can be very useful for graduate and postgraduate students to develop their own code.

Originality/value

This paper offers practical help to an individual starting his/her research in the finite element technique and numerical methods.

Keywords

Citation

Vujičić, M. (2006), "Finite element solution of transient heat conduction using iterative solvers", Engineering Computations, Vol. 23 No. 4, pp. 408-431. https://doi.org/10.1108/02644400610661172

Download as .RIS

Publisher

:

Emerald Group Publishing Limited

Copyright © 2006, Emerald Group Publishing Limited

Please note you might not have access to this content

You may be able to access this content by login via Shibboleth, Open Athens or with your Emerald account.
If you would like to contact us about accessing this content, click the button and fill out the form.
To rent this content from Deepdyve, please click the button.