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



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.


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.


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.


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



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

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