Iterative Solvers in the Finite Element Solution of Transient Heat Conduction
Mile R. Vujičić, Steve G.R. Brown · FME Transaction · 2004
In this paper three-dimensional transient heat conduction in homogeneous materials using different iterative solvers based on the conjugate gradient method are studied. The methods used are preconditioned conjugate gradient least square conjugate gradient, conjugate gradient squared, preconditioned conjugate squared, biconjugate gradient, preconditioned bi-conjugate gradient, bi-conjugate gradient stabilized and preconditioned bi-conjugate stabilized method as well as a Gaussian elimination method with incomplete Cholesky factorisation as a comparison. Time dependence is solved using both the finite difference and the finite element scheme. The finite difference scheme includes backward and forward Euler method and method (Crank-Nicholson). The finite element scheme includes the weighted residual method and the least squares method. For the analysis, in the aim to analyse dependence between numerical scheme and obtained temperatures, we use a brick that is divided into different number 8-noded or 20-noded hexahedral elements with Dirichlet boundary conditions.