Solution of nonlinear thermal transient problems by a reduction method
Abstract
A new algorithm for solving transient thermal problems in a reduced subspace of the original space of discretization is described. The basis of the subspace is formed by using the system response at the first time step (or an approximation to it) and a set of orthogonal vectors obtained by the algorithm of Lanczos. Derivatives of these vectors are included when treating nonlinear cases. The method allows one to handle the sharp gradients that appear in thermally loaded structures, and the response is accurately predicted by using only a small number of degrees of freedom in the reduced system. The algorithm is specially well suited for treating largescale problems. Examples dealing with one, two and threedimensional cases of linear and nonlinear conduction problems are presented.
 Publication:

International Journal for Numerical Methods in Engineering
 Pub Date:
 June 1986
 DOI:
 10.1002/nme.1620230604
 Bibcode:
 1986IJNME..23.1023C
 Keywords:

 Finite Element Method;
 Heat Transfer;
 Thermal Analysis;
 Transient Heating;
 Linear Systems;
 Nonlinear Systems;
 Temperature Dependence;
 Temperature Profiles;
 Vectors (Mathematics);
 Fluid Mechanics and Heat Transfer