Lanczos method for heat conduction analysis

✍ Scribed by Bahram Nour-Omid

• Publisher: John Wiley and Sons
• Year: 1987
• Tongue: English
• Weight: 576 KB
• Volume: 24
• Category: Article
• ISSN: 0029-5981
• DOI: 10.1002/nme.1620240117

✦ Synopsis

An analysis technique that uses the Lanczos vectors to construct a Reyleigh-Ritz solution for the transient heat conduction problem is presented. The Lanczos vectors are derived from the heat supply vector and incorporate all the information peculiar to a given problem. They are orthonormal with respect to the heat capacitance matrix and are generated with a minimum of computational effort. Furthermore, an error bound is derivcd that can be used to terminate the Lanczos algorithm as soon as the number of vectors required to obtain a desired degree of accuracy has been generated. A summary of the algorithm is presented and the accuracy and efficiency of the method i s illustrated using a numerical example.