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An element‐by‐element method for heat conduction CAE including composite problems
Author(s) -
Buratynski Edward K.
Publication year - 1988
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620260114
Subject(s) - finite element method , dimension (graph theory) , element (criminal law) , factorization , stability (learning theory) , algorithm , mixed finite element method , operator (biology) , mathematical optimization , computer science , mathematics , structural engineering , engineering , law , biochemistry , chemistry , repressor , machine learning , political science , pure mathematics , transcription factor , gene
Mechanical computer aided engineering (CAE) implies large finite element problems due to the geometric complexity of the ‘true’ 3D designs. Application of the standard finite element technique is not practical for such problems because the direct solution of the global matrix equations is too costly. This paper considers the element‐by‐element implicit algorithm for the CAE application of transient heat conduction. The direct solution is avoided by an operator splitting or approximate factorization technique. This results in both the execution time and storage requirements for each time step being linearly proportional to the number of elements while retaining unconditional stability. However, the approximate factorization introduces additional truncation error and incorrect jump conditions at material interfaces. Detailed analyses and numerical experiments are carried out in one dimension to assess the nature and mechanism of these inaccuracies. A three dimensional implementation is then compared with one dimensional results. The need for an additional predictor–corrector element‐by‐element algorithm for 3D composite problems is also presented.