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New hybrid Laplace transform/finite element method for three‐dimensional transient heat conduction problem
Author(s) -
Chen Cha'oKuang,
Chen TzerMing
Publication year - 1991
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.1620320104
Subject(s) - laplace transform applied to differential equations , laplace transform , two sided laplace transform , finite element method , extended finite element method , inverse laplace transform , mathematics , laplace–stieltjes transform , mixed finite element method , mathematical analysis , method of fundamental solutions , mellin transform , green's function for the three variable laplace equation , hp fem , boundary knot method , laplace's equation , smoothed finite element method , partial differential equation , finite element limit analysis , fourier transform , fractional fourier transform , boundary element method , fourier analysis , structural engineering , engineering
The paper presents results obtained by the implementation of a new hybrid Laplace transform/finite element method developed by the authors. The present method removes the time derivatives from the governing differential equation using the Laplace transform and then solves the associated equation with the finite element method. Previously reported hybrid Laplace transform/finite element methods 1 have been confined to one nodal solution at a time. When applied to many nodes it takes an excessive amount of computer time. By using a similarity transform method on the matrix of the complex number coefficients this restriction is removed and the reported new method provides a more useful tool for the solution of linear transient problems. Test examples are used to show that the basic accuracy is comparable to that obtainable by analytical, finite difference and finite element methods.