Premium
Solution of the partial eigenproblem by iterative methods
Author(s) -
Papadrakakis M.
Publication year - 1984
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.1620201209
Subject(s) - conjugate gradient method , iterative method , mathematics , rayleigh quotient , derivation of the conjugate gradient method , relaxation (psychology) , finite element method , quotient , matrix (chemical analysis) , conjugate residual method , mathematical optimization , mathematical analysis , algorithm , eigenvalues and eigenvectors , computer science , combinatorics , gradient descent , physics , quantum mechanics , machine learning , artificial neural network , composite material , thermodynamics , social psychology , psychology , materials science
A combined iterative method is formulated for the partial solution of the eigenproblem Ax = λ Bx that arises from the application of the finite element method. The method is a combination of the conjugate gradient (CG) method and the symmetric successive co‐ordinate overrelaxation (SSCOR) method. Both of these methods belong to the same family of iterative methods which retain their vectorial form and approach the solution by seeking stationary points of the Rayleigh quotient. The formulation consists in splitting a characteristic matrix into the sum of two matrices, one of which corresponds to the SSCOR matrix, and then accelerating the associated iteration using the CG. The behaviour of the method is illustrated for five test cases and comparisons are made with other iterative methods. The influence of the relaxation parameter ω on the computational efficiency of the methods is also studied.