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Multilevel matrix decomposition algorithm for analysis of electrically large electromagnetic problems in 3‐D
Author(s) -
Rius Juan M.,
Parrón Josep,
Úbeda Eduard,
Mosig Juan R.
Publication year - 1999
Publication title -
microwave and optical technology letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.304
H-Index - 76
eISSN - 1098-2760
pISSN - 0895-2477
DOI - 10.1002/(sici)1098-2760(19990805)22:3<177::aid-mop8>3.0.co;2-2
Subject(s) - conjugate gradient method , biconjugate gradient method , matrix (chemical analysis) , basis function , mathematics , piecewise , discretization , matrix decomposition , iterative method , algorithm , planar , mathematical analysis , computer science , physics , nonlinear conjugate gradient method , eigenvalues and eigenvectors , materials science , quantum mechanics , composite material , computer graphics (images) , gradient descent , machine learning , artificial neural network
The multilevel matrix decomposition algorithm (MLMDA) has been implemented in 3‐D for the solution of large electromagnetic problems. The electric field integral equation is solved for arbitrary surfaces discretized using N Rao, Wilton, and Glisson basis functions. The MLMDA accelerates the matrix–vector products in a conjugate gradient or biconjugate gradient iterative solution of the resulting system of equations. The computational cost of each iteration is proportional to N log 2 N for very large problems, and is particularly small for planar or piecewise planar objects. ©1999 John Wiley & Sons, Inc. Microwave Opt Technol Lett 22: 177–182, 1999.