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Repairing near‐singularity for dense EMC problems by adaptive basis techniques
Author(s) -
Verbeek Menno E.
Publication year - 2000
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/1099-1506(200010/12)7:7/8<617::aid-nla215>3.0.co;2-a
Subject(s) - preconditioner , mathematics , singularity , solver , discretization , computation , basis (linear algebra) , basis function , mathematical analysis , algorithm , iterative method , mathematical optimization , geometry
A standard boundary element method discretization for the electromagnetic compatibility problem is analysed, revealing the near‐singularity of the dense linear system for the lower frequency range. Next, a new basis transformation is presented, that separates the dominating capacitive effects from the small, but important, inductive effects. On this basis, a sparse approximate inverse is constructed that is used not only as a preconditioner but also as a smoother for a multi‐level preconditioner. The number of matrix‐vector multiplications for the iterative solver is further reduced by reusing information: Ritz vectors, obtained from previous right‐hand side solves, are injected into the search space of GMRESR, thereby skipping the stagnation phase. Reuse of information from the previous frequency computations has also been attempted, but this is less effective. Test results for the different methods are presented and compared. Copyright © 2000 John Wiley & Sons, Ltd.