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Optimal FEM solutions of one‐dimensional EM problems
Author(s) -
Petrović V. V.,
Popović B. D.
Publication year - 2001
Publication title -
international journal of numerical modelling: electronic networks, devices and fields
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.249
H-Index - 30
eISSN - 1099-1204
pISSN - 0894-3370
DOI - 10.1002/1099-1204(200101/02)14:1<49::aid-jnm395>3.0.co;2-z
Subject(s) - classification of discontinuities , finite element method , mathematics , mathematical analysis , basis function , basis (linear algebra) , field (mathematics) , node (physics) , domain (mathematical analysis) , ranging , plane (geometry) , geometry , computer science , engineering , structural engineering , pure mathematics , telecommunications
Simple basis functions for weak and strong one‐dimensional FEM formulations are proposed. These functions are of arbitrary order, of hierarhical type, and are not node based. They also satisfy automatically continuity conditions on the boundaries between elements and on medium discontinuities, for both the total field and (partial) scattered field formulations. The functions are applied in six different formulations of the FEM solution of a plane‐wave propagation in (continuously and/or discontinuously) inhomogeneous medium. The error of the results is shown against the number of unknowns, for the order of elements ranging from 1 to 14. It is shown that all six formulations yield very accurate results, and that, with respect to the number of unknowns, entire‐domain approximations (i.e. elements of higher order) are optimal. Copyright © 2001 John Wiley & Sons, Ltd.