Premium
Scaling and sparsity in an accurate implementation of the method of moments in 2‐D
Author(s) -
Sandström SvenErik,
Akeab Imad K.
Publication year - 2014
Publication title -
radio science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.371
H-Index - 84
eISSN - 1944-799X
pISSN - 0048-6604
DOI - 10.1002/2013rs005357
Subject(s) - mathematics , integral equation , mathematical analysis , kernel (algebra) , scaling , a priori and a posteriori , matrix (chemical analysis) , basis function , method of moments (probability theory) , mathematical optimization , geometry , philosophy , statistics , materials science , epistemology , combinatorics , estimator , composite material
The integral equations of electromagnetic scattering are often solved numerically by means of the method of moments. At high frequencies, this method typically leads to a large linear system with a dense matrix. The use of higher‐order basis functions is a means to improve the accuracy. B‐splines are used here for a two‐dimensional test bed study that avoids the complexity of 3‐D implementation. For smooth convex scatterers one may use a priori knowledge about the oscillatory behavior of the solution to reformulate the integral equation. This fast scale of variation is included in the kernel of the integral equation. An extension of this idea deals with the variation in the shadow, particularly for circular geometry, and is an improvement that is presented in this study. Generally, the transverse electric (TE) case is less studied at high frequencies and our numerical results therefore relate to this harder problem. A sparse matrix can be obtained by modification of the integration path in the integral equation. The decay of the modified kernel makes this possible for high frequencies but the modified path reduces the accuracy in the deep shadow. This study investigates these modified paths for the case where the shadow region is not omitted from the formulation.