## Improving condition number and convergence of the surface integral-equation method of moments for penetrable bodies |

Optics Express, Vol. 20, Issue 15, pp. 17237-17249 (2012)

http://dx.doi.org/10.1364/OE.20.017237

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### Abstract

Most of the surface integral equation (SIE) formulations for composite conductor and/or penetrable objects suffer from balancing problems mainly because of the very different scales of the equivalent electric and magnetic currents. Consequently, the impedance matrix usually has high- or ill-condition number due to the imbalance between the different blocks. Using an efficient left and right preconditioner the elements of the impedance matrix are balanced. The proposed approach improves the matrix balance without modifying the underlying SIE formulation, which can be selected solely in terms of accuracy. The numerical complexity of this preconditioner is *O*(*N*) with *N* the number of unknowns, and it can be easily included on any existing SIE code implementation.

© 2012 OSA

**OCIS Codes**

(000.4430) General : Numerical approximation and analysis

(160.2100) Materials : Electro-optical materials

(260.2110) Physical optics : Electromagnetic optics

**ToC Category:**

Physical Optics

**History**

Original Manuscript: May 15, 2012

Revised Manuscript: June 26, 2012

Manuscript Accepted: June 26, 2012

Published: July 13, 2012

**Citation**

Luis Landesa, Marta Gómez Araújo, José Manuel Taboada, Luis Bote, and Fernando Obelleiro, "Improving condition number and convergence of the surface integral-equation method of moments for penetrable bodies," Opt. Express **20**, 17237-17249 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-15-17237

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