In this chapter, we summarize the method of moments for surface and volume integral equations. In the first half, surface and volume modeling techniques are outlined along with the definitions of frequently used flat and curvilinear elements. Basis functions and differential operators (gradient, divergence, and curl) are given in curvilinear coordinates, and details of the MoM implementation are presented. Construction of the MoM matrix, numerical integrations, and careful handling of singular integrals are given in detail, as these constitute the main steps in the implementation. We conclude by providing volumetric modeling for material regions and several numerical examples.

Chapter Contents:

• 6.1 Scattering by Metallic Bodies
• 6.2 Curved Triangular and Quadrilateral Elements
• 6.3 Evaluation of MoM Matrix Entries
• 6.4 Volumetric Modeling
• 6.5 Scattering Examples
• 6.6 Step by Step Moment Method Example
• Bibliography

Inspec keywords: method of moments; matrix algebra; integral equations; electromagnetic wave scattering

Other keywords: three-dimensional scattering; differential operators; curvilinear elements; material regions; volume integral equations; integral equation methods; surface modeling techniques; MoM matrix; volume modeling techniques; volumetric modeling; surface integral equations; singular integrals; method of moments; numerical integrations; electromagnetics; careful handling; MoM implementation; flat elements; basis functions; curvilinear coordinates

Subjects: Algebra; Electromagnetic waves: theory; Function theory, analysis; Integral equations (numerical analysis); Numerical approximation and analysis; Algebra, set theory, and graph theory; Electromagnetic wave propagation