Method of Moments
Also known as: MoM, Boundary element method (electromagnetics)
The Method of Moments (MoM) is a powerful numerical technique for solving electromagnetic boundary integral equations derived from Maxwell equations. Pioneered by Roger Harrington in 1968, MoM discretizes only radiating surfaces and boundaries (antennas, conductors, dielectrics), not the surrounding space, making it efficient for radiation and scattering problems. MoM remains the standard tool for antenna design, electromagnetic compatibility analysis, and RF/microwave engineering.
Key highlights
- Only radiating surfaces discretized; no mesh for free space, reducing problem size
- Naturally handles unbounded (radiation) problems with proper Green functions
- Efficient for thin structures and open-region geometries (antennas, FSS, metamaterials)
- Can directly compute far-field radiation patterns and impedance
Intuition
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How it works
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When to use it
MoM is ideal for radiation and scattering problems: antenna analysis, electromagnetic shielding, RCS (radar cross section) prediction, and EMC (electromagnetic compatibility) assessments. Efficient when the radiating structure is much smaller than infinite space. Less efficient for large enclosed volumes with complex dielectrics; finite element methods (FEM) may be better. Requires careful mesh generation for accurate results.
Strengths & limitations
- Only radiating surfaces discretized; no mesh for free space, reducing problem size
- Naturally handles unbounded (radiation) problems with proper Green functions
- Efficient for thin structures and open-region geometries (antennas, FSS, metamaterials)
- Can directly compute far-field radiation patterns and impedance
- Dense matrix system grows as O(N^2) memory and O(N^3) compute time; scales poorly for large problems
- Difficult to include complex dielectrics or lossy materials; Green function becomes complicated
- Requires careful treatment of singular integrals on the mesh; accuracy sensitive to mesh quality
- Poor for very small structures (wavelength << geometry) or high frequencies where small details matter
Common pitfalls
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Applications
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Frequently asked
How does MoM differ from FEM (Finite Element Method)?
MoM discretizes only boundaries and radiating surfaces; FEM meshes the entire domain. MoM is superior for unbounded (radiation) problems; FEM is better for enclosed structures with complex materials. MoM scales worse but avoids artificial boundaries.
What is a basis function and why does it matter?
Basis functions represent the unknown surface currents (e.g., triangular patches, sinusoids). Finer basis functions give higher accuracy but larger matrix. Choice affects convergence and computational cost.
How do I know when my mesh is fine enough?
The rule of thumb is segments smaller than λ/10 (where λ is free-space wavelength). Check convergence: refine the mesh and compare results; converged results are reliable.
Can MoM handle lossy materials and conductivity?
Yes, but it complicates the Green function and matrix formulation. For lossy dielectrics, volume integrals become necessary, partially offsetting the MoM advantage. MoM is most efficient for good conductors.
Sources
- 1.Harrington, R. F. (1968). Field Computation by Moment Methods. Macmillan.
- 2.Gibson, W. C. (1980). The method of moments in electromagnetics. Chapman and Hall.
- 3.Wandzura, S., & Xia, G. (1997). Computing the characteristic modes of complex structures. IEEE Transactions on Antennas and Propagation, 45(3), 467-475.
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Cite this page
ScholarGate. (2026, June 3). Method of Moments. ScholarGate. https://scholargate.app/electrical-engineering/method-of-moments