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Electromagnetic Scattering and Analysis
Research Guide
What is Electromagnetic Scattering and Analysis?
Electromagnetic Scattering and Analysis is the application of numerical methods such as integral equations, boundary element methods, and fast multipole methods to solve Maxwell's equations for scattering problems by arbitrary objects.
This field encompasses 61,678 works that develop techniques like the method of moments, surface integral equations, and domain decomposition for efficient computation of electromagnetic fields. Key approaches include hierarchical matrices and characteristic basis functions to handle large-scale scattering simulations. Growth data over the past five years is not available.
Topic Hierarchy
Research Sub-Topics
Method of Moments for Electromagnetic Scattering
This sub-topic develops the method of moments (MoM) to solve surface integral equations for scattering from arbitrary objects, addressing ill-conditioning via basis function selection. Researchers apply pulse and RWG basis for PEC and dielectric bodies.
Fast Multipole Method in Electromagnetics
Studies accelerate MoM matrix-vector products using the fast multipole method (FMM) for large-scale scattering problems, expanding fields in spherical harmonics. Extensions handle dielectrics and wideband frequencies.
Boundary Element Method for Scattering
This area applies boundary element methods (BEM) to formulate and solve electromagnetic scattering via surface integrals, emphasizing Green's function discretizations. Research optimizes for non-smooth geometries.
Hierarchical Matrices in Integral Equations
Researchers employ H-matrices and H2-matrices to approximate dense impedance matrices from integral equations, achieving near-linear scaling for high-frequency EM solvers. Applications include MoM and BEM acceleration.
Domain Decomposition Methods for EM Scattering
This sub-topic explores non-overlapping and overlapping domain decomposition for parallel solution of large EM scattering systems, using iterative Schwarz and FETI solvers. Focus on transmission conditions for dielectrics.
Why It Matters
Electromagnetic Scattering and Analysis enables accurate prediction of radar cross-sections and antenna performance in engineering applications. K.S. Yee (1966) introduced finite-difference approximations to Maxwell's equations, allowing simulation of scattering from perfectly conducting surfaces, which has been cited 14,484 times and forms the basis for time-domain analysis in antenna design. S. Rao, Donald R. Wilton, and A.W. Glisson (1982) formulated the electric field integral equation with triangular surface patches, facilitating solutions for arbitrarily shaped objects and cited 5,278 times in aerospace and telecommunications for modeling complex scatterers like aircraft fuselages.
Reading Guide
Where to Start
'Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media' by K.S. Yee (1966), as it provides the foundational finite-difference discretization of Maxwell's equations with a clear scattering example, serving as an accessible entry before integral methods.
Key Papers Explained
K.S. Yee (1966) establishes time-domain finite differences in 'Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media,' complemented by Roger F. Harrington (1993)'s frequency-domain method of moments in 'Field Computation by Moment Methods.' S. Rao, Donald R. Wilton, and A.W. Glisson (1982) extend this to surface integral equations for arbitrary shapes in 'Electromagnetic scattering by surfaces of arbitrary shape.' Yousef Saad and Martin H. Schultz (1986) provide solvers like GMRES in 'GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems,' while Leslie Greengard and Vladimir Rokhlin (1987) accelerate computations in 'A fast algorithm for particle simulations.'
Paper Timeline
Most-cited paper highlighted in red. Papers ordered chronologically.
Advanced Directions
Current work emphasizes hierarchical matrices and characteristic basis functions for high-frequency scattering, though no recent preprints are available. Domain decomposition methods remain active for parallel solutions of large-scale Maxwell problems.
Papers at a Glance
| # | Paper | Year | Venue | Citations | Open Access |
|---|---|---|---|---|---|
| 1 | Numerical solution of initial boundary value problems involvin... | 1966 | IEEE Transactions on A... | 14.5K | ✕ |
| 2 | Generalized Gradient Approximation Made Simple [Phys. Rev. Let... | 1997 | Physical Review Letters | 14.0K | ✓ |
| 3 | Iterative Methods for Sparse Linear Systems | 2003 | Society for Industrial... | 13.5K | ✕ |
| 4 | GMRES: A Generalized Minimal Residual Algorithm for Solving No... | 1986 | SIAM Journal on Scient... | 10.9K | ✕ |
| 5 | Computational Electrodynamics: The Finite-Difference Time-Doma... | 1995 | — | 10.6K | ✕ |
| 6 | Field Computation by Moment Methods | 1993 | — | 6.7K | ✕ |
| 7 | Electromagnetic scattering by surfaces of arbitrary shape | 1982 | IEEE Transactions on A... | 5.3K | ✕ |
| 8 | A two-dimensional interpolation function for irregularly-space... | 1968 | — | 4.9K | ✕ |
| 9 | A fast algorithm for particle simulations | 1987 | Journal of Computation... | 4.8K | ✕ |
| 10 | Inverse Acoustic and Electromagnetic Scattering Theory | 2012 | Applied mathematical s... | 4.1K | ✕ |
Frequently Asked Questions
What is the method of moments in electromagnetic scattering?
The method of moments solves integral equations from Maxwell's equations by expanding fields over basis functions and enforcing boundary conditions. Roger F. Harrington (1993) presented a unified approach in 'Field Computation by Moment Methods,' applied to electromagnetic field problems with 6,694 citations. It models surface currents on scatterers using subdomain basis functions.
How does the finite-difference time-domain method work for Maxwell's equations?
The finite-difference time-domain method replaces Maxwell's equations with finite-difference equations on a grid, suitable for boundaries with perfectly conducting surfaces. K.S. Yee (1966) demonstrated this in 'Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media,' with an example of plane wave scattering. Allen Taflove (1995) expanded it in 'Computational Electrodynamics: The Finite-Difference Time-Domain Method' for practical engineering simulations.
What are surface integral equations used for in scattering analysis?
Surface integral equations formulate electromagnetic scattering problems on object boundaries, solved via methods like the electric field integral equation. S. Rao, Donald R. Wilton, and A.W. Glisson (1982) applied it to arbitrary shapes using planar triangular patches in 'Electromagnetic scattering by surfaces of arbitrary shape.' This approach reduces dimensionality compared to volume methods.
What role do fast multipole methods play in electromagnetic simulations?
Fast multipole methods accelerate matrix-vector products in integral equation solvers for large scattering problems. Leslie Greengard and Vladimir Rokhlin (1987) introduced a fast algorithm in 'A fast algorithm for particle simulations,' adaptable to N-body electromagnetic interactions. It reduces computational complexity from O(N^2) to O(N).
What are common iterative solvers for scattering linear systems?
GMRES minimizes the residual norm over Krylov subspaces for nonsymmetric systems from method of moments. Yousef Saad and Martin H. Schultz (1986) developed it in 'GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems,' with 10,887 citations. Yousef Saad (2003) covers it in 'Iterative Methods for Sparse Linear Systems' alongside preconditioners.
Open Research Questions
- ? How can hierarchical matrices be optimized for ill-conditioned surface integral equations at high frequencies?
- ? What domain decomposition strategies best parallelize fast multipole methods for very large scatterers?
- ? How do characteristic basis functions reduce degrees of freedom without losing accuracy in broadband scattering?
- ? Which preconditioners most effectively handle the impedance matrix conditioning from method of moments?
Recent Trends
The field maintains 61,678 works with no specified five-year growth rate.
Highly cited classics like K.S. Yee (1966, 14,484 citations) and S. Rao et al. (1982, 5,278 citations) continue dominating, indicating sustained reliance on established integral equation and finite-difference methods.
No recent preprints or news coverage from the last six to twelve months are available.
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