SAF is an electromagnetic scattering, radiation, and coupling computational program used to calculate the radar scattering from complex targets.

SAF is an electromagnetic scattering, radiation, and coupling computational program based on the method of moments solution of the hybrid volume-surface integral equation. In addition to traditional LU decomposition, SAF has a multilevel fast multipole method acceleration option making it very efficient in computation memory and speed.


SAF is used to calculate the radar scattering from three-dimensional complex targets that have any combination of the following:

  • Conducting objects
  • Dielectric objects with complex permittivity and permeability
  • Impedance boundary conditions
  • Resistive sheets

The software can also solve problems involving infinite ground planes, both perfectly conducting (exact solution) and material layers over a dielectric half space (approximate solution).


The multipole method of discretization of the volume-surface integral equation can be set to correspond to either the electric field integral equation (EFIE), magnetic field integral equation (MFIE), or the combined field integral equation (CFIE).

For a triangular mesh, Rao-Wilton-Glisson basis functions are used, and for quad-patch meshes the generalized roof-top basis functions are used. Any combination of the following mesh types are supported:

  • Flat triangular patches
  • Flat quad patches
  • Curvilinear quad patches
  • Flat-faced tetrahedron cells
  • Flat-faced hexahedron cells
  • Curvilinear hexahedron cells
  • Flat-faced prism
  • Wire segments

After solving the matrix equation, SAF can output many system parameters such as:

  • Radar cross section
  • In-Situ antenna pattern
  • Antenna S-parameters and impedance
  • Power coupling between arrays
  • Near-field and far-field magnitude and phase
  • Surface currents


SAF can provide a fast and flexible accurate solution to many computational electromagnetic problems. SAF has been parallelized with OpenMP, Messaging Passing Interface (MPI), and Compute Unified Device Architecture (CUDA) for high performance computing with multiple cores, processors, and GPUs.

For the novice user default settings for standard or high accuracy are provided, but the advanced user has full control over the formulation. SAF has utilities like mesh27 (CAD tool for building simple targets), sample antenna pattern-generation tools (circular waveguides, rectangular waveguides, dipoles), and much more. This solver links up with Xpatch® to allow for hybrid domain decomposition solutions and shares many of the same input and output file formats.

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