Serenity - 3D Method of Moments Simulation

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Serenity is an electromagnetic signature code that calculates the scattered fields and radar cross section of arbitrarily shaped, three-dimensional objects using the 3D Method of Moments (MoM) and RWG triangular basis functions. It is intended to be used for electrically small objects that the asymptotic techniques are ill-suited to handle.

Serenity implements the Electric Field Integral Equation (EFIE) and Magnetic Field Integral Equation (MFIE) making possible the simulation of thin, open structures (EFIE) and closed bodies (MFIE/CFIE). Serenity is compatible with Xpatch and FISC facet files.

Serenity uses the traditional, full-matrix approach to the MoM problem, and the novel Multilevel Fast Multipole Algorithm (MLFMA) for the simulation of larger problems possessing many more unknowns.

Brief capability summary:

  • Conducting (PEC) objects
  • Electric and Magnetic field integral equations
  • RWG basis functions
  • Full matrix solver using LU decomposition
  • Parallelized Multilevel Fast Multipole Method (MLFMA) solver for problems of greater size
  • Conjugate Gradient Squared (CGS), Biconjugate Gradient Stabilized (Bicg-Stab), and Generalized Minimum Residual (GMRES) iterative solvers
  • ILU preconditioners to improve MLFMA solver performance
  • Fully parallelized matrix fill
  • Written completely in C
  • Surface current output suitable for viewing by Emerald
  • Binaries available for Windows and x86 Linux platforms


  • The Addition Theorem is a powerful mathematical relationship that forms the basis of the Fast Multipole Method and the MLFMA.


    The FMM allows for the representation of interactions between clusters of sources in a group by considering that group as a whole, reducing the required storage and computational complexity. The MLFMA extension of the FMM accelerates the matrix-vector product in an iterative solver from O(N2) to O(Nlog(N)).

    Click to Enlarge
    The MLFMA allows for MoM simulation of objects of far greater electrical size than a traditional full-matrix approach. Where before a simulation would be limited to objects a few electrical wavelengths in size, the MLFMA allows for objects of many tens of wavelengths on the same computing hardware and memory.



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