Serenity - 3D Method of Moments Simulation

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)).

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.

A Brief Explanation of the 3D Method of Moments