# Efield Frequency-Domain Solvers

The Efield frequency domain solvers (EfieldFD) are based on the Method of Moments (MoM) technique applied to surface integral formulation of the electric and magnetic field of an arbitrarily shaped object consisting of conductors, dielectrics and thin wires. In MoM the analysis is accurately carried out by representing the conductors, dielectrics and thin wires using surface triangular elements and wire segments. Since only the surfaces are modeled in MoM, the size of the model in terms of unknowns is much smaller than for differential equation methods. The technique leads to a matrix system that has to be solved where the matrix is dense. Also the mesh generation is much faster and simpler than for example finite element methods (FEM) using tetrahedral or hexahedral elements.

Different solver modes and integral formulations are available in the EfieldFD solvers to be able to cover a very wide range of applications including antenna design, antenna integration, waveguides and radar cross section analysis. While standard MoM is the preferable choice for electrically small antenna or waveguide design problems the Multilevel Fast Multipole Method (MLFMM) or the Physical Optics method (PO) is the preferable choice for applications involving electrically large structures. Examples of applications where MLFMM and PO is the preferred choice are radar cross section analysis or antenna installation analysis. In addition to these three basic solver modes the EfieldFD solvers also include hybrid MoM-PO and hybrid MLFMM-PO solver modes.

## Solver Modes

Different solver modes and integral formulations are available in EfieldFD to be able to cover a very wide range of applications including antenna design, antenna integration, waveguides and radar cross section analysis. Solver modes available are MoM, MLFMM, PO, MoM-PO and MLFMM-PO.

## The MoM mode

The standard MoM is limited to structures that are electrically small and applications include antennas and waveguides. Typically structures of the size up to five or ten wavelengths can be treated.

In the MoM mode the classical Gaussian elimination process is used to solve the matrix system. This requires solution time proportional to N3 and memory usage proportional to N2, where N is the number of unknowns in the system. However, since the Efield MoM solver is parallelized and the resulting matrix and right hand side can be stored on disc the size of the problem that can be treated can be increased quite a lot using a cluster of computers.

## Parallelization and out-of-core

The MoM formulation leads to a linear system of equations and depending on the problem size, the memory need to store the system matrix can exceed the available main memory on the computer system. There are two different options in this case. One is to run the EfieldFD solver on a parallel computer and use the memory on the PCs or workstations. The other is to store the system matrix (and right hand side) on disk rather than in the main memory using the EfieldFD out-of-core solver.

All EfieldFD solvers are parallelized and the solvers will run effectively on both shared memory and distributed memory machines. The solvers can be run either in out-of-core mode or in in-core mode depending on available memory. In the case of out-of-core mode the storage is on files on disc whereas for the in-core mode storage is only in the internal memory.