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## 7.1. Parameters

Clicking on the Solver → Parameters option, the next panel is opened. Solver Panel

• Solver Method: the method used to solve the solution. Two options are available:
• PO (Physical Optics). It is a high-frequency approximation that computes the currents on the surfaces from the Physical Optics technique, so the iterative process of the resolution method is not carried out. The normal vectors of the geometry must be pointing to the proper direction.
• MoM (Method of Moments). It is an accurate full wave method that may be used to solve all types of situations. Selecting the Method of Moments solver, the Subdomains option with the MLFMA-MoM (Multi-Level Fast Multipole Algorithm – Method of Moments) technique is applied. This is the most conventional technique.
• Architecture Strategy: method to divide the problem based on hardware properties. Two different options are available:
• MPI (Message Passing Interface). It is valid for all types of computer architectures, but more memory may be required for shared memory machines.
• OpenMPIt is only valid for shared memory machines, where it may require fewer memory resources than the MPI strategy.
• Hybrid (MPI + OpenMP). This architecture uses both MPI + OpenMP. It is commonly used with computational clusters.
• Electromagnetic Equation: equation used to solve the solution. Further information about this options is explained in next section.
• EFIE (Electric Field Integral Equation)
• MFIE (Magnetic Field Integral Equation)
• CFIE (Combined Field Integral Equation)
• Relative Error: it is the maximum value error allowed in the iterative process. When the relative error of any iteration is lower than the value specified, the current computation stay is considered as a valid solution and the iterative process is finished. The smaller is the Relative Error the more accurate is the provided solution, but the larger is the computation time.
• Maximum number of iterations: maximum number of iterative steps used to search an iteration that satisfies the specified Relative Error. If the Maximum number of iterations is reached without getting a valid solution, the last iteration solution is saved.

Click on Save button to confirm the updated configuration.

### 7.1.1. Method of Moments

In the Method of Moments option, different parameters can be selected to configure the analysis.

Firstly, the user needs to choose the Electromagnetic Equation to solve:

• EFIE: the Electric Field Integral Equation is considered. This options solves the most of problems and is the most accurate one, but the convergence may be slow or even it may not be achieved in some cases.
• MFIE: the Magnetic Field Integral Equation is considered. This option provides valid results only for closed bodies, whenever the normal vectors of the geometry is pointing to the proper direction (outside the objects).
• CFIE: the Combined Field Integral Equation is considered. It is also recommended only for closed bodies, whenever the normal vectors of the geometry is pointing to the proper direction (outside the objects), and it uses a weighted combination of the two previous methods. The CFIE parameter must be defined between 0 and 1, and it weigths the rate in which the EFIE is considered. A value close to 1 is recommended for this parameter to ensure accurate results provided by the EFIE solution, but with the benefits of speeding-up the iterative process with the MFIE formulation (0.8 or 0.9, for example). The CFIE solution combines the two previous methods according to the next formula:
CFIE = EFIE · CFIEparameter + (1 - CFIEparameter) · MFIE

After clicking on the Advanced Options button, the following configuration dialog will appear:

Main Properties tab: Solver Advanced Options. Main Properties tab

• Solver: Algorithm to solve the iterative method. BICGSTAB (BiConjugate Gradient STAbilized method) and GMRES (Generalized Minimal Residual method) are available. If no convergence is achieved by using any of this methods, try to use the other one.
The Max. number of unknowns for Direct Solver option is the threshold of the maximum allowed unknowns to compute the currents of the Method of Moments by using a direct solution method, instead of using the iterative process. For using always the iterative solver, set this parameter to zero. Note that the direct solution method may require huge memory and time resources when a large number of unknowns is considered.

• More properties: The user can specify the next parameters:
• Conductor losses: the metallic structures may induce the conduction losses defined by its parameter, specified in Ohm/m. By default, no conductor losses are considered.
• Region Size: this parameter defines the size edge (in terms of wavelengths) of the regions generated in the MLFMA-MoM (Multi-Level Fast Multipole Algorithm – Method of Moments) algorithm.
• Maximum Multipole Level: it is an advanced parameter that defines the maximum number of levels considered in the MLFMA-MoM solver to consider the coupling effect. The default value (-1) consider the coupling in every levels, whereas an integer positive value specifies that the coupling is only considered betweeb the regions up to this level. The more levels consider the coupling effect, the more accurate is the provided solution but also the slower is the solution process.
• Radiation Level: this parameter sets the maximum radiation level in the multipole generation to obtain the radiated fields. The default value (-1) let the program to adjust automatically this configuration. For very large simulations, it may be used to save memory and time resources by avoiding the computation of radiated far field in the largest regions.
• Compute 3D Pattern. The 3D Pattern is a spherical diagram that shows the field distribution of the analyzed problem. The resolution of the spherical diagram may be modified by the user with the Angle Step parameter (in degrees), that specifies the angular step taken into account in the diagram computation. Disable the Compute 3D Pattern to avoid the 3D Pattern generation whenever it is not required, the simulation time may be reduced.

Preconditioner tab: In the subdomains analysis, the user can enable the preconditioner to speed up the resolution of the problem with the Enable Preconditioner option. The user can choose between two different preconditioners:

• Diagonal Preconditioner:  The diagonal preconditioner is fast to compute and requires a reduced amount of memory, although the improvement in the convergence rate it produces is normally moderate. This preconditioner it is only recommended when more than 8 divisions per wavelenth is set in the meshing process, as a shorter number of divisions slows down the convergence instead not using this preconditioner.
• Sparse Approximate Inverse Preconditioner (SAI): This preconditioner will generally result in a faster convergence than the diagonal preconditioner.
• Sparsity Distance: this parameter is expressed in wavelengths (0.25 as the default value) and indicates how accurately this preconditioner will resemble the inverse of the rigorous MoM matrix. Higher values will normally involve a faster convergence, but the memory required to store the preconditioner data will grow fast, non-linearly. We advice to keep the default value or increase it slightly in case of specially ill-conditioned systems.
• Filtering Threshold: These parameters should contain a value between 0.0 and 1.0. The default values should be adequate in most cases.
• Pre-Processing: This parameter controls the amount of data considered to generate the preconditioner. Lower values entail a more accurate generation, while higher values entail a faster computation.
• Post-Processing: This parameter controls the amount of data to be stored after the generation of the preconditioner. Lower values entail better convergence, while higher values entail less RAM required to store the preconditioner.
• MPI Data Exchange Frequency: This parameter sets up how often the MPI nodes request more coupling terms to generate the preconditioner. Larger values require less interactions speeding up the simulation, although more memory will be needed to store these terms. A negative or 0 value indicates that the coupling terms are only exchanged once.
• Hybrid (Diagonal + SAI): This preconditioner is suited for memory-shared machines, in which case will use both Diagonal and SAI preconditioners.

Due to its numerical nature, the SAI preconditioner is better suited for the case of shared memory parallelization (OpenMP), while the conventional diagonal preconditioner can be used either for OpenMP or for the MPI paradigm.

In order to save the solver configuration press the Save button.

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