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Feko Solution Methods
One of the key features in Feko is that it includes a broad set of unique and hybridised solution methods. Effective use of Feko features requires an understanding of the available methods.
Full Wave and Asymptotic Solution Methods
The Solver includes multiple frequency and time domain solution methods. True hybridisation of some of these methods enables efficient analysis of a broad spectrum of electromagnetic problems. You can also use more than one solver method for cross-validation purposes.
Full Wave Solutions
Full wave solutions rigorously solve Maxwell's equations without making any assumptions regarding the nature of the electromagnetic problem. The solution can be either in the frequency or the time domain.
The MoM for Full-Wave Solutions
Discretizing the Currents
Discretizing the object or solution space is commonly referred to as meshing. It is a necessary step to solve the integral equations.

Welcome
Release Notes
See what's new in the latest release.
Get Started
The Feko Getting Started Guide contains step-by-step instructions on how to get started with Feko.
Examples
The Feko Example Guide contains a collection of examples that teaches you Feko concepts and essentials.
Introduction to Feko
Feko is a comprehensive electromagnetic solver with multiple solution methods that is used for electromagnetic field analyses involving 3D objects of arbitrary shapes.
CADFEKO
CADFEKO is used to create and mesh the geometry or model mesh, specify the solution settings and calculation requests in a graphical environment.
POSTFEKO
POSTFEKO, the Feko post processor, is used to display the model (configuration and mesh), results on graphs and 3D views.
EDITFEKO
EDITFEKO is used to construct advanced models (both the geometry and solution requirements) using a high-level scripting language which includes loops and conditional statements.
Feko Solution Methods
One of the key features in Feko is that it includes a broad set of unique and hybridised solution methods. Effective use of Feko features requires an understanding of the available methods.
- Basic Concepts
  Basic antenna and EM concepts are given that provide a foundation for understanding the different solver methods in Feko.
- Source Methods and Field Methods
  Solver methods can be categorized as either source-based methods or field-based methods. Understanding the main differences between these two categories helps to understand and choose an appropriate solution method for each application.
- Full Wave and Asymptotic Solution Methods
  The Solver includes multiple frequency and time domain solution methods. True hybridisation of some of these methods enables efficient analysis of a broad spectrum of electromagnetic problems. You can also use more than one solver method for cross-validation purposes.
  - Full Wave Solutions
    Full wave solutions rigorously solve Maxwell's equations without making any assumptions regarding the nature of the electromagnetic problem. The solution can be either in the frequency or the time domain.
    - Introduction to the Method of Moments
      The MoM is the default solver in Feko. A simple electrostatic example is used to convey the basics of the solver.
    - The MoM for Full-Wave Solutions
      - Specifying the Relevant Integral Equation
        Specify the integral equation by decomposing the fields into two parts.
      - Applying Boundary Conditions
        Boundary conditions refer to already known properties of the physics of the problem. These help to derive the solvable integral equations.
      - Discretizing the Currents
        Discretizing the object or solution space is commonly referred to as meshing. It is a necessary step to solve the integral equations.
        Basis Functions
        Basis functions are elementary functions for the modelling of the unknown quantity on a mesh element.
      - Testing and Solving the Integral Equation
        The testing of the integral equation applies the integral equation over each triangle edge to obtain N equations with N unknowns which can readily be solved on a computer.
      - Integrating the Currents
        Summing or integrating the vector currents is the last step in the MoM procedure. This step leads to specific output parameters such as far fields and impedance.
    - MoM Computational Resources Scaling
      The usage of a dense matrix in the MoM implies a limit to the size of the problem that can be solved. The limit is determined by the available computational resources.
    - Other Methods Based on the MoM
      Specific methods, which can also be categorized as MoM methods, are tailor-made for solving dielectric bodies.
    - Additional Features and Extensions for the Method of Moments
      Numerous features and optimised electromagnetic (EM) analysis options for the method of moments (MoM) are available.
    - Multilevel Fast Multipole Method (MLFMM)
      The multilevel fast multipole method (MLFMM) is an alternative formulation of the technology behind the method of moments (MoM) and applies to much larger structures (in terms of the wavelength) than the MoM, making full-wave current-based solutions of electrically large structures a possibility.
    - Integral Equation Methods (EFIE, MFIE and CFIE)
      The relevant integral equation method can be used to solve a model to either obtain faster iterative or higher numerical accuracy when using the MoM or MLFMM.
    - Adaptive Cross-Approximation (ACA)
      The adaptive cross-approximation (ACA) is a fast method similar to the multilevel fast multipole method (MLFMM) but is also applicable to low-frequency problems or when using a special Green’s function.
    - Finite Element Method (FEM)
      The finite element method (FEM) is a solution method that employs tetrahedra to mesh arbitrarily shaped volumes accurately where the dielectric properties may vary between neighbouring tetrahedra.
    - Finite Difference Time Domain (FDTD)
      The finite difference time domain (FDTD) is a full wave time domain solution method, and Fourier transforms are applied to convert the native time domain results to the frequency domain.
  - Asymptotic Solutions
    Asymptotic solution methods solve Maxwell's equations, but make certain assumptions regarding the nature of the problem. Feko provides various high frequency asymptotic solution methods that assume the frequency of interest is high enough that the structure is much larger than the wavelength.
  - Solution Methods per Application
    A solution method is selected based on the electrical size of a problem, the geometrical complexity and available computational resources.
  - Supported Solution Method and Technique Combinations
    When selecting a solution method or technique in Feko, it is important to know which method and technique combinations may be used in a model, else CADFEKO and the Solver will give an error.
  - Cable Coupling
    Model complex cable-bundle networks using full-wave simulations.
  - Arrays and Infinite Periodic Structures
    Infinite and finite periodic structures are efficiently modelled using special features available in Feko.
  - General Non-Radiating Networks
    Complex feed networks can be simplified by including them as a circuit representation using general network blocks.
  - Windscreen Modelling
    The windscreen antenna solution method reduces the computational requirements by meshing only metallic elements while analysing the behaviour of the integrated windscreen antennas within their operating environment. The analysis can take into account the physical features of windscreen antennas and their surroundings.
  - Symmetry Planes
    Geometric symmetry, electric symmetry and magnetic planes of symmetry in a model can be exploited to reduce runtime and memory requirements.
  - Media
    Provided are the formulations and concepts to define frequency-dependent dielectric media and anisotropic media (3D).
Optimisation in Feko
Feko offers state-of-the-art optimisation engines based on generic algorithm (GA) and other methods, which can be used to automatically optimise the design and determine the optimum solution.
Feko Utilities
The Feko utilities consist of PREFEKO, OPTFEKO, ADAPTFEKO, the Launcher utility, Updater and the crash reporter.
Description of the Output File of Feko
Feko writes all the results to an ASCII output file .out as well as a binary output file .bof for usage by POSTFEKO. Use the .out file to obtain additional information about the solution.
Feko Application Macros
A large collection of application macros are available for CADFEKO and POSTFEKO.
Scripts and Application Programming Interface (API)
CADFEKO and POSTFEKO have a powerful, fast, lightweight scripting language integrated into the application allowing you to create models, get hold of simulation results and model configuration information as well as manipulation of data and automate repetitive tasks.
Appendix
Reference information is provided in the appendix.

Discretizing the Currents

Discretizing the object or solution space is commonly referred to as meshing. It is a necessary step to solve the integral equations.

Similar to the procedure followed to solve the charge distribution on the straight wire, the surface of the PEC body is discretized into triangles. Therefore the currents on the triangles are approximated as follows (similar to Equation 3):

J_{s c a t} = \sum_{n = 1}^{N} a_{n} g_{n}

Figure 1. The arbitrary shaped conducting body meshed into triangles.

The equation for the discretized currents can then be substituted into the EFIE (Equation 1) to yield:

\sum_{n = 1}^{N} a_{n} ℒ {g_{n}}_{\tan} = - E_{i n c, \tan}

In Equation 2, the current coefficients represented by $a_{n}$ are the only unknown quantity.

Before proceeding to the next step, it is necessary to take a closer look at basis functions.