It is a type of Integral Equation Method.
It is a unique method that improves and integrates the Magnetic Moment Method, Surface Charge Method, and Alternate Charge Method.
The Integral Equation Method is a method for solving electromagnetic interactions using simultaneous equations.

No spatial mesh is required.
No boundary conditions are required.
Spatial electric and magnetic field evaluation is continuous.
Accurate calculations are possible even with coarse elements.
Calculation speed is fast.
Calculation of motion is easy.

The Integral Equation Method is a technique for solving electromagnetic interactions with simultaneous equations.
However, solving by setting up simple simultaneous equations may result in unnatural solutions.
Therefore, it is difficult to establish it as a commercial software.
The ELF series uses a unique analytical method to formulate simultaneous equations to obtain natural solutions.

The FEM solves the differential form of Maxwell's equations.
The FEM takes the potential as a variable.
The FEM requires a spatial mesh and boundary conditions.

The Integral Equation Method solves the integral form of Maxwell's equation.
The sources of the electric and magnetic fields are used as variables.
No spatial mesh or boundary conditions are required.

For example, the boundary element method divides only the boundary.
Because it divides only the boundary, it is difficult to analyze magnetic and dielectric materials with uneven surfaces, and it is also difficult to handle magnetic saturation.

The Surface Charge Method is also similar to the Boundary Element Method.
The ELF Series uses the Surface Charge Method in combination with the ELF Series for stable and accurate areas such as electrodes that provide electric potential.

Furthermore, the Magnetic Moment Method is fast, but the magnetic flux flow may be disturbed.
The ELF series incorporates the Magnetic Moment Method and has been independently improved in 1985, 1993, 2003, and 2013 to obtain natural solutions with undisturbed magnetic flux flow.

Magnets, complex coil geometries, problems with large spaces, and bodies in motion can also be easily computed.

Complex electrodes, dielectrics with high dielectric constant, etc. can be easily calculated.
Precise space electric field can be calculated.

There is no need to create a spatial mesh at the location where the charged particles fly, and the electric and magnetic fields at the particle point can be calculated with high accuracy using the analytical formula from the source.
It is also possible to stop the particles in the middle of the path, for example, with a wall.

The included pre- and post-processor makes it easy to create geometry data and display the results.
It is also possible to read and convert geometry data in NASTRAN or UNIVERSAL format or Femap for calculation.

We believe that this number of elements is sufficient for the analysis examples, but larger problems can be solved.
Also, a very small number of elements will give similar accuracy compared to the FEM.

Time solved on a CPU 10980XE 18-core PC.
15,000 DOF (1.7GB) dense matrix 4 sec.
30,000 DOF (6.7GB) dense matrix 25 sec.
60,000 DOF (26.8GB) dense matrix 173 sec.

The ELF series is highly parallelized.
Therefore, when computed on multiple cores, it is faster in almost every part of the process.

CPU of the computer used Xeon 16 cores

Number of Parallels168421
Matrix assembly time(velocity ratio)
Matrix solver time(velocity ratio)
Spatial field calculation time(velocity ratio)

OS must be 64-bit. (Windows 10,11 recommended)
Memory is 32 GB or more recommended.
SSD is recommended for the hard disk.
CPU must be made by Intel.
 ◎ CPU supporting AVX512.
 ○ CPU supporting AVX2.
A PC with more cores than the number of parallelization is recommended.
Hyper-threading should be off.

This is an example of a recommended PC for ELF/MAGIC.

This is an example of a recommended PC for ELFIN.

This is an example of a recommended PC for ELF/BEAM.

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