solver

Example of electric field analysis ≫

## ELFIN Electric Field Analysis

The FEM method uses potentials as variables.

Therefore, elements are required not only for bodies such as electrodes and dielectrics, but also for the entire space to be analyzed.

ELFIN, on the other hand, uses a source, such as an electric charge, as a variable.

Therefore, it can be analyzed with elements only for bodies for which a source exists.

Since there is no source in space, no elements are needed.

In ELFIN, the analysis domain is inclusive until infinity.

Therefore, there is no need to specify boundary conditions.

ELFIN uses analytical expressions for the surface of elements rather than numerical integrations over multiple points.

Thus, calculations are accurate until close to the surface.

The FEM calculates the spatial electric field from the potential of the spatial mesh, which is less accurate, but ELFIN calculates the electric field directly from the source, which is not less accurate.

The calculation of the electric field created by the source is based on the analytical integral formula.

Thus, the electric field is highly accurate until near the elements.

It is highly accurate because Maxwell stress is calculated from a highly accurate spatial electric field.

The electric field decreases rapidly outside the body.

Therefore, the potential changes in a complex way outside the body.

The potentials used in the FEM vary greatly outside the body.

Therefore, the spatial part requires a finer element division than the interior of the body.

Furthermore, 3D analysis requires a finer division of elements than 2D analysis because the 3D electric field changes more rapidly than the 2D electric field because it spreads in three directions.

On the other hand, the sources used in ELFIN exist only inside or on the surface of the body and not outside of it.

Even where the potential is complex and varied, the elements themselves are unnecessary if there is no source there.

In addition, the source changes slowly within the body or on the surface requiring elements.

Therefore, ELFIN generally does not require as fine element partitioning as the FEM.

The FEM is fast for 2D calculations but slow for 3D calculations.

The reason is.

・The number of elements increases in the depth direction, including the space section.

・The bandwidth of the matrix increases.

・More detailed division of elements is required than in a 2D analysis.

・In ELFIN, the metal that gives the potential can be analyzed by dividing the surface only into elements.

## Analysis Type

Analyzes electric fields that do not change with time.

Dielectric saturation can be handled.

## Model Type

Analyze the electric field of a 3D shaped body.

It is calculated using the analytical integral formula for the electric potential and electric field created by the source of a 3D shape.

This is the basic ELFIN analysis.

Analyzes the electric field of a body of infinitely long geometry in the Z direction.

By defining a cross-section of the body in the XY plane, the electric potential and electric field created by the infinitely long source in the Z direction is calculated using the analytical integral formula.

Analyze the electric field of an object with an axisymmetric shape, such as a cylinder.

By defining a cross-section of a body in the XZ plane, a source of axisymmetric geometry is placed and analyzed.

## Element type

Electrostatic field analysis.

Charges on a conductor collect on the conductor surface.

The conductor surface is divided by plane elements with surface charges.

It is represented by 3D elements with surface charges on their surfaces.

Therefore, complex polarization distributions that cannot be represented by elements with constant polarization within an element can be represented.

This element can represent the curved surface of a dielectric in detail.

If a part of the dielectric is curved, using poly elements for that part and dividing the other parts with hexahedral elements, etc., will enable accurate analysis without increasing the number of elements too much.

It is useful for modeling solid spheres.

## Calculation conditions

Gives the potential of conductors.

Specifies the material number of insulated conductors whose potential is unknown.

The potential of the conductor is calculated.

Dielectric saturation can be handled by entering a DE curve.

Input either a polygonal line or an equation parameter.

Specifies the symmetry of the model and electrodes.

Symmetry, antisymmetry, and periodic symmetry conditions are available.

Reduce the number of elements.

## output (result)

The surface charge density and total charge of the conductor are calculated.

The average value of the flux density of each element is obtained as a vector value.

Potential and electric field are calculated for a spatial point whose coordinates are entered.

It is highly accurate because it is calculated directly from a highly accurate source.

Force is calculated from the space electric field using Maxwell stress.

It is highly accurate because it is calculated from a highly accurate space electric field.

## acceleration

The ELF series is highly vectorized and parallelized.

As a result, when computed on multiple cores, it is faster in almost every part of the system.

CPU of computer used **Xeon** 16 cores

Number of Parallels | 16 | 8 | 4 | 2 | 1 |
---|---|---|---|---|---|

Matrix assembly time (speed ratio) | 4.0 | 3.3 | 2.5 | 1.6 | 1.0 |

Matrix solver time (speed ratio) | 10.0 | 6.5 | 3.6 | 1.9 | 1.0 |

Spatial magnetic field calculation time ( speed ratio) | 11.0 | 6.5 | 3.6 | 1.9 | 1.0 |

**Example of using ELF Series 4.90**

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.

120,000 DOF (107.2GB) dense matrix 23 minutes (estimated)

180,000 DOF (241.2GB) dense matrix 78 minutes (estimated)

## Applications

Electron Microscope

Electron Gun

Accelerators

Sputtering

Electron holography

MEMS

Capacitors

Insulator

Photocopiers

Power transmission systems

ELFIN is also used in many other areas.

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