Examples of Magnetic Field Analysis ≫

ELF/MAGIC Electromagnetic field analysis

The FEM uses potential as a variable.
Therefore, elements are required not only for bodies such as magnets and coils, but also for the entire space to be analyzed.

ELF/MAGIC, on the other hand, uses the source, such as a magnetic charge, as a variable.
Therefore, the analysis can be done with elements only for bodies where the source exists.
Since there is no source in space, no elements are needed.

In ELF/MAGIC, the analysis domain includes the area until infinity.
Therefore, there is no need to specify boundary conditions.

In ELF/MAGIC, the integration of elements is not done by numerical integration over multiple points, but by analytical expressions on the surface of the elements.
Therefore, calculations can be performed with high accuracy until close to the surface.

With the FEM, the calculation of the spatial magnetic field is less accurate because it is calculated from the potential of the spatial mesh, but with ELF/MAGIC, the magnetic field is calculated directly from the source, so there is no loss of accuracy.

It is highly accurate because Maxwell stress is calculated from highly accurate spatial magnetic fields.

The magnetic field decreases rapidly outside the body.
Therefore, the potential varies in a complex way outside of the body.

The potentials used in the FEM vary greatly outside the body.
Therefore, the spatial part requires a finer Mesh Division than the interior of the body.
Furthermore, the 3D magnetic field changes more rapidly than the 2D magnetic field because it spreads in three directions.
Therefore, 3D analysis requires finer Mesh Division than 2D analysis.

On the other hand, the sources used in ELF/MAGIC exist only inside or on the surface of the body and not outside of it.
Even where the potential is varied in a complex way, 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, ELF/MAGIC generally does not require as fine Mesh Division as the FEM.

The FEM is fast for 2D calculations but slow for 3D calculations.
The reason for this is
・In 2D, the potential has one degree of freedom, but in 3D it has three degrees of freedom.
・The number of elements, including the spatial part, increases in the depth direction.
・The bandwidth of the matrix increases.
・Mesh Division is required to be finer than in 2D analysis.

ELF/MAGIC also has more variables, but it can be solved with fewer elements to begin with.

ELF/MAGIC does not require a spatial mesh.
Thus, the spatial mesh will not twist or collapse as the mutual positions of the parts change.

ELF/MAGIC does not require a spatial mesh.
Thus, any coil shape and current direction can be freely specified.
There is no need to consider changes in the magnetic field within the coil, so there is no need for a fine mesh.

Analysis Type

Analyzes magnetic fields that do not vary with time.
Eddy currents and induced currents are not calculated.
B-H curves (nonlinear) of magnetic materials can be handled.

Calculate when currents change and when bodies are in motion.
Calculates eddy and induced currents.
Handles B-H curves (nonlinear) for magnetic materials.
Handles free motion because there is no spatial mesh.

Sinusoidal response analysis.
Calculate eddy and induced currents.
Calculate the sinusoidal variation of input currents, magnetization, and eddy currents using complex numbers.
You can also input complex permeability to calculate inductance in a short time.

Model Type

Analyzes the magnetic field of a 3D shaped body.
It is calculated using the analytical integral formula for the magnetic field created by a 3D shaped source.
This is the basic ELF/MAGIC analysis.

Analyzes the magnetic 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 magnetic field created by an infinitely long source in the Z direction is calculated using the analytic integral formula.

Analyze the magnetic field in an axisymmetric body, 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

ELF's unique analysis method can represent complex magnetization distributions that cannot be represented by elements with constant magnetization within an element.
It also supports B-H curves (nonlinear), so it can handle magnetic saturation problems.

The calculation method was significantly improved in 2013.

There are elements whose magnetic poles are determined by the geometry and elements for which the direction of the poles can be specified.
B-H curves (nonlinear) are supported, so the effect of external magnetic fields on the magnets can be taken into account.
Attractive and repulsive forces between magnets can be calculated with high accuracy until the magnets are in contact.
Low-temperature demagnetization and high-temperature demagnetization can be calculated.

Coils, for example, can be represented as 3D elements using current elements, such as hexahedrons and triangular prisms.
Line elements can be used to represent individual wires.
Plane elements include quadrilaterals and triangles.
Both elements are converted to line current groups and calculated using the analytical integral formula according to Biot-Savart's law.

Conductor elements are available for calculating eddy currents.
Conductor elements also include magnetic conductor elements that can account for magnetism.

The calculation method was significantly improved in 2003.

These elements can represent the curved surface shape of a magnetic material in detail.
If a part of the magnetic body is curved, using poly elements for that part and dividing the other parts with hexahedral elements, etc., allows for accurate analysis without increasing the number of elements too much.
This is useful when modeling a solid sphere rather than a hollow sphere.

Calculation conditions

Enter either a broken line or as a parameter in a formula.
It has a library.

For magnetic materials, enter the curve from the origin.
For magnets, enter the 3rd quadrant, 2nd quadrant, and 1st quadrant of the BH curve.

If the BH curve is nonlinear, the Newton-Raphson and iterative modification methods are used.
Converges even if the S-shaped BH curve or the broken line is coarse.

To calculate eddy currents, specify the volume resistivity of the conductor.
For magnetic conductors, a BH curve is also given.

If the current flowing through the coil is input directly, the electrical resistance of the coil is not required.
The current value flowing through the cross-section of the coil is input.
This is useful for static magnetic field analysis because the effect of induced voltage is ignored.

When considering the effect of induced voltage in a dynamic magnetic field analysis, enter the driving voltage applied to the coil.
The voltage applied to the coil is determined by the drive voltage input and the induced voltage due to the change in the interlinkage flux, and the current is calculated from the electrical resistance.
This current is used to calculate the change in interlinkage flux, etc.

Specifies the symmetry of the model and magnetic poles.
Symmetry, antisymmetry, and periodic symmetry conditions are available.

It is not a boundary condition.
It reduces the number of elements.

Enter the permeability multiplier (ratio).
The permeability can be changed according to the direction, and anisotropy can be expressed.

By inputting the occupancy of the laminate, the magnetic permeability changes depending on the direction.
This is achieved by treating the laminate as a kind of anisotropic magnetic material.

Overlapping electromagnetic steel plates, including air gaps, can be represented by a single element.
Prevents the number of variables from increasing.

output (result)

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

The magnetic field is calculated for the spatial point whose coordinates are input.
It is highly accurate because it is calculated directly from a high-precision source.

Based on the vector potentials at spatial points, a magnetic flux diagram is drawn for 2D analytical elements and a pseudo-flux diagram for axisymmetric analytical elements.

Calculated from spatial magnetic field using Maxwell stress.
It is highly accurate because it is calculated from a high-precision spatial magnetic field.

Cogging torque can be calculated with high accuracy.
Cogging torque in the presence of skew can also be calculated with high accuracy.

The current density at the nodes of each element is obtained as a vector value.
Joule heat for each element is obtained from the volume resistivity and current density.

It is calculated by Stokes' theorem.
There is no need to create a mesh to calculate the magnetic flux in space.

Interlinkage fluxes for spiral coils and figure-8 coils can also be calculated.
Magnetic materials and eddy currents can also be calculated.

Calculated from the interlinkage flux of the coil.

Treats the induced current as a variable.
Associate with the interlinkage flux of the coil.


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 Parallels168421
Matrix assembly time (speed ratio)
Matrix solver time (speed ratio)
Spatial magnetic field calculation time ( speed ratio)

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)


・Electron microscope
・Magnet Products
・Magnetic shields
・Linear motors
・Electron holography
・Magnetic heads

ELF/MAGIC is also used in many other areas.

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