3. Potentials and Gauge Conditions#

Specifies the electromagnetic potentials to use and other options.

Input settings#

3_Potential_Gauge_Conditions JSON key: potentials and gauge conditions object

POTENTIAL(3) Sets the potentials to use.

NODAL_FORCE_METHOD(3) Nodal force calculation option

PHI_OPTION(3) Sets the electric scalar potential.

FIXED_COORDINATE(3) Active for steady-current eddy-current analysis (STEADY_CURRENT = 1)

TREE_GAUGE(3) Disabled (tree-based gauge setting; currently unreliable)

REGULARIZATION(3) Sets equation regularization for current and magnetic-field sources

RENUMBERING(3) Sets matrix renumbering

SCALING(3) Sets diagonal matrix scaling

LINE_SEARCH(3) Sets the line-search method for nonlinear calculation

MATRIX_ASYMMETRICITY(3) Sets matrix asymmetry when using an asymmetric matrix

Input format#

Text-format section

Type:

Fixed parameter set

Number of rows:

2

Number of parameters:

4, 6
Text format#
* POTENTIAL * NODAL_FORCE_METHOD * PHI_OPTION * FIXED_COORDINATE *
    I              I                 I              I
* TREE_GAUGE * REGULARIZATION * RENUMBERING * SCALING * LINE_SEARCH * MATRIX_ASYMMETRICITY *
    I              I               I           I            I                 I
Important

The TREE_GAUGE option is disabled. Specify -1.

JSON format#

JSON format from 2024.11#

"3_Potential_Gauge_Conditions": {
    "POTENTIAL": I,
    "NODAL_FORCE_OPTION": I,
    "PHI_OPTION": I,
    "FIXED_COORDINATE": I,
    "TREE_GAUGE": I,
    "REGULARIZATION": I,
    "RENUMBERING": I,
    "SCALING": I,
    "LINE_SEARCH": I,
    "MATRIX_ASYMMETRICITY": I
},

Important

Release 2024.11

In JSON format, default values are used when these parameters are not defined. See the detailed descriptions for default values.

Examples#

Static analysis#

Text-format section

Text format#

* POTENTIAL * NODAL_FORCE_METHOD * PHI_OPTION * FIXED_COORDINATE *
    0              0                 0              0
* TREE_GAUGE * REGULARIZATION * RENUMBERING * SCALING * LINE_SEARCH * MATRIX_ASYMMETRICITY *
    -1              0               0           0            0                 0

JSON format from 2024.11#

"3_Potential_Gauge_Conditions": {
    "POTENTIAL": 0,
    "NODAL_FORCE_OPTION": 0,
    "PHI_OPTION": 0,
    "FIXED_COORDINATE": 0,
    "TREE_GAUGE": -1,
    "REGULARIZATION": 0,
    "RENUMBERING": 0,
    "SCALING": 0,
    "LINE_SEARCH": 0,
    "MATRIX_ASYMMETRICITY": 0
},

"3_Potential_Gauge_Conditions": {
    "POTENTIAL": 0,
},

Transient analysis#

For eddy-current analysis, POTENTIAL = 2 is appropriate.

Text-format section

Text format#

* POTENTIAL * NODAL_FORCE_METHOD * PHI_OPTION * FIXED_COORDINATE *
    2              0                 0              0
* TREE_GAUGE * REGULARIZATION * RENUMBERING * SCALING * LINE_SEARCH * MATRIX_ASYMMETRICITY *
    -1              0               0           0            0                 0

JSON format from 2024.11#

"3_Potential_Gauge_Conditions": {
    "POTENTIAL": 2,
    "NODAL_FORCE_OPTION": 0,
    "PHI_OPTION": 0,
    "FIXED_COORDINATE": 0,
    "TREE_GAUGE": -1,
    "REGULARIZATION": 0,
    "RENUMBERING": 0,
    "SCALING": 0,
    "LINE_SEARCH": 0,
    "MATRIX_ASYMMETRICITY": 0
},

"3_Potential_Gauge_Conditions": {
    "POTENTIAL": 2,
},

Steady-state AC analysis#

For eddy-current analysis, POTENTIAL = 2 is appropriate.

Text-format section

Text format#

* POTENTIAL * NODAL_FORCE_METHOD * PHI_OPTION * FIXED_COORDINATE *
    2              0                 0              0
* TREE_GAUGE * REGULARIZATION * RENUMBERING * SCALING * LINE_SEARCH * MATRIX_ASYMMETRICITY *
    -1              0               0           0            0                 0

JSON format from 2024.11#

"3_Potential_Gauge_Conditions": {
    "POTENTIAL": 2,
    "NODAL_FORCE_OPTION": 0,
    "PHI_OPTION": 0,
    "FIXED_COORDINATE": 0,
    "TREE_GAUGE": -1,
    "REGULARIZATION": 0,
    "RENUMBERING": 0,
    "SCALING": 0,
    "LINE_SEARCH": 0,
    "MATRIX_ASYMMETRICITY": 0
},

"3_Potential_Gauge_Conditions": {
    "POTENTIAL": 2,
},

Detailed description#

3_Potential_Gauge_Conditions#

3_Potential_Gauge_Conditions#

JSON key:: Potentials and gauge conditions object

POTENTIAL#

POTENTIAL(3)#

Text-format section

Fixed parameter set 1#
[row, col] = [1, 1]

Specifies the electromagnetic potentials to use.

Potential option#
Setting value	Description
0: Default	\(A, Ar\)
2	\(A + \phi, Ar\)
4	\(As + \phi\)

\(A\): total magnetic vector potential

\(Ar\): reduced magnetic vector potential

\(\phi\): electric scalar potential

\(As\): magnetic vector potential produced by the applied field of COIL(17.1).

Runs induced-current analysis under low-frequency magnetic-field variation. \(As\) is calculated using COIL(17.1), and \(\phi\) is solved as an unknown. Set TRANSIENT(2) = 1, define the entire analysis region as a conductor without air, and set FAR_BOUNDARY_CONDITION(13) = 1.

Set to 0 when not performing eddy-current analysis. A value of 2 is recommended for analysis including eddy currents.

Tip

Using \(\phi\) increases the number of variables, but often improves ICCG convergence. It is particularly effective for analysis including eddy currents or using SUFCUR.

NODAL_FORCE_METHOD#

NODAL_FORCE_METHOD(3)#

Text-format section

Fixed parameter set 1#
[row, col] = [1, 2]

Nodal force calculation option#
Setting value	Description
0: Default	Includes Maxwell stress inside magnetic materials.
1	Ignores Maxwell stress inside magnetic materials. Maxwell stress is calculated in the air region adjoining the magnetic-material surface.

Tip

Set to 1 when only the total force or torque on magnetic materials is required. It is faster than NODAL_FORCE_METHOD(3) = 0, but is not normally used.

PHI_OPTION#

PHI_OPTION(3)#

Text-format section

Fixed parameter set 1#
[row, col] = [1, 3]

Electric scalar potential option#
Setting value	Description
0: Default	Uses the time integral of the electric scalar potential as \(\phi\).
1	Uses the electric scalar potential itself as \(\phi\). CG-method convergence is faster.

Note

Release 2024.11

Up to r12.0, this option was used for steady-current eddy-current analysis (STEADY_CURRENT(2) = 1). From 2023.11 onward, it can also be used for ordinary eddy-current analysis, but setting it to 0 is recommended.

FIXED_COORDINATE#

FIXED_COORDINATE(3)#

Text-format section

Fixed parameter set 1#
[row, col] = [1, 4]

Steady-current eddy-current analysis coordinate-system option#
Setting value	Description
0: Default	Uses a moving coordinate system fixed to the conductor.
1	Uses a coordinate system fixed in space. Specify this option when conductors move while in electrical contact during `STEADY_CURRENT(2)` = 1 analysis.

TREE_GAUGE#

TREE_GAUGE(3)#

Text-format section

Fixed parameter set 1#
[row, col] = [2, 1]

Tree-based gauge option#
Setting value	Description
-1 Default	Does not impose a tree-based gauge.
0	Fully fixes the gauge using a tree structure. Zero-fixed edges are selected in element order and are not regular.
1	Sets tree edges in the x direction to zero.
2	Sets tree edges in the y direction to zero.
3	Sets tree edges in the z direction to zero.

Warning

Currently unreliable. Set to -1.

Original setting: 0 reduces the number of variables and the analysis memory requirement, but ICCG convergence becomes extremely slow compared with -1. Values 1, 2, and 3 are specialized and normally unnecessary.

REGULARIZATION#

REGULARIZATION(3)#

Text-format section

Fixed parameter set 1#
[row, col] = [2, 2]

Regularization option#
Setting value	Description
0: Default	Does not perform regularization.
1	Regularizes equations for `COIL(17.1)`, `ELMCUR(17.2)`, and `SDEFCOIL(17.3)`. This improves ICCG convergence, but use caution when current discontinuities are present.

Important

Regularization is applied to each current and magnetic-field source series; therefore, each series must satisfy zero current divergence.

RENUMBERING#

RENUMBERING(3)#

Text-format section

Fixed parameter set 1#
[row, col] = [2, 3]

Renumbering option#
Setting value	Description
0: Default	Renumbers the matrix. This accelerates ICCG convergence.
-1	Does not renumber the matrix. This reduces the required memory.

Note

Renumbering generally improves convergence behavior.

SCALING#

SCALING(3)#

Text-format section

Fixed parameter set 1#
[row, col] = [2, 4]

Scaling option#
Setting value	Description
0: Default	Applies diagonal scaling to the matrix.
-1	Does not apply diagonal scaling to the matrix. It is rarely effective.

Note

Scaling generally improves convergence behavior.

LINE_SEARCH#

LINE_SEARCH(3)#

Text-format section

Fixed parameter set 1#
[row, col] = [2, 5]

Line-search option#
Setting value	Description
0: Default	Does not determine automatically.
1	For nonlinear analysis (`NON_LINEAR(2)`), automatically determines the Newton-Raphson step width using the line-search method.

Note

This function can be effective when magnetic saturation is strong and nonlinear-iteration residuals decrease very slowly.

MATRIX_ASYMMETRICITY#

MATRIX_ASYMMETRICITY(3)#

Text-format section

Fixed parameter set 1#
[row, col] = [2, 6]

Matrix asymmetry option#
Setting value	Description
0: Default	Uses symmetric magnetic properties or forces a symmetric analysis. When `ANISOTROPY(16.1)` = 1 and BH-curve anisotropy is weak, symmetrization converges and has almost no effect on results.
1	Uses asymmetric magnetic properties. Select this when anisotropy is strong and symmetrization does not converge. The analysis requires more memory. This setting is mandatory when using the Jiles-Atherton model `J_A_Model(16.1)` or the play model `Play_Model(16.1)`.

3. Potentials and Gauge Conditions

Contents

3. Potentials and Gauge Conditions#

Input settings#

Input format#

JSON format#

Examples#

Static analysis#

Transient analysis#

Steady-state AC analysis#

Detailed description#

3_Potential_Gauge_Conditions#

POTENTIAL#

NODAL_FORCE_METHOD#

PHI_OPTION#

FIXED_COORDINATE#

TREE_GAUGE#

REGULARIZATION#

RENUMBERING#

SCALING#

LINE_SEARCH#

MATRIX_ASYMMETRICITY#