13. Boundary Conditions#

Sets boundary conditions. A far-boundary condition is automatically applied to the outermost boundary surfaces that are not explicitly specified in the surface definitions.

Settings#

13_Boundary_Conditions JSON key: Boundary condition object

FAR_BOUNDARY_CONDITION(13) Sets the far-boundary condition

PHI_BOUNDARY_CONDITION(13) Sets the far-boundary condition for the electric scalar potential

Infinite-boundary condition settings (when FAR_BOUNDARY_CONDITION = 2)

NO_BE_TERMS(13) Expansion order of infinite boundary elements

BE_CENTER(13) Coordinates (m) of the infinite-boundary-element center

DISTANCE_JUDGE(13) Distance (m) below which a node coordinate is considered to be on the boundary surface

NO_DIRICHLET_PLANE(13) Number of planes on which to impose the condition that the magnetic field is tangent to the surface

NO_NEUMANN_PLANE(13) Number of planes on which to impose the condition that the magnetic field enters normal to the surface

DIRICHLET_PLANE(13) JSON key: Imposes the condition that the magnetic field is tangent to the surface

NEUMANN_PLANE(13) JSON key: Imposes the condition that the magnetic field enters normal to the surface

CXYZ/C / OPTION(13) Plane equations for specifying DIRICHLET_PLANE and NEUMANN_PLANE

NO_A_0_LINE(13) Number of lines on which to set A=0

A_0_LINE(13) JSON key: Line on which to set A=0

S_XYZ E_XYZ(13) Start and end coordinates of the edge on which A=0 is specified

Input format#

Text-format section

Type:: Fixed parameter set 1
Number of rows:: 1
Number of parameters:: 2

Text format#

* FAR_BOUNDARY_CONDITION * PHI_BOUNDARY_CONDITION *
        I                           I

Type:

Additional parameter set 1

Number of rows:

1

Number of parameters:

4

Text format#

* NO_BE_TERMS * BE_CENTER_X * BE_CENTER_Y * BE_CENTER_Z *
    I             E             E            E

Type:

Fixed parameter set 2

Number of rows:

1

Number of parameters:

1

Text format#

* DISTANCE_JUDGE  *
        E

Type:

Fixed parameter set 3

Number of rows:

1

Number of parameters:

1

Text format#

* NO_DIRICHELET_PLANE *
        I

Type:

Fixed parameter set 4

Number of rows:

1

Number of parameters:

1

Text format#

* NO_NEUMANN_PLANE *
        I

Type:

Additional parameter set 2

Number of rows:

1*NO_DIRICHELET_PLANE or 1*NO_NEUMANN_PLANE

Number of parameters:

4

Text format#

* CX * CY * CZ * C * OPTION *
E    E    E   E     I

Type:

Fixed parameter set 5

Number of rows:

1

Number of parameters:

1

Text format#

* NO_A_0_LINE *
    I

Type:

Additional parameter set 4

Number of rows:

1*NO_A_0_LINE

Number of parameters:

6

Text format#

* SX * SY * SZ * EX * EY * EZ *
E    E    E    E    E    E

Text example

1/8 model, far boundary: \(\mathbf{B}_n = 0\)

Text format#

* FAR_BOUNDARY_CONDITION * PHI_BOUNDARY_CONDITION *
    0
* DISTANCE_JUDGE *
    1.e-6
* NO_DIRICHELET_PLANE *
    2
* CX * CY * CZ * C *
1    0    0    0
0    1    0    0
* NO_NEUMANN_PLANE *
    1
* CX * CY * CZ * C *
0    0    1    0
* NO_A_0_LINE *
    0

JSON format#

JSON format from 2024.11#

"13_Boundary_Conditions" :
{
    "FAR_BOUNDARY_CONDITION" : I,
    "PHI_BOUNDARY_CONDITION" : I,
    "INFINITE_BOUNDARY_CONDITION" :
    {
        "NO_BE_TERMS" : I,
        "BE_CENTER" : [ E, E, E ]
    },
    "DISTANCE_JUDGE" : E,
    "DIRICHLET_PLANE" :
    {
        "CXYZ" :
        [
            [ E, E, E, E, I ]
        ]
    },
    "NEUMANN_PLANE" :
    {
        "CXYZ" :
        [
            [ E, E, E, E, I ]
        ]
    },
    "A0_LINES" : [ E, E, E, E, E, E ]
},

JSON example

JSON format from 2024.11#

"13_Boundary_Conditions" :
{
    "FAR_BOUNDARY_CONDITION" : 0,
    "PHI_BOUNDARY_CONDITION" : 0,
    "DISTANCE_JUDGE" : 1.0e-06,
    "DIRICHLET_PLANE" :
    {
        "CXYZ" :
        [
            [ 1.0, 0.0, 0.0, 0.0, 0 ],
            [ 0.0, 1.0, 0.0, 0.0, 0 ]
        ]
    },
    "NEUMANN_PLANE" :
    {
        "CXYZ" :
        [
            [ 0.0, 0.0, 1.0, 0.0, 0 ]
        ]
    }
},

Detailed description#

13_Boundary_Conditions#

13_Boundary_Conditions#

JSON key:: Boundary condition object

FAR_BOUNDARY_CONDITION#

FAR_BOUNDARY_CONDITION(13)#

Text-format section

Fixed parameter set 1#

[row, col] = [1, 1]

Sets the far-boundary condition.

<For magnetic-field analysis>

Far-boundary condition#
Value	Description
0	Imposes \(\pmb{B}_n = 0\) (the magnetic field is tangent to the surface) on the far boundary. This is an electric-wall condition ( \(\pmb{A} \times n = 0\) ).
1	Imposes \(\pmb{H}_t = 0\) (the magnetic field enters normal to the surface) on the far boundary. This is a magnetic-wall condition ( \(\pmb{A} \times n = free\) ).
2	Imposes the infinite-boundary-element condition.
3	Performs the calculation by applying the \(\pmb{H}_t\) generated by the external current magnetic-field source `COIL(17.1)` at the far boundary. `COIL(17.1)` must be outside the calculation mesh, and the entire region must be a total-potential region.

Caution

If the far boundary is in a total-potential region, the condition is imposed on the total magnetic field. If it is in a reduced-potential region, the condition is imposed on the induced magnetic field excluding the external current magnetic-field source.

<For electrostatic analysis (STATIC(2)=2)>

Far-boundary condition#
Value	Description
0	Imposes \(\pmb{E}_t = 0\) (the electric field enters normal to the surface) on the far boundary. This is a magnetic-wall condition ( \(\phi = 0\) ).
1	Imposes \(\pmb{D}_n = 0\) (the electric field is tangent to the surface) on the far boundary. This is an electric-wall condition ( \(\phi = free\) ).

<For steady-current analysis (STATIC(2)=3)>

Far-boundary condition#
Value	Description
0	Imposes \(\pmb{E}_t = 0\) (the electric field enters normal to the surface) on the far boundary. This is a magnetic-wall condition ( \(\phi = 0\) ).
1	Imposes \(\pmb{J}_n = 0\) (the current is tangent to the surface) on the far boundary. This is an electric-wall condition ( \(\phi = free\) ).

<For induced-current analysis under low-frequency magnetic-field variation (TRANSIENT(2)=1, POTENTIAL(3)=4)>

Far-boundary condition#
Value	Description
1	Imposes \(\pmb{J}_t = 0\) (the current is normal to the surface) on the far boundary.

Note

Revision history

Release 10.1.2

Added an enhanced induced-current analysis function for low-frequency magnetic-field variation.

PHI_BOUNDARY_CONDITION#

PHI_BOUNDARY_CONDITION(13)#

Text-format section

Fixed parameter set#

[row, col] = [2, 1]

Far-boundary condition for the electric scalar potential#
Value	Description
0	Imposes a zero-potential condition ( \(\phi = 0\) ). Default value
1	Imposes \(\pmb{D}_n = 0\) (the electric field is tangent to the surface) on the far boundary ( \(\phi = free\) ).

Effective for Darwin-model and full-wave analyses.

Infinite-boundary condition settings (when `FAR_BOUNDARY_CONDITION` = 2)#

NO_BE_TERMS#

NO_BE_TERMS(13)#

Text-format section

Semi-fixed parameter set 1#

[row, col] = [1, 1]

Type:: Integer (I)
Description:: Infinite-boundary-element expansion order >= 1. A value of approximately 3 is appropriate.

BE_CENTER#

BE_CENTER(13)#

Text-format section

Semi-fixed parameter set 1#

[row, col] = [1, 2]~[1, 4]

Type:: Real number (E)
Unit:: m
Description:: Specifies the coordinates (x,y,z) of the infinite-boundary-element center.

DISTANCE_JUDGE#

DISTANCE_JUDGE(13)#

Text-format section

Fixed parameter set 2#

[row, col] = [1, 1]

Type:: Real number (E)
Value:: > 0
Unit:: m
Description:: Distance below which a node coordinate is considered to be on the boundary surface (on the boundary line for a two-dimensional mesh). Set it smaller than the minimum nodal spacing. Approximately one tenth of the minimum nodal spacing is appropriate.

Note

The following operations are particularly susceptible to its effects; use caution.

Matching of periodic boundary surfaces when setting a rotational periodic boundary condition
Extraction of sliding-motion surfaces (determining whether they are concentric)

Text-format section

NO_DIRICHLET_PLANE(13)#

NO_DIRICHLET_PLANE

Fixed parameter set 3#

[row, col] = [1, 1]
Type=I

DIRICHLET_PLANE#

DIRICHLET_PLANE(13)#

<For magnetic-field analysis>

Number of planes on which to impose \(\pmb{B}_n = 0\) (the magnetic field is tangent to the surface).

Specify the boundary-condition surfaces CX / CY / CZ / C / OPTION for the number of NO_DIRICHELET_PLANE planes.

Note

(Hint)

For example, the Z=0 plane in a case that is symmetric about the top and bottom, with current flowing in opposite directions above and below.

<For electrostatic-field analysis (STATIC(2)=2,3)>

Number of planes on which to impose the zero-potential condition (\(\phi = 0\)).

Default value = 0

In JSON format, enter the following values as an empty array [].

Text-format section

NO_NEUMANN_PLANE(13)#

NO_NEUMANN_PLANE

Fixed parameter set 4#

[row, col] = [1, 1]
Type=I

NEUMANN_PLANE#

NEUMANN_PLANE(13)#

<For magnetic-field analysis>

Number of planes on which to impose \(\pmb{H}_t = 0\) (the magnetic field enters normal to the surface).

Specify the boundary-condition surfaces CX / CY / CZ / C / OPTION for the number of NO_NEUMANN_PLANE planes.

Note

(Hint)

For example, the Z=0 plane in a case that is symmetric about the top and bottom, with current flowing in the same direction above and below.
On surfaces with \(\pmb{H}_t = 0\) (the far boundary when FAR_BOUNDARY_CONDITION = 1 and the surfaces specified by this parameter), imposes a free boundary condition (Neumann condition) on \(\pmb{A}_t\).

<For electrostatic analysis (STATIC(2)=2)>

Number of planes on which to impose \(\pmb{D}_n = 0\) (the electric field is tangent to the surface).

<For electrostatic analysis (STATIC(2)=3)>

Number of planes on which to impose \(\pmb{J}_n = 0\) (the current is tangent to the surface).

Default value = 0

In JSON format, enter the following values as an empty array [].

CXYZ/C / OPTION#

CXYZ/C / OPTION(13)#

Text-format section

Type:: Additional parameter set
Number of rows:: 1*NO_DIRICHLET_PLANE or 1*NO_NEUMANN_PLANE
Number of parameters:: 5

Additional parameter set#

[row, col] = [1, 1]

Specify a plane by an equation for each NO_DIRICHELET_PLANE and NO_NEUMANN_PLANE entry.

Type:: Array of 4 real numbers (E) and 1 integer (I)
Unit:: m
Count:: 4E, 1I
Description:: Specifies the plane equation. The plane equation is expressed as follows.

Plane equation

\[C_x x + C_y y + C_z z + C = 0\]

For OPTION, specify the condition to impose on the configured boundary surfaces as shown below.

OPTION#
Value	Description
0	Imposes a zero-potential condition ( \(\phi = 0\) ) on the configured boundary surface.
1	Imposes \(\pmb{D}_n = 0\) (the electric field is tangent to the surface) on the configured boundary surface ( \(\phi = free\) ).

Effective for Darwin-model and full-wave analyses.

Note

For example,

x=0 plane: [1.0, 0.0, 0.0, 0.0, 0], x=1.0 plane: [1.0, 0.0, 0.0, 1.0, 0]

NO_A_0_LINE#

NO_A_0_LINE(13)#

A_0_LINE(13)#

Text-format section

Fixed parameter set 5#

[row, col] = [1, 1]

Type:: Integer (I)
Description:: Number of lines on which A (the magnetic vector potential) is set to zero for edges lying on the defined lines, including their extensions.
Default value:: 0

In JSON format, enter the following values as an empty array [].

Note

(Hint) Apply this when no essential boundary condition (\(\pmb{B}_n = 0\), i.e. \(\pmb{A} \times n = 0\)) is imposed on \(\pmb{A}\) anywhere and no reference with \(\pmb{A} = 0\) exists. Use it on the central axis when there is rotational symmetry without a symmetry plane and the far-boundary condition FAR_BOUNDARY_CONDITION = 1 is specified. It is usually unnecessary ( NO_A_0_LINE = 0).

S_XYZ E_XYZ#

S_XYZ E_XYZ(13)#

Text-format section

Type:: Additional parameter set
Number of rows:: 1*NO_A_0_LINE
Number of parameters:: 6

Fixed parameter set 5#

[row, col] = [1, 1]

Repeat NO_A_0_LINE times.

Type:: Real-number array (E)
Unit:: m
Count:: 6
Description:: Start and end coordinates of the edge on which A=0 is specified.

S_XYZ: Start coordinates of the line.
E_XYZ: End coordinates of the line.

Note

(Hint) For example, the z axis is [SX,SY,SZ, EX,EY,EZ] = [0,0,0, 0,0,1.0].

13. Boundary Conditions

Contents

13. Boundary Conditions#

Settings#

Input format#

JSON format#

Detailed description#

13_Boundary_Conditions#

FAR_BOUNDARY_CONDITION#

PHI_BOUNDARY_CONDITION#

Infinite-boundary condition settings (when FAR_BOUNDARY_CONDITION = 2)#

NO_BE_TERMS#

BE_CENTER#

DISTANCE_JUDGE#

DIRICHLET_PLANE#

NEUMANN_PLANE#

CXYZ/C / OPTION#

NO_A_0_LINE#

S_XYZ E_XYZ#

Infinite-boundary condition settings (when `FAR_BOUNDARY_CONDITION` = 2)#