electromagneticSource
Specify current density, charge density, and magnetization for electromagnetic model
Since R2021a
Domain-specific electromagnetic workflow is not recommended. New features might not be compatible with this workflow. For help migrating your existing code to the unified finite element workflow, see Migration from Domain-Specific to Unified Workflow.
Syntax
Description
electromagneticSource(
specifies the current density. The solver uses a current density for magnetostatic or
harmonic (time-harmonic) analyses.emagmodel
,"CurrentDensity",J
)
For a 3-D magnetostatic analysis, you can specify current density by using the DC
conduction results. See ConductionResults
.
The toolbox does not support conduction results as a source of current density for a 2-D
magnetostatic analysis, in which case current density must be a scalar or a function handle
returning a scalar that represents out-of-plane current.
electromagneticSource(___,
specifies the charge or current density for the specified geometry region. Use this syntax
with any of the input argument combinations in the previous syntaxes.RegionType
,RegionID
)
returns the electromagnetic source object.emagSource
= electromagneticSource(___)
Examples
Specify Charge Density on Entire Geometry
Specify charge density on the entire geometry for an electrostatic analysis.
emagmodel = createpde("electromagnetic","electrostatic"); importGeometry(emagmodel,"PlateHoleSolid.stl"); electromagneticSource(emagmodel,"ChargeDensity",10)
ans = ElectromagneticSourceAssignment with properties: RegionType: 'Cell' RegionID: 1 ChargeDensity: 10 CurrentDensity: [] Magnetization: []
Specify Current Density on Entire Geometry
Specify current density on the entire geometry for harmonic analysis.
Create an electromagnetic model for harmonic analysis.
model = createpde("electromagnetic","harmonic");
Include a square geometry in the model. Plot the geometry with the edge labels.
geometryFromEdges(model,@squareg); pdegplot(model,"EdgeLabels","on") xlim([-1.1 1.1]) ylim([-1.1 1.1])
Specify current density on the entire geometry. For a 2-D harmonic analysis model with the electric field type, the current density must be a column vector of two elements. When solving the model, the toolbox multiplies the specified current density value by -i
and by frequency.
electromagneticSource(model,"CurrentDensity",[1;0])
ans = ElectromagneticSourceAssignment with properties: RegionType: 'Face' RegionID: 1 ChargeDensity: [] CurrentDensity: [2x1 double] Magnetization: []
Specify Charge Density on Each Face
Specify charge density on individual faces in electrostatic analysis.
Create an electromagnetic model for electrostatic analysis.
emagmodel = createpde("electromagnetic","electrostatic");
Create a 2-D geometry with two faces. First, import and plot a 2-D geometry representing a plate with a hole.
gm = importGeometry(emagmodel,"PlateHolePlanar.stl"); pdegplot(gm,"EdgeLabels","on","FaceLabels","on")
Then, fill the hole by adding a face and plot the resulting geometry.
gm = addFace(gm,5); pdegplot(gm,"FaceLabels","on")
Specify charge density values separately for faces 1 and 2.
sc1 = electromagneticSource(emagmodel,"Face",1,"ChargeDensity",0.3)
sc1 = ElectromagneticSourceAssignment with properties: RegionType: 'Face' RegionID: 1 ChargeDensity: 0.3000 CurrentDensity: [] Magnetization: []
sc2 = electromagneticSource(emagmodel,"Face",2,"ChargeDensity",0.28)
sc2 = ElectromagneticSourceAssignment with properties: RegionType: 'Face' RegionID: 2 ChargeDensity: 0.2800 CurrentDensity: [] Magnetization: []
Specify Nonconstant Charge Density
Use a function handle to specify a charge density that depends on the coordinates.
Create an electromagnetic model for electrostatic analysis.
emagmodel = createpde("electromagnetic","electrostatic");
Create a unit circle geometry and include it in the model.
geometryFromEdges(emagmodel,@circleg);
Specify the charge density as a function of the x- and y-coordinates, .
rho = @(location,~)0.3.*sqrt(location.x.^2 + location.y.^2);
electromagneticSource(emagmodel,"ChargeDensity",rho)
ans = ElectromagneticSourceAssignment with properties: RegionType: 'Face' RegionID: 1 ChargeDensity: @(location,~)0.3.*sqrt(location.x.^2+location.y.^2) CurrentDensity: [] Magnetization: []
Use DC Conduction Solution as Current Density
Use a solution obtained by performing DC conduction analysis to specify current density for a magnetostatic model.
Create an electromagnetic model for DC conduction analysis.
emagmodel = createpde("electromagnetic","conduction");
Import and plot a geometry representing a plate with a hole.
gm = importGeometry(emagmodel,"PlateHoleSolid.stl"); pdegplot(gm,"FaceLabels","on","FaceAlpha",0.3)
Specify the conductivity of the material.
electromagneticProperties(emagmodel,"Conductivity",6e4);
Apply the voltage boundary conditions on the left, right, and back faces of the plate.
electromagneticBC(emagmodel,"Voltage",0,"Face",[1 3 5]);
Specify the surface current density on the front face of the geometry and on the face bordering the hole.
electromagneticBC(emagmodel,"SurfaceCurrentDensity",100,"Face",[2 7]);
Generate the mesh.
generateMesh(emagmodel);
Solve the model.
R = solve(emagmodel);
Change the analysis type of the model to magnetostatic.
emagmodel.AnalysisType = "magnetostatic";
This model already has a quadratic mesh that you generated for the DC conduction analysis. For a 3-D magnetostatic model, the mesh must be linear. Generate a new linear mesh. The generateMesh
function creates a linear mesh by default if the model is 3-D and magnetostatic.
generateMesh(emagmodel);
Specify the current density for the entire geometry using the DC conduction solution.
electromagneticSource(emagmodel,"CurrentDensity",R)
ans = ElectromagneticSourceAssignment with properties: RegionType: 'Cell' RegionID: 1 ChargeDensity: [] CurrentDensity: [1x1 pde.ConductionResults] Magnetization: []
Specify Magnetization
Specify magnetization on a face in a magnetostatic analysis.
Create a unit square geometry with a circle in its center. The circle represents a permanent magnet.
L = 0.8; r = 0.25; sq = [3 4 -L L L -L -L -L L L]'; circ = [1 0 0 r 0 0 0 0 0 0]'; gd = [sq,circ]; sf = "sq + circ"; ns = char('sq','circ'); ns = ns'; g = decsg(gd,sf,ns);
Plot the geometry with the face labels.
pdegplot(g,"FaceLabels","on")
Create a magnetostatic model and include the geometry in the model.
emagmodel = createpde("electromagnetic","magnetostatic"); geometryFromEdges(emagmodel,g);
Specify the magnetization magnitude.
M = 1;
To make the circle represent a permanent magnet, specify the uniform magnetization in the positive x-direction.
electromagneticSource(emagmodel,"Face",2,"Magnetization",M*[1;0])
ans = ElectromagneticSourceAssignment with properties: RegionType: 'Face' RegionID: 2 ChargeDensity: [] CurrentDensity: [] Magnetization: [2x1 double]
Input Arguments
emagmodel
— Electromagnetic model
ElectromagneticModel
object
Electromagnetic model, specified as an ElectromagneticModel
object. The model contains a geometry, a mesh, the
electromagnetic properties of the material, the electromagnetic sources, and the
boundary conditions.
rho
— Charge density
real number | function handle
Charge density, specified as a real number or a function handle. Use a function handle to specify a charge density that depends on the coordinates. For details, see More About.
Data Types: double
| function_handle
J
— Current density
real number | column vector | function handle | ConductionResults
object
Current density, specified as a real number, a column vector, a function handle, or
a ConductionResults
object. Use a function handle to specify a nonconstant current density.
For magnetostatic analysis, the current density must be
A real number or a function handle for a 2-D model. The toolbox does not support conduction results as a source of current density for a 2-D magnetostatic analysis.
A column vector of three elements, a
ConductionResults
object, or a function handle for a 3-D model.
For harmonic analysis with the electric field type, the toolbox multiplies the
specified current density by -i
and by frequency. The current density
must be
A column vector of two elements or a function handle that depends on the coordinates for a 2-D model.
A column vector of three elements or a function handle that depends on the coordinates for a 3-D model.
For harmonic analysis with the magnetic field type, the toolbox uses the curl of the specified current density. The current density must be
A scalar or a function handle that depends on the coordinates for a 2-D model.
A column vector of three elements or a function handle that depends on the coordinates for a 3-D model.
For details, see More About.
Data Types: double
| function_handle
M
— Magnetization
column vector | function handle
Magnetization, specified as a column vector of two elements for a 2-D model, a column vector of three elements for a 3-D model, or a function handle. Use a function handle to specify a magnetization that depends on the coordinates. For details, see More About.
Data Types: double
| function_handle
RegionType
— Geometric region type
"Face"
for a 2-D model | "Cell"
for a 3-D model
Geometric region type, specified as "Face"
for a 2-D model or
"Cell"
for a 3-D model.
Data Types: char
| string
RegionID
— Region ID
vector of positive integers
Region ID, specified as a vector of positive integers. Find the face or cell IDs by
using pdegplot
with the
FaceLabels
or CellLabels
name-value argument set
to "on"
.
Example: electromagneticSource(emagmodel,"CurrentDensity",10,"Face",1:3)
Data Types: double
Output Arguments
emagSource
— Handle to electromagnetic source
ElectromagneticSourceAssignment
object
Handle to the electromagnetic source, returned as an
ElectromagneticSourceAssignment
object. For more information, see
ElectromagneticSourceAssignment Properties.
More About
Specifying Nonconstant Parameters of Electromagnetic Model
In Partial Differential Equation Toolbox™, use a function handle to specify these electromagnetic parameters when they depend on the coordinates and, for a harmonic analysis, on the frequency:
Relative permittivity of the material
Relative permeability of the material
Conductivity of the material
Charge density as source (can depend on space only)
Current density as source (can depend on space only)
Magnetization (can depend on space only)
Voltage on the boundary (can depend on space only)
Magnetic potential on the boundary (can depend on space only)
Electric field on the boundary (can depend on space only)
Magnetic field on the boundary (can depend on space only)
Surface current density on the boundary (can depend on space only)
For example, use function handles to specify the relative permittivity, charge density, and
voltage on the boundary for emagmodel
.
electromagneticProperties(emagmodel, ... "RelativePermittivity", ... @myfunPermittivity) electromagneticSource(emagmodel, ... "ChargeDensity",@myfunCharge, ... "Face",2) electromagneticBC(emagmodel, ... "Voltage",@myfunBC, ... "Edge",2)
The function must be of the form:
function emagVal = myfun(location,state)
The solver computes and populates the data in the location
and
state
structure arrays and passes this data to your function. You can
define your function so that its output depends on this data. You can use any names in place of
location
and state
.
If you call electromagneticBC
with Vectorized
set to
"on"
, then location
can contain several evaluation
points. If you do not set Vectorized
or set Vectorized
to
"off"
, then the solver passes just one evaluation point in each
call.
location
— A structure array containing these fields:location.x
— The x-coordinate of the point or pointslocation.y
— The y-coordinate of the point or pointslocation.z
— For a 3-D or an axisymmetric geometry, the z-coordinate of the point or pointslocation.r
— For an axisymmetric geometry, the r-coordinate of the point or points
Furthermore, for boundary conditions, the solver passes this data in the
location
structure:location.nx
— The x-component of the normal vector at the evaluation point or pointslocation.ny
— The y-component of the normal vector at the evaluation point or pointslocation.nz
— For a 3-D or an axisymmetric geometry, the z-component of the normal vector at the evaluation point or pointslocation.nr
— For an axisymmetric geometry, the r-component of the normal vector at the evaluation point or points
state
— A structure array containing this field for a harmonic electromagnetic problem:state.frequency
- Frequency at evaluation points
Relative permittivity, relative permeability, and conductivity get this data from the solver:
location.x
,location.y
,location.z
,location.r
state.frequency
for a harmonic analysisSubdomain ID
Charge density, current density, magnetization, surface current density on the boundary, and electric or magnetic field on the boundary get this data from the solver:
location.x
,location.y
,location.z
,location.r
Subdomain ID
Voltage or magnetic potential on the boundary get these data from the solver:
location.x
,location.y
,location.z
,location.r
location.nx
,location.ny
,location.nz
,location.nr
When you solve an electrostatic, magnetostatic, or DC conduction problem, the output
returned by the function handle must be of the following size. Here, Np =
numel(location.x)
is the number of points.
1
-by-Np
if a function specifies the nonconstant relative permittivity, relative permeability, or charge density. For the charge density, the output can also beNp
-by-1
.1
-by-Np
for a 2-D model and3
-by-Np
for a 3-D model if a function specifies the nonconstant current density and magnetic potential on the boundary. For the current density, the output can also beNp
-by-1
orNp
-by-3
.2
-by-Np
for a 2-D model and3
-by-Np
for a 3-D model if a function specifies the nonconstant magnetization or surface current density on the boundary.
When you solve a harmonic problem, the output returned by the function handle must be of the
following size. Here, Np = numel(location.x)
is the number of points.
1
-by-Np
if a function specifies the nonconstant relative permittivity, relative permeability, and conductivity.2
-by-Np
for a 2-D problem and3
-by-Np
for a 3-D problem if a function specifies the nonconstant electric or magnetic field.2
-by-Np
orNp
-by-2
for a 2-D problem and3
-by-Np
orNp
-by-3
for a 3-D problem if a function specifies the nonconstant current density and the field type is electric.1
-by-Np
orNp
-by-1
for a 2-D problem and3
-by-Np
orNp
-by-3
for a 3-D problem if a function specifies the nonconstant current density and the field type is magnetic.
If relative permittivity, relative permeability, or conductivity for a harmonic analysis
depends on the frequency, ensure that your function returns a matrix of NaN
values of the correct size when state.frequency
is NaN
.
Solvers check whether a problem is nonlinear by passing NaN
state values and
looking for returned NaN
values.
Additional Arguments in Functions for Nonconstant Electromagnetic Parameters
To use additional arguments in your function, wrap your function (that takes additional arguments) with an anonymous function that takes only the location
and state
arguments. For example:
emagVal = @(location,state) myfunWithAdditionalArgs(location,arg1,arg2,...) electromagneticBC(model,"Edge",3,"Voltage",emagVal)
Version History
Introduced in R2021aR2023a: Nonlinear magnetostatics
Magnetization and current density can depend on the magnetic flux density, magnetic potential, and its gradients.
R2022b: Magnetization value for permanent magnets
Magnetization can be specified to account for materials generating their own magnetic fields in a magnetostatic analysis workflow.
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