interpolateMagneticField
Interpolate magnetic field in magnetostatic result at arbitrary spatial locations
Since R2021a
Syntax
Description
returns the interpolated magnetic field values at the 2-D points specified in
Hintrp
= interpolateMagneticField(magnetostaticresults
,xq
,yq
)xq
and yq
.
uses 3-D points specified in Hintrp
= interpolateMagneticField(magnetostaticresults
,xq
,yq
,zq
)xq
, yq
, and
zq
.
returns the interpolated magnetic field values at the points specified in
Hintrp
= interpolateMagneticField(magnetostaticresults
,querypoints
)querypoints
.
Examples
Interpolate Magnetic Field in 2-D Magnetostatic Analysis
Create a square geometry and plot it with the edge labels.
R1 = [3,4,-1,1,1,-1,1,1,-1,-1]'; g = decsg(R1,'R1',('R1')'); pdegplot(g,EdgeLabels="on") xlim([-1.1 1.1]) ylim([-1.1 1.1])
Create an femodel
object for magnetostatic analysis and include the geometry into the model.
model = femodel(AnalysisType="magnetostatic", ... Geometry=g);
Specify the vacuum permeability in the SI system of units.
model.VacuumPermeability = 1.2566370614E-6;
Specify the relative permeability of the material.
model.MaterialProperties = ...
materialProperties(RelativePermeability=5000);
Apply the magnetic potential boundary conditions on the boundaries of the square.
model.EdgeBC([1 3]) = edgeBC(MagneticPotential=0); model.EdgeBC([2 4]) = edgeBC(MagneticPotential=0.01);
Specify the current density for the entire geometry.
model.FaceLoad = faceLoad(CurrentDensity=0.5);
Generate the mesh.
model = generateMesh(model);
Solve the problem and plot the magnetic field.
R = solve(model); pdeplot(R.Mesh,FlowData=[R.MagneticField.Hx ... R.MagneticField.Hy]) axis equal
Interpolate the resulting magnetic field to a grid covering the central portion of the geometry, for x
and y
from -0.5
to 0.5
.
v = linspace(-0.5,0.5,51); [X,Y] = meshgrid(v); Hintrp = interpolateMagneticField(R,X,Y)
Hintrp = FEStruct with properties: Hx: [2601x1 double] Hy: [2601x1 double]
Reshape Hintrp.Hx
and Hintrp.Hy
and plot the resulting electric field.
HintrpX = reshape(Hintrp.Hx,size(X));
HintrpY = reshape(Hintrp.Hy,size(Y));
figure
quiver(X,Y,HintrpX,HintrpY,Color="red")
Alternatively, you can specify the grid by using a matrix of query points.
querypoints = [X(:),Y(:)]'; Hintrp = interpolateMagneticField(R,querypoints);
Interpolate Magnetic Field in 3-D Magnetostatic Analysis
Create an femodel
object for magnetostatic analysis and include a geometry of a plate with a hole into the model.
model = femodel(AnalysisType="magnetostatic", ... Geometry="PlateHoleSolid.stl");
Plot the geometry.
pdegplot(model.Geometry,FaceLabels="on",FaceAlpha=0.3)
Specify the vacuum permeability value in the SI system of units.
model.VacuumPermeability = 1.2566370614E-6;
Specify the relative permeability of the material.
model.MaterialProperties = ...
materialProperties(RelativePermeability=5000);
Specify the current density for the entire geometry.
model.CellLoad = cellLoad(CurrentDensity=[0;0;0.5]);
Apply the magnetic potential boundary conditions on the side faces and the face bordering the hole.
model.FaceBC(3:6) = faceBC(MagneticPotential=[0;0;0]); model.FaceBC(7) = faceBC(MagneticPotential=[0;0;0.01]);
Generate the linear mesh.
model = generateMesh(model,GeometricOrder="linear");
Solve the problem.
R = solve(model)
R = MagnetostaticResults with properties: MagneticPotential: [1x1 FEStruct] MagneticField: [1x1 FEStruct] MagneticFluxDensity: [1x1 FEStruct] Mesh: [1x1 FEMesh]
Plot the magnetic field density.
pdeplot3D(R.Mesh,FlowData=[R.MagneticField.Hx ... R.MagneticField.Hy ... R.MagneticField.Hz])
Interpolate the resulting magnetic field to a grid covering the central portion of the geometry, for x, y, and z.
x = linspace(3,7,5); y = linspace(0,1,5); z = linspace(8,12,5); [X,Y,Z] = meshgrid(x,y,z); Hintrp = interpolateMagneticField(R,X,Y,Z)
Hintrp = FEStruct with properties: Hx: [125x1 double] Hy: [125x1 double] Hz: [125x1 double]
Reshape Hintrp.Hx
, Hintrp.Hy
, and Hintrp.Hz
.
HintrpX = reshape(Hintrp.Hx,size(X)); HintrpY = reshape(Hintrp.Hy,size(Y)); HintrpZ = reshape(Hintrp.Hz,size(Z));
Plot the resulting magnetic field.
figure
quiver3(X,Y,Z,HintrpX,HintrpY,HintrpZ,Color="red")
view([30 10])
view([10 15])
Input Arguments
magnetostaticresults
— Solution of magnetostatic problem
MagnetostaticResults
object
Solution of a magnetostatic problem, specified as a MagnetostaticResults
object. Create magnetostaticresults
using the solve
function.
xq
— x-coordinate query points
real array
x-coordinate query points, specified as a real array.
interpolateMagneticField
evaluates the magnetic field at the 2-D
coordinate points [xq(i) yq(i)]
or at the 3-D coordinate points
[xq(i) yq(i) zq(i)]
for every i
. Because of
this, xq
, yq
, and (if present)
zq
must have the same number of entries.
interpolateMagneticField
converts the query points to column
vectors xq(:)
, yq(:)
, and (if present)
zq(:)
. It returns magnetic field values as a column vector of the
same size. To ensure that the dimensions of the returned solution are consistent with
the dimensions of the original query points, use reshape
. For
example, use HintrpX = reshape(Hintrp.Hx,size(xq))
.
Example: xq = [0.5 0.5 0.75 0.75]
Data Types: double
yq
— y-coordinate query points
real array
y-coordinate query points, specified as a real array.
interpolateMagneticField
evaluates the magnetic field at the 2-D
coordinate points [xq(i) yq(i)]
or at the 3-D coordinate points
[xq(i) yq(i) zq(i)]
for every i
. Because of
this, xq
, yq
, and (if present)
zq
must have the same number of entries.
interpolateMagneticField
converts the query points to column
vectors xq(:)
, yq(:)
, and (if present)
zq(:)
. It returns magnetic field values as a column vector of the
same size. To ensure that the dimensions of the returned solution are consistent with
the dimensions of the original query points, use reshape
. For
example, use HintrpY = reshape(Hintrp.Hy,size(yq))
.
Example: yq = [1 2 0 0.5]
Data Types: double
zq
— z-coordinate query points
real array
z-coordinate query points, specified as a real array.
interpolateMagneticField
evaluates the magnetic field at the 3-D
coordinate points [xq(i) yq(i) zq(i)]
. Therefore,
xq
, yq
, and zq
must have
the same number of entries.
interpolateMagneticField
converts the query points to column
vectors xq(:)
, yq(:)
, and
zq(:)
. It returns magnetic field values as a column vector of the
same size. To ensure that the dimensions of the returned solution are consistent with
the dimensions of the original query points, use reshape
. For
example, use HintrpZ = reshape(Hintrp.Hz,size(zq))
.
Example: zq = [1 1 0 1.5]
Data Types: double
querypoints
— Query points
real matrix
Query points, specified as a real matrix with either two rows for 2-D geometry or
three rows for 3-D geometry. interpolateMagneticField
evaluates
magnetic field at the coordinate points querypoints(:,i)
for every
i
, so each column of querypoints
contains
exactly one 2-D or 3-D query point.
Example: For a 2-D geometry, querypoints = [0.5 0.5 0.75 0.75; 1 2 0
0.5]
Data Types: double
Output Arguments
Hintrp
— Magnetic field at query points
FEStruct
Magnetic field at query points, returned as an FEStruct
object
with the properties representing the spatial components of the magnetic field at the
query points. For query points that are outside the geometry,
Hintrp.Hx(i)
, Hintrp.Hy(i)
, and
Hintrp.Hz(i)
are NaN
. Properties of an
FEStruct
object are read-only.
Version History
Introduced in R2021a
See Also
Objects
Functions
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