interpolateMagneticPotential
Interpolate magnetic potential in magnetostatic result at arbitrary spatial locations
Since R2021a
Syntax
Description
returns the interpolated magnetic potential values at the 2-D points specified in
Aintrp
= interpolateMagneticPotential(magnetostaticresults
,xq
,yq
)xq
and yq
.
uses 3-D points specified in Aintrp
= interpolateMagneticPotential(magnetostaticresults
,xq
,yq
,zq
)xq
, yq
, and
zq
.
returns the interpolated magnetic potential values at the points specified in
Aintrp
= interpolateMagneticPotential(magnetostaticresults
,querypoints
)querypoints
.
Examples
Interpolate Magnetic Potential 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 potential.
R = solve(model); pdeplot(R.Mesh,XYData=R.MagneticPotential, ... Contour="on") axis equal
Interpolate the resulting magnetic potential 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); Aintrp = interpolateMagneticPotential(R,X,Y);
Reshape Aintrp
and plot the resulting magnetic potential.
Aintrp = reshape(Aintrp,size(X)); figure contourf(X,Y,Aintrp) colormap(cool) colorbar
Alternatively, you can specify the grid by using a matrix of query points.
querypoints = [X(:),Y(:)]'; Aintrp = interpolateMagneticPotential(R,querypoints);
Interpolate Magnetic Potential 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);
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 potential.
pdeplot3D(R.Mesh,FlowData=[R.MagneticPotential.Ax ... R.MagneticPotential.Ay ... R.MagneticPotential.Az])
Interpolate the resulting magnetic potential to a grid covering the entire geometry, for x, y, and z.
x = linspace(0,10,11); y = linspace(0,1,5); z = linspace(0,20,11); [X,Y,Z] = meshgrid(x,y,z); Aintrp = interpolateMagneticPotential(R,X,Y,Z);
Reshape Aintrp.Ax
, Aintrp.Ay
, and Aintrp.Az
to match the shape of the input grid.
AintrpX = reshape(Aintrp.Ax,size(X)); AintrpY = reshape(Aintrp.Ay,size(Y)); AintrpZ = reshape(Aintrp.Az,size(Z));
Plot the resulting magnetic potential.
figure
quiver3(X,Y,Z,AintrpX,AintrpY,AintrpZ,Color="red")
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.
interpolateMagneticPotential
evaluates the magnetic potential 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.
interpolateMagneticPotential
converts query points to column
vectors xq(:)
, yq(:)
, and (if present)
zq(:)
. It returns magnetic potential 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 Aintrp = reshape(Aintrp,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.
interpolateMagneticPotential
evaluates the magnetic potential at
the coordinate points [xq(i),yq(i)]
for every i
.
Because of this, xq
and yq
must have the same
number of entries.
interpolateMagneticPotential
converts query points to column
vectors xq(:)
, yq(:)
, and (if present)
zq(:)
. It returns magnetic potential 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 Aintrp = reshape(Aintrp,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.
interpolateMagneticPotential
evaluates the magnetic potential at
the 3-D coordinate points [xq(i) yq(i) zq(i)]
. Therefore,
xq
, yq
, and zq
must have
the same number of entries.
interpolateMagneticPotential
converts the query points to column
vectors xq(:)
, yq(:)
, and
zq(:)
. It returns magnetic potential 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 Aintrp = reshape(Aintrp,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. interpolateMagneticPotential
evaluates
the magnetic potential 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
Aintrp
— Magnetic potential at query points
vector | FEStruct
object
Magnetic potential at query points, returned as a vector for a 2-D problem or an
FEStruct
object for a 3-D problem. The properties of
FEStruct
contain the components of the magnetic potential at query
points. For query points i
that are outside the geometry,
Aintrp(i)
, Aintrp.Ax(i)
,
Aintrp.Ay(i)
, and Aintrp.Az(i)
are
NaN
. Properties of an FEStruct
object are
read-only.
Version History
Introduced in R2021a
See Also
Objects
Functions
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