interpolateMagneticPotential

Interpolate magnetic potential in magnetostatic result at arbitrary spatial locations

Since R2021a

collapse all in page

    Syntax

    Aintrp = interpolateMagneticPotential(magnetostaticresults,xq,yq)
    Aintrp = interpolateMagneticPotential(magnetostaticresults,xq,yq,zq)
    Aintrp = interpolateMagneticPotential(magnetostaticresults,querypoints)

    Description

    Aintrp = interpolateMagneticPotential(magnetostaticresults,xq,yq) returns the interpolated magnetic potential values at the 2-D points specified in xq and yq.

    example

    Aintrp = interpolateMagneticPotential(magnetostaticresults,xq,yq,zq) uses 3-D points specified in xq, yq, and zq.

    example

    Aintrp = interpolateMagneticPotential(magnetostaticresults,querypoints) returns the interpolated magnetic potential values at the points specified in querypoints.

    example

    Examples

    collapse all

    Open Live Script

    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])

    Figure contains an axes object. The axes object contains 5 objects of type line, text.

    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

    Figure contains an axes object. The axes object contains 12 objects of type patch, line.

    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
axis equal

    Figure contains an axes object. The axes object contains an object of type contour.

    Alternatively, you can specify the grid by using a matrix of query points.

    querypoints = [X(:),Y(:)]';
Aintrp = interpolateMagneticPotential(R,querypoints);
    Open Live Script

    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)

    Figure contains an axes object. The axes object contains 6 objects of type quiver, text, patch, line.

    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: [1×1 FEStruct]
          MagneticField: [1×1 FEStruct]
    MagneticFluxDensity: [1×1 FEStruct]
                   Mesh: [1×1 FEMesh]

    Plot the magnetic potential.

    pdeplot3D(R.Mesh,FlowData=[R.MagneticPotential.Ax ...
                           R.MagneticPotential.Ay ...
                           R.MagneticPotential.Az])

    Figure contains an axes object. The hidden axes object contains 5 objects of type quiver, text.

    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")

    Figure contains an axes object. The axes object contains an object of type quiver.

    Input Arguments

    collapse all

    Solution of a magnetostatic problem, specified as a MagnetostaticResults object. Create magnetostaticresults using the solve function.

    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

    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

    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

    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

    collapse all

    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