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interpolateElectricFlux

Interpolate electric flux density in electrostatic result at arbitrary spatial locations

Since R2021a

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    Syntax

    Dintrp = interpolateElectricFlux(electrostaticresults,xq,yq)
    Dintrp = interpolateElectricFlux(electrostaticresults,xq,yq,zq)
    Dintrp = interpolateElectricFlux(electrostaticresults,querypoints)

    Description

    Dintrp = interpolateElectricFlux(electrostaticresults,xq,yq) returns the interpolated electric flux density at the 2-D points specified in xq and yq.

    example

    Dintrp = interpolateElectricFlux(electrostaticresults,xq,yq,zq) uses 3-D points specified in xq, yq, and zq.

    example

    Dintrp = interpolateElectricFlux(electrostaticresults,querypoints) returns the interpolated electric flux density at the points specified in querypoints.

    example

    Examples

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    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 electrostatic analysis and include the geometry into the model.

    model = femodel(AnalysisType="electrostatic", ...
                Geometry=g);

    Specify the vacuum permittivity in the SI system of units.

    model.VacuumPermittivity = 8.8541878128E-12;

    Specify the relative permittivity of the material.

    model.MaterialProperties = ...
    materialProperties(RelativePermittivity=1);

    Apply the voltage boundary conditions on the edges of the square.

    model.EdgeBC([1 3]) = edgeBC(Voltage=0);
model.EdgeBC([2 4]) = edgeBC(Voltage=1000);

    Specify the charge density for the entire geometry.

    model.FaceLoad = faceLoad(ChargeDensity=5E-9);

    Generate the mesh.

    model = generateMesh(model);

    Solve the problem and plot the electric flux density.

    R = solve(model);
pdeplot(R.Mesh,FlowData=[R.ElectricFluxDensity.Dx ...
                         R.ElectricFluxDensity.Dy])
axis equal

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

    Interpolate the resulting electric flux density 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);

Dintrp = interpolateElectricFlux(R,X,Y)
    Dintrp = 
  FEStruct with properties:

    Dx: [2601x1 double]
    Dy: [2601x1 double]

    Reshape Dintrp.Dx and Dintrp.Dy and plot the resulting electric flux density.

    DintrpX = reshape(Dintrp.Dx,size(X));
DintrpY = reshape(Dintrp.Dy,size(Y));

figure
quiver(X,Y,DintrpX,DintrpY,Color="red")
axis equal

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

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

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

    Create an femodel object for electrostatic analysis and include a geometry of a plate with a hole into the model.

    model = femodel(AnalysisType="electrostatic", ...
                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 permittivity in the SI system of units.

    model.VacuumPermittivity = 8.8541878128E-12;

    Specify the relative permittivity of the material.

    model.MaterialProperties = ...
    materialProperties(RelativePermittivity=1);

    Specify the charge density for the entire geometry.

    model.CellLoad = cellLoad(ChargeDensity=5E-9);

    Apply the voltage boundary conditions on the side faces and the face bordering the hole.

    model.FaceBC(3:6) = faceBC(Voltage=0);
model.FaceBC(7) = faceBC(Voltage=1000);

    Generate the mesh.

    model = generateMesh(model);

    Solve the problem.

    R = solve(model)
    R = 
  ElectrostaticResults with properties:

      ElectricPotential: [4747x1 double]
          ElectricField: [1x1 FEStruct]
    ElectricFluxDensity: [1x1 FEStruct]
                   Mesh: [1x1 FEMesh]

    Plot the electric flux density.

    pdeplot3D(R.Mesh,FlowData=[R.ElectricFluxDensity.Dx ...
                           R.ElectricFluxDensity.Dy ...
                           R.ElectricFluxDensity.Dz])

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

    Interpolate the resulting electric flux density to a grid covering the central portion of the geometry, for x, y, and z.

    x = linspace(3,7,7);
y = linspace(0,1,7);
z = linspace(8,12,7);
[X,Y,Z] = meshgrid(x,y,z);

Dintrp = interpolateElectricFlux(R,X,Y,Z);

    Reshape Dintrp.Dx, Dintrp.Dy, and Dintrp.Dz.

    DintrpX = reshape(Dintrp.Dx,size(X));
DintrpY = reshape(Dintrp.Dy,size(Y));
DintrpZ = reshape(Dintrp.Dz,size(Z));

    Plot the resulting electric flux density.

    figure
quiver3(X,Y,Z,DintrpX,DintrpY,DintrpZ,Color="red")
view([10 10])

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

    Input Arguments

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    Solution of thermal problem, specified as an ElectrostaticResults object. Create electrostaticresults using the solve function.

    x-coordinate query points, specified as a real array. interpolateElectricFlux evaluates the electric flux density 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.

    interpolateElectricFlux converts the query points to column vectors xq(:), yq(:), and (if present) zq(:). It returns electric flux density 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 DintrpX = reshape(Dintrp.Dx,size(xq)).

    Example: xq = [0.5 0.5 0.75 0.75]

    Data Types: double

    y-coordinate query points, specified as a real array. interpolateElectricFlux evaluates the electric flux density 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.

    interpolateElectricFlux converts the query points to column vectors xq(:), yq(:), and (if present) zq(:). It returns electric flux density 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 DintrpY = reshape(Dintrp.Dy,size(yq)).

    Example: yq = [1 2 0 0.5]

    Data Types: double

    z-coordinate query points, specified as a real array. interpolateElectricFlux evaluates the electric flux density at the 3-D coordinate points [xq(i) yq(i) zq(i)]. Therefore, xq, yq, and zq must have the same number of entries.

    interpolateElectricFlux converts the query points to column vectors xq(:), yq(:), and zq(:). It returns electric flux density 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 DintrpZ = reshape(Dintrp.Dz,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. interpolateElectricFlux evaluates the electric flux density 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

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    Electric flux density at query points, returned as an FEStruct object with the properties representing the spatial components of the electric flux density at the query points. For query points that are outside the geometry, Dintrp.Dx(i), Dintrp.Dy(i), and Dintrp.Dz(i) are NaN. Properties of an FEStruct object are read-only.

    Version History

    Introduced in R2021a

    See Also

    Objects

    Functions