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interpolateElectricPotential

Interpolate electric potential in electrostatic or DC conduction result at arbitrary spatial locations

Since R2021a

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    Syntax

    Vintrp = interpolateElectricPotential(results,xq,yq)
    Vintrp = interpolateElectricPotential(results,xq,yq,zq)
    Vintrp = interpolateElectricPotential(results,querypoints)

    Description

    Vintrp = interpolateElectricPotential(results,xq,yq) returns the interpolated electric potential values at the 2-D points specified in xq and yq.

    example

    Vintrp = interpolateElectricPotential(results,xq,yq,zq) uses 3-D points specified in xq, yq, and zq.

    example

    Vintrp = interpolateElectricPotential(results,querypoints) returns the interpolated electric potential values 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 model and plot the electric potential.

    R = solve(model);
pdeplot(R.Mesh,XYData=R.ElectricPotential, ...
               Contour="on")

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

    Interpolate the resulting electric 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);

Vintrp = interpolateElectricPotential(R,X,Y);

    Reshape Vintrp and plot the resulting electric potential.

    Vintrp = reshape(Vintrp,size(X));

figure
contourf(X,Y,Vintrp)
colormap(cool)
colorbar

    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(:)]';
Vintrp = interpolateElectricPotential(R,querypoints);
    Open Live Script

    Create an femodel object model 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 model.

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

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

    Plot the electric potential.

    pdeplot3D(R.Mesh,ColorMapData=R.ElectricPotential)

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

    Interpolate the resulting electric 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);

Vintrp = interpolateElectricPotential(R,X,Y,Z);

    Reshape Vintrp.

    Vintrp = reshape(Vintrp,size(X));

    Plot the resulting electric potential as a contour slice plot for two values of the y-coordinate.

    figure
contourslice(X,Y,Z,Vintrp,[],[0 1],[])
view([10,10,-10])
axis equal
colorbar

    Figure contains an axes object. The axes object contains 40 objects of type patch.

    Input Arguments

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    Solution of an electrostatic or DC conduction problem, specified as an ElectrostaticResults or ConductionResults object. Create results using the solve function.

    x-coordinate query points, specified as a real array. interpolateElectricPotential evaluates the electric 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.

    interpolateElectricPotential converts the query points to column vectors xq(:), yq(:), and (if present) zq(:). It returns electric 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 Vintrp = reshape(Vintrp,size(xq)).

    Example: xq = [0.5 0.5 0.75 0.75]

    Data Types: double

    y-coordinate query points, specified as a real array. interpolateElectricPotential evaluates the electric 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.

    interpolateElectricPotential converts the query points to column vectors xq(:), yq(:), and (if present) zq(:). It returns electric 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 Vintrp = reshape(Vintrp,size(yq)).

    Example: yq = [1 2 0 0.5]

    Data Types: double

    z-coordinate query points, specified as a real array. interpolateElectricPotential evaluates the electric 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.

    interpolateElectricPotential converts the query points to column vectors xq(:), yq(:), and zq(:). It returns electric 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 Vintrp = reshape(Vintrp,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. interpolateElectricPotential evaluates the electric 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

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    Electric potential at query points, returned as a vector. For query points that are outside the geometry, Vintrp(i) = NaN.

    Version History

    Introduced in R2021a

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    See Also

    Objects

    Functions