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interpolateElectricField

Interpolate electric field in electrostatic result at arbitrary spatial locations

    Description

    example

    Eintrp = interpolateElectricField(electrostaticresults,xq,yq) returns the interpolated electric field values at the points specified in xq and yq.

    example

    Eintrp = interpolateElectricField(electrostaticresults,querypoints) returns the interpolated electric field values at the points specified in querypoints.

    Examples

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    Create an electromagnetic model for electrostatic analysis.

    emagmodel = createpde('electromagnetic','electrostatic');

    Create a square geometry and include it in the model. Plot the geometry with the edge labels.

    R1 = [3,4,-1,1,1,-1,1,1,-1,-1]';
    g = decsg(R1,'R1',('R1')');
    geometryFromEdges(emagmodel,g);
    pdegplot(emagmodel,'EdgeLabels','on')
    xlim([-1.5 1.5])
    axis equal

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

    Specify the vacuum permittivity in the SI system of units.

    emagmodel.VacuumPermittivity = 8.8541878128E-12;

    Specify the relative permittivity of the material.

    electromagneticProperties(emagmodel,'RelativePermittivity',1);

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

    electromagneticBC(emagmodel,'Voltage',0,'Edge',[1 3]);
    electromagneticBC(emagmodel,'Voltage',1000,'Edge',[2 4]);

    Specify the charge density for the entire geometry.

    electromagneticSource(emagmodel,'ChargeDensity',5E-9);

    Generate the mesh.

    generateMesh(emagmodel);

    Solve the model and plot the electric field.

    R = solve(emagmodel);
    pdeplot(emagmodel,'FlowData',[R.ElectricField.Ex ...
                                  R.ElectricField.Ey])
    axis equal

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

    Interpolate the resulting electric 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);
    
    Eintrp = interpolateElectricField(R,X,Y)
    Eintrp = 
      FEStruct with properties:
    
        Ex: [2601x1 double]
        Ey: [2601x1 double]
    
    

    Reshape Eintrp.Ex and Eintrp.Ey and plot the resulting electric field.

    EintrpX = reshape(Eintrp.Ex,size(X));
    EintrpY = reshape(Eintrp.Ey,size(Y));
    
    figure
    quiver(X,Y,EintrpX,EintrpY,'Color','red')

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

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

    querypoints = [X(:),Y(:)]';
    Eintrp = interpolateElectricField(R,querypoints);

    Input Arguments

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

    Example: electrostaticresults = solve(emagmodel)

    x-coordinate query points, specified as a real array. interpolateElectricField evaluates the electric field at the coordinate points [xq(i) yq(i)] for every i. Because of this, xq and yq must have the same number of entries.

    interpolateElectricField converts the query points to column vectors xq(:) and yq(:). It returns electric 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 EintrpX = reshape(Eintrp.Ex,size(xq)).

    Example: xq = [0.5 0.5 0.75 0.75]

    Data Types: double

    y-coordinate query points, specified as a real array. interpolateElectricField evaluates the electric field at the coordinate points [xq(i) yq(i)] for every i. Because of this, xq and yq must have the same number of entries.

    interpolateElectricField converts the query points to column vectors xq(:) and yq(:). It returns electric 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 EintrpY = reshape(Eintrp.Ey,size(yq)).

    Example: yq = [1 2 0 0.5]

    Data Types: double

    Query points, specified as a real matrix with two rows for 2-D geometry. interpolateElectricField evaluates the electric field at the coordinate points querypoints(:,i) for every i, so each column of querypoints contains exactly one 2-D query point.

    Example: querypoints = [0.5 0.5 0.75 0.75; 1 2 0 0.5]

    Data Types: double

    Output Arguments

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    Electric field at query points, returned as an FEStruct object with the properties representing the spatial components of the electric field at the query points. For query points that are outside the geometry, Eintrp.Ex(i) and Eintrp.Ey(i) are NaN. Properties of an FEStruct object are read-only.

    Introduced in R2021a