interpolateElectricFlux

Interpolate electric flux density in electrostatic result at arbitrary spatial locations

Since R2021a

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.

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

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

Examples

Interpolate Electric Flux Density in 2-D Electrostatic 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 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

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: [2601×1 double]
    Dy: [2601×1 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

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

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

Interpolate Electric Flux Density in 3-D Electrostatic Analysis

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)

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: [4747×1 double]
          ElectricField: [1×1 FEStruct]
    ElectricFluxDensity: [1×1 FEStruct]
                   Mesh: [1×1 FEMesh]

Plot the electric flux density.

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

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])

Input Arguments

electrostaticresults — Solution of electrostatic problem

ElectrostaticResults object

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

xq — x-coordinate query points

real array

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

yq — y-coordinate query points

real array

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

zq — z-coordinate query points

real array

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

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. 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

Dintrp — Electric flux density at query points

FEStruct

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