interpolateElectricPotential

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

Since R2021a

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.

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

Vintrp = interpolateElectricPotential(results,querypoints) returns the interpolated electric potential values at the points specified in querypoints.

Examples

Interpolate Electric Potential 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 model and plot the electric potential.

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

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
axis equal

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

querypoints = [X(:),Y(:)]';
Vintrp = interpolateElectricPotential(R,querypoints);

Interpolate Electric Potential in 3-D Electrostatic Analysis

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)

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

Plot the electric potential.

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

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

Input Arguments

results — Solution of electrostatic or DC conduction problem

ElectrostaticResults object | ConductionResults object

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

xq — x-coordinate query points

real array

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

yq — y-coordinate query points

real array

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

zq — z-coordinate query points

real array

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

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. 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

Vintrp — Electric potential at query points

vector

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

R2022b: Electric potential in DC conduction results

The function now interpolates electric potential in DC conduction results in addition to electrostatic results.