interpolateCurrentDensity

Interpolate current density in DC conduction result at arbitrary spatial locations

Since R2022b

Syntax

Jintrp = interpolateCurrentDensity(results,xq,yq)

Jintrp = interpolateCurrentDensity(results,xq,yq,zq)

Jintrp = interpolateCurrentDensity(results,querypoints)

Description

Jintrp = interpolateCurrentDensity(results,xq,yq) returns the interpolated current density values at the 2-D points specified in xq and yq.

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

Jintrp = interpolateCurrentDensity(results,querypoints) returns the interpolated current density values at the points specified in querypoints.

Examples

Interpolate Current Density in 2-D DC Conduction Analysis

Create an femodel object for DC conduction analysis and include a 2-D geometry of a plate with a hole into the model.

model = femodel(AnalysisType="dcConduction", ...
                Geometry="PlateHolePlanar.stl");

Plot the geometry.

pdegplot(model.Geometry,EdgeLabels="on");

Specify the conductivity of the material.

model.MaterialProperties = ...
    materialProperties(ElectricalConductivity=6e4);

Apply the voltage boundary conditions on the top and bottom edges of the plate.

model.EdgeBC(3) = edgeBC(Voltage=100);
model.EdgeBC(2) = edgeBC(Voltage=200);

Specify the surface current density on the edge representing the hole.

model.EdgeLoad(5) = edgeLoad(SurfaceCurrentDensity=200000);

Generate a mesh.

model = generateMesh(model);

Solve the problem.

R = solve(model);

Plot the electric potential and current density.

figure
pdeplot(R.Mesh,XYData=R.ElectricPotential,ColorMap="jet", ...
               FlowData=[R.CurrentDensity.Jx R.CurrentDensity.Jy])
axis equal

Interpolate the resulting current density to a grid covering the central portion of the geometry.

[X,Y] = meshgrid(2:0.25:8,8:0.25:12);
Jintrp = interpolateCurrentDensity(R,X,Y)

Jintrp = 
  FEStruct with properties:

    Jx: [425×1 double]
    Jy: [425×1 double]

Reshape Jintrp.Jx and Jintrp.Jy, and plot the resulting current density.

JintrpX = reshape(Jintrp.Jx,size(X));
JintrpY = reshape(Jintrp.Jy,size(Y));
quiver(X,Y,JintrpX,JintrpY,Color="red")
axis equal

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

querypoints = [X(:),Y(:)]';
Jintrp = interpolateCurrentDensity(R,querypoints);

Interpolate Current Density in 3-D DC Conduction Analysis

Create an femodel object for DC conduction analysis and include a geometry representing a 10-by-10-by-1 solid plate into the model.

model = femodel(AnalysisType="dcConduction", ...
                Geometry="Plate10x10x1.stl");

Plot the geometry.

pdegplot(model.Geometry,FaceLabels="on",FaceAlpha=0.3)

Specify the conductivity of the material.

model.MaterialProperties = ...
    materialProperties(ElectricalConductivity=6e4);

Apply the voltage boundary conditions on the two faces of the plate.

model.FaceBC([1 3]) = faceBC(Voltage=0);

Specify the surface current density on the top of the plate.

model.FaceLoad(5) = faceLoad(SurfaceCurrentDensity=100);

Generate a mesh.

model = generateMesh(model);

Solve the problem.

R = solve(model);

Plot the electric potential.

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

Plot the current density.

figure
pdeplot3D(R.Mesh,FlowData=[R.CurrentDensity.Jx, ...
                           R.CurrentDensity.Jy, ...
                           R.CurrentDensity.Jz])

Interpolate the resulting current density to a coarser grid.

[X,Y,Z] = meshgrid(0:10,0:10,0:0.5:1);
Jintrp = interpolateCurrentDensity(R,X,Y,Z)

Jintrp = 
  FEStruct with properties:

    Jx: [363×1 double]
    Jy: [363×1 double]
    Jz: [363×1 double]

Reshape Jintrp.Jx, Jintrp.Jy, and Jintrp.Jz.

JintrpX = reshape(Jintrp.Jx,size(X));
JintrpY = reshape(Jintrp.Jy,size(Y));
JintrpZ = reshape(Jintrp.Jz,size(Z));

Plot the resulting current density.

figure
quiver3(X,Y,Z,JintrpX,JintrpY,JintrpZ,Color="red")

Input Arguments

results — Solution of DC conduction problem

ConductionResults object

Solution of a DC conduction problem, specified as a ConductionResults object. Create results using the solve function.

xq — x-coordinate query points

real array

x-coordinate query points, specified as a real array. interpolateCurrentDensity evaluates the current 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.

interpolateCurrentDensity converts the query points to column vectors xq(:), yq(:), and (if present) zq(:). It returns current 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 Jintrp = reshape(Jintrp,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. interpolateCurrentDensity evaluates the current 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.

interpolateCurrentDensity converts the query points to column vectors xq(:), yq(:), and (if present) zq(:). It returns current 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 Jintrp = reshape(Jintrp,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. interpolateCurrentDensity evaluates the current 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.

interpolateCurrentDensity converts the query points to column vectors xq(:), yq(:), and zq(:). It returns current 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 Jintrp = reshape(Jintrp,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. interpolateCurrentDensity evaluates the current 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

Jintrp — Current density at query points

FEStruct object

Current density at query points, returned as an FEStruct object with the properties representing the spatial components of the current density at the query points. For query points that are outside the geometry, Jintrp.Jx(i), Jintrp.Jy(i), and Jintrp.Jz(i) are NaN. Properties of an FEStruct object are read-only.

Version History

Introduced in R2022b