# interpolateElectricFlux

Interpolate electric flux density in electrostatic result at arbitrary spatial locations

*Since R2021a*

## Syntax

## Description

returns the interpolated electric flux density at the 2-D points specified in
`Dintrp`

= interpolateElectricFlux(`electrostaticresults`

,`xq`

,`yq`

)`xq`

and `yq`

.

uses 3-D points specified in `Dintrp`

= interpolateElectricFlux(`electrostaticresults`

,`xq`

,`yq`

,`zq`

)`xq`

, `yq`

, and
`zq`

.

returns the interpolated electric flux density at the points specified in
`Dintrp`

= interpolateElectricFlux(`electrostaticresults`

,`querypoints`

)`querypoints`

.

## Examples

### Interpolate Electric Flux Density in 2-D Electrostatic Analysis

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

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 flux density.

R = solve(emagmodel); pdeplot(emagmodel,"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: [2601x1 double] Dy: [2601x1 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")

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 electromagnetic model for electrostatic analysis.

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

Import and plot the geometry representing a plate with a hole.

importGeometry(emagmodel,"PlateHoleSolid.stl"); pdegplot(emagmodel,"FaceLabels","on","FaceAlpha",0.3)

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);`

Specify the charge density for the entire geometry.

`electromagneticSource(emagmodel,"ChargeDensity",5E-9);`

Apply the voltage boundary conditions on the side faces and the face bordering the hole.

electromagneticBC(emagmodel,"Voltage",0,"Face",3:6); electromagneticBC(emagmodel,"Voltage",1000,"Face",7);

Generate the mesh.

generateMesh(emagmodel);

Solve the model.

R = solve(emagmodel)

R = ElectrostaticResults with properties: ElectricPotential: [4359x1 double] ElectricField: [1x1 FEStruct] ElectricFluxDensity: [1x1 FEStruct] Mesh: [1x1 FEMesh]

Plot the electric flux density.

pdeplot3D(emagmodel,"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)

Dintrp = FEStruct with properties: Dx: [343x1 double] Dy: [343x1 double] Dz: [343x1 double]

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.

**Example: **`electrostaticresults = solve(emagmodel)`

`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**

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