# interpolateHarmonicField

Interpolate electric or magnetic field in harmonic result at arbitrary spatial locations

*Since R2022a*

## Syntax

## Description

returns the interpolated electric or magnetic field values at the 2-D points specified in
`EHintrp`

= interpolateHarmonicField(`harmonicresults`

,`xq`

,`yq`

)`xq`

and `yq`

.

uses 3-D points specified in `EHintrp`

= interpolateHarmonicField(`harmonicresults`

,`xq`

,`yq`

,`zq`

)`xq`

, `yq`

, and
`zq`

.

returns the interpolated electric or magnetic field values at the points specified in
`EHintrp`

= interpolateHarmonicField(`harmonicresults`

,`querypoints`

)`querypoints`

.

## Examples

### Interpolate Electric Field in 2-D Harmonic Analysis

Solve a simple scattering problem and interpolate the *x*-component of the resulting electric field. A scattering problem computes the waves reflected by a square object illuminated by incident waves.

Specify the wave number $\mathit{k}=\omega /\alpha $ as $4\pi $.

k = 4*pi;

Represent the square surface with a diamond-shaped hole. Define a diamond in a square, place them in one matrix, and create a set formula that subtracts the diamond from the square.

square = [3; 4; -5; -5; 5; 5; -5; 5; 5; -5]; diamond = [2; 4; 2.1; 2.4; 2.7; 2.4; 1.5; 1.8; 1.5; 1.2]; gd = [square,diamond]; ns = char('square','diamond')'; sf = 'square - diamond';

Create the geometry.

g = decsg(gd,sf,ns);

Plot the geometry with the edge labels.

```
figure;
pdegplot(g,EdgeLabels="on");
xlim([-6,6])
ylim([-6,6])
```

Create an `femodel`

object for harmonic electromagnetic analysis with the electric field type. Include the geometry into the model.

model = femodel(AnalysisType="electricHarmonic", ... Geometry=g);

Specify the vacuum permittivity and permeability values as 1.

model.VacuumPermittivity = 1; model.VacuumPermeability = 1;

Specify the relative permittivity, relative permeability, and conductivity of the material.

model.MaterialProperties = ... materialProperties(RelativePermittivity=1, ... RelativePermeability=1, ... ElectricalConductivity=0);

Apply the absorbing boundary condition on the edges of the square. Specify the thickness and attenuation rate for the absorbing region by using the `Thickness`

, `Exponent`

, and `Scaling`

arguments.

ffbc = farFieldBC(Thickness=2,Exponent=4,Scaling=1); model.EdgeBC(1:4) = edgeBC(FarField=ffbc);

Apply the boundary condition on the edges of the diamond.

```
innerBCFunc = @(location,~) [-exp(-1i*k*location.x); ...
zeros(1,length(location.x))];
model.EdgeBC(5:8) = edgeBC(ElectricField=innerBCFunc);
```

Generate a mesh.

model = generateMesh(model,Hmax=0.1);

Solve the harmonic analysis model for the frequency `k`

= $4\pi $.

R = solve(model,k);

Plot the real part of the *x*-component of the resulting electric field.

u = R.ElectricField; figure pdeplot(R.Mesh,XYData=real(u.Ex)); colormap(jet)

Interpolate the resulting electric field to a grid covering the portion of the geometry, for *x* and *y* from -1 to 4.

v = linspace(-1,4,101); [X,Y] = meshgrid(v); Eintrp = interpolateHarmonicField(R,X,Y);

Reshape `Eintrp.Ex`

and plot the *x*-component of the resulting electric field.

```
EintrpX = reshape(Eintrp.ElectricField.Ex,size(X));
figure
surf(X,Y,real(EintrpX),LineStyle="none");
view(0,90)
colormap(jet)
```

### Interpolate Magnetic Field in 3-D Harmonic Analysis

Interpolate the *x*-component of the magnetic field in a harmonic analysis of a 3-D model.

Create an `femodel`

object for harmonic electromagnetic analysis with the magnetic field type. Include the geometry representing a plate with a hole into the model.

model = femodel(AnalysisType="magneticHarmonic", ... Geometry="PlateHoleSolid.stl");

Plot the geometry.

`pdegplot(model,FaceLabels="on",FaceAlpha=0.3)`

Specify the vacuum permittivity and permeability values in the SI system of units.

model.VacuumPermittivity = 8.8541878128E-12; model.VacuumPermeability = 1.2566370614E-6;

Specify the relative permittivity, relative permeability, and conductivity of the material.

model.MaterialProperties = ... materialProperties(RelativePermittivity=1, ... RelativePermeability=6, ... ElectricalConductivity=60);

Specify the current density for the entire geometry. For harmonic analysis with the magnetic field type, the toolbox uses the curl of the specified current density.

model.CellLoad = cellLoad(CurrentDensity=[1;1;1]);

Apply the absorbing boundary condition with a thickness of 0.1 on the side faces.

ffbc = farFieldBC(Thickness=0.1); model.FaceBC(3:6) = faceBC(FarField=ffbc);

Specify the magnetic field on the face bordering the round hole in the center of the geometry.

model.FaceBC(7) = faceBC(MagneticField=[1000;0;0]);

Generate a mesh.

model = generateMesh(model);

Solve the model for a frequency of 50.

result = solve(model,50);

Plot the real part of the *x*-component of the resulting magnetic field.

u = result.MagneticField; figure pdeplot3D(result.Mesh,ColorMapData=real(u.Hx)); colormap jet title("Real Part of x-Component of Magnetic Field")

Interpolate the resulting magnetic field to a grid covering the central portion of the geometry, for *x*, *y*, and *z*.

x = linspace(3,7,51); y = linspace(0,1,51); z = linspace(8,12,51); [X,Y,Z] = meshgrid(x,y,z); Hintrp = interpolateHarmonicField(result,X,Y,Z)

`Hintrp = `*struct with fields:*
MagneticField: [1x1 FEStruct]

Reshape H`intrp.Hx`

and plot the *x*-component of the resulting magnetic field as a slice plot for *y* = 0.

HintrpX = reshape(Hintrp.MagneticField.Hx,size(X)); figure slice(X,Y,Z,real(HintrpX),[],0,[],"cubic") axis equal colorbar colormap(jet)

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

querypoints = [X(:),Y(:),Z(:)]'; Hintrp = interpolateHarmonicField(result,querypoints)

`Hintrp = `*struct with fields:*
MagneticField: [1x1 FEStruct]

## Input Arguments

`harmonicresults`

— Solution of harmonic electromagnetic problem

`HarmonicResults`

object

Solution of a harmonic electromagnetic problem, specified as a `HarmonicResults`

object. Create `harmonicresults`

using the `solve`

function.

`xq`

— *x*-coordinate query points

real array

*x*-coordinate query points, specified as a real array.
`interpolateHarmonicField`

evaluates the electric or magnetic field
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 index
`i`

.Therefore, `xq`

, `yq`

, and (if
present) `zq`

must have the same number of entries.

`interpolateHarmonicField`

converts the query points to column
vectors `xq(:)`

, `yq(:)`

, and (if present)
`zq(:)`

. It returns electric or magnetic 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 ```
EHintrpX =
reshape(EHintrp.Ex,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.
`interpolateHarmonicField`

evaluates the electric or magnetic field
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 index `i`

.
Therefore, `xq`

, `yq`

, and (if present)
`zq`

must have the same number of entries.

`interpolateHarmonicField`

converts the query points to column
vectors `xq(:)`

, `yq(:)`

, and (if present)
`zq(:)`

. It returns electric or magnetic 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 ```
EHintrpY =
reshape(EHintrp.Ey,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.
`interpolateHarmonicField`

evaluates the electric or magnetic field
at the 3-D coordinate points `[xq(i) yq(i) zq(i)]`

for every index
`i`

. Therefore, `xq`

, `yq`

, and
`zq`

must have the same number of entries.

`interpolateHarmonicField`

converts the query points to column
vectors `xq(:)`

, `yq(:)`

, and
`zq(:)`

. It returns electric or magnetic 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 ```
EHintrpZ =
reshape(EHintrp.Ez,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 a 2-D geometry or
three rows for a 3-D geometry. `interpolateHarmonicField`

evaluates the
electric or magnetic field at the coordinate points `querypoints(:,i)`

for every index `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

`EHintrp`

— Electric or magnetic field at query points

`FEStruct`

object

Electric or magnetic field at query points, returned as an
`FEStruct`

object with the properties representing the spatial
components of the electric or magnetic field at the query points. For query points that
are outside the geometry, `EHintrp.Ex(i)`

,
`EHintrp.Ey(i)`

, `EHintrp.Ez(i)`

,
`EHintrp.Hx(i)`

, `EHintrp.Hy(i)`

, and
`EHintrp.Hz(i)`

are `NaN`

. Properties of an
`FEStruct`

object are read-only.

## Version History

**Introduced in R2022a**

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