# interpolateHarmonicField

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

## 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.

Create an electromagnetic model for harmonic analysis.

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

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); geometryFromEdges(emagmodel,g);

Include the geometry in the model and plot it with the edge labels.

figure; pdegplot(emagmodel,"EdgeLabels","on"); xlim([-6,6]) ylim([-6,6])

Specify the vacuum permittivity and permeability values as 1.

emagmodel.VacuumPermittivity = 1; emagmodel.VacuumPermeability = 1;

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

electromagneticProperties(emagmodel,"RelativePermittivity",1, ... "RelativePermeability",1, ... "Conductivity",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.

electromagneticBC(emagmodel,"Edge",[1 2 7 8], ... "FarField","absorbing", ... "Thickness",2, ... "Exponent",4, ... "Scaling",1);

Apply the boundary condition on the edges of the diamond.

innerBCFunc = @(location,~) [-exp(-1i*k*location.x); zeros(1,length(location.x))]; bInner = electromagneticBC(emagmodel,"Edge",[3 4 5 6], ... "ElectricField",innerBCFunc);

Generate a mesh.

`generateMesh(emagmodel,"Hmax",0.1);`

Solve the harmonic analysis model for the frequency `k`

= $4\pi $.

`result = solve(emagmodel,"Frequency",k);`

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

u = result.ElectricField; figure pdeplot(emagmodel,"XYData",real(u.Ex),"Mesh","off"); 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(result,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 electromagnetic model for harmonic analysis.

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

By default, the field type is electric. Use the `FieldType`

property of the model to change the field type to magnetic.

`emagmodel.FieldType = "magnetic";`

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 and permeability values in the SI system of units.

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

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

electromagneticProperties(emagmodel,"RelativePermittivity",1, ... "RelativePermeability",6, ... "Conductivity",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.

`electromagneticSource(emagmodel,"CurrentDensity",[1;1;1]);`

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

electromagneticBC(emagmodel,"Face",3:6, ... "FarField","absorbing", ... "Thickness",0.1);

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

electromagneticBC(emagmodel,"Face",7,"MagneticField",[1000;0;0]);

Generate a mesh.

generateMesh(emagmodel);

Solve the model for a frequency of 50.

`result = solve(emagmodel,"Frequency",50);`

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

u = result.MagneticField; figure pdeplot3D(emagmodel,"ColorMapData",real(u.Hx)); colormap jet xlabel 'x' ylabel 'y' 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.

**Example: **```
harmonicresults =
solve(emagmodel,"Frequency",omega)
```

`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**

## See Also

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