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 as .
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
= .
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 Hintrp.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
Comando MATLAB
Hai fatto clic su un collegamento che corrisponde a questo comando MATLAB:
Esegui il comando inserendolo nella finestra di comando MATLAB. I browser web non supportano i comandi MATLAB.
Select a Web Site
Choose a web site to get translated content where available and see local events and offers. Based on your location, we recommend that you select: .
You can also select a web site from the following list:
How to Get Best Site Performance
Select the China site (in Chinese or English) for best site performance. Other MathWorks country sites are not optimized for visits from your location.
Americas
- América Latina (Español)
- Canada (English)
- United States (English)
Europe
- Belgium (English)
- Denmark (English)
- Deutschland (Deutsch)
- España (Español)
- Finland (English)
- France (Français)
- Ireland (English)
- Italia (Italiano)
- Luxembourg (English)
- Netherlands (English)
- Norway (English)
- Österreich (Deutsch)
- Portugal (English)
- Sweden (English)
- Switzerland
- United Kingdom (English)