interpolateElectricPotential
Interpolate electric potential in electrostatic or DC conduction result at arbitrary spatial locations
Since R2021a
Syntax
Description
returns the interpolated electric potential values at the points specified in
Vintrp
= interpolateElectricPotential(results
,querypoints
)querypoints
.
Examples
Interpolate Electric Potential in 2-D Electrostatic Analysis
Create a square geometry and plot it with the edge labels.
R1 = [3,4,-1,1,1,-1,1,1,-1,-1]'; g = decsg(R1,'R1',('R1')'); pdegplot(g,EdgeLabels="on") xlim([-1.1 1.1]) ylim([-1.1 1.1])
Create an femodel
object for electrostatic analysis and include the geometry into the model.
model = femodel(AnalysisType="electrostatic", ... Geometry=g);
Specify the vacuum permittivity in the SI system of units.
model.VacuumPermittivity = 8.8541878128E-12;
Specify the relative permittivity of the material.
model.MaterialProperties = ...
materialProperties(RelativePermittivity=1);
Apply the voltage boundary conditions on the edges of the square.
model.EdgeBC([1 3]) = edgeBC(Voltage=0); model.EdgeBC([2 4]) = edgeBC(Voltage=1000);
Specify the charge density for the entire geometry.
model.FaceLoad = faceLoad(ChargeDensity=5E-9);
Generate the mesh.
model = generateMesh(model);
Solve the model and plot the electric potential.
R = solve(model); pdeplot(R.Mesh,XYData=R.ElectricPotential, ... Contour="on")
Interpolate the resulting electric potential 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); Vintrp = interpolateElectricPotential(R,X,Y);
Reshape Vintrp
and plot the resulting electric potential.
Vintrp = reshape(Vintrp,size(X)); figure contourf(X,Y,Vintrp) colormap(cool) colorbar
Alternatively, you can specify the grid by using a matrix of query points.
querypoints = [X(:),Y(:)]'; Vintrp = interpolateElectricPotential(R,querypoints);
Interpolate Electric Potential in 3-D Electrostatic Analysis
Create an femodel
object model for electrostatic analysis and include a geometry of a plate with a hole into the model.
model = femodel(AnalysisType="electrostatic", ... Geometry="PlateHoleSolid.stl");
Plot the geometry.
pdegplot(model.Geometry,FaceLabels="on",FaceAlpha=0.3)
Specify the vacuum permittivity in the SI system of units.
model.VacuumPermittivity = 8.8541878128E-12;
Specify the relative permittivity of the material.
model.MaterialProperties = ...
materialProperties(RelativePermittivity=1);
Specify the charge density for the entire geometry.
model.CellLoad = cellLoad(ChargeDensity=5E-9);
Apply the voltage boundary conditions on the side faces and the face bordering the hole.
model.FaceBC(3:6) = faceBC(Voltage=0); model.FaceBC(7) = faceBC(Voltage=1000);
Generate the mesh.
model = generateMesh(model);
Solve the model.
R = solve(model)
R = ElectrostaticResults with properties: ElectricPotential: [4747x1 double] ElectricField: [1x1 FEStruct] ElectricFluxDensity: [1x1 FEStruct] Mesh: [1x1 FEMesh]
Plot the electric potential.
pdeplot3D(R.Mesh,ColorMapData=R.ElectricPotential)
Interpolate the resulting electric potential to a grid covering the entire geometry, for x
, y
, and z
.
x = linspace(0,10,11); y = linspace(0,1,5); z = linspace(0,20,11); [X,Y,Z] = meshgrid(x,y,z); Vintrp = interpolateElectricPotential(R,X,Y,Z);
Reshape Vintrp
.
Vintrp = reshape(Vintrp,size(X));
Plot the resulting electric potential as a contour slice plot for two values of the y-coordinate.
figure
contourslice(X,Y,Z,Vintrp,[],[0 1],[])
view([10,10,-10])
axis equal
colorbar
Input Arguments
results
— Solution of electrostatic or DC conduction problem
ElectrostaticResults
object | ConductionResults
object
Solution of an electrostatic or DC conduction problem, specified as an ElectrostaticResults
or ConductionResults
object. Create results
using the solve
function.
xq
— x-coordinate query points
real array
x-coordinate query points, specified as a real array.
interpolateElectricPotential
evaluates the electric potential 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.
interpolateElectricPotential
converts the query points to column
vectors xq(:)
, yq(:)
, and (if present)
zq(:)
. It returns electric potential 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 Vintrp = reshape(Vintrp,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.
interpolateElectricPotential
evaluates the electric potential 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.
interpolateElectricPotential
converts the query points to column
vectors xq(:)
, yq(:)
, and (if present)
zq(:)
. It returns electric potential 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 Vintrp = reshape(Vintrp,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.
interpolateElectricPotential
evaluates the electric potential at
the 3-D coordinate points [xq(i) yq(i) zq(i)]
. Therefore,
xq
, yq
, and zq
must have
the same number of entries.
interpolateElectricPotential
converts the query points to column
vectors xq(:)
, yq(:)
, and
zq(:)
. It returns electric potential 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 Vintrp = reshape(Vintrp,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. interpolateElectricPotential
evaluates
the electric potential 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
Vintrp
— Electric potential at query points
vector
Electric potential at query points, returned as a vector. For query points that are
outside the geometry, Vintrp(i)
= NaN
.
Version History
Introduced in R2021aR2022b: Electric potential in DC conduction results
The function now interpolates electric potential in DC conduction results in addition to electrostatic results.
See Also
Objects
Functions
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