slPotOp = createLaplace3dSingleLayerPotentialOperator(context)
dlPotOp = createLaplace3dDoubleLayerPotentialOperator(context)
# Define points at which the solution should be evaluated
rCount = 51;
thetaCount = 361;
r, theta, z = np.mgrid[1:2:rCount*1j, 0:2*np.pi:thetaCount*1j, 0:0:1j]
x = r * np.cos(theta)
y = r * np.sin(theta)
# put the x, y and z coordinates in successive rows of a matrix
evaluationPoints = np.vstack((x.ravel(), y.ravel(), z.ravel()))
# Use the Green's representation formula to evaluate the solution
evaluationOptions = createEvaluationOptions()
field = (-slPotOp.evaluateAtPoints(solFun, evaluationPoints,
evaluationOptions) +
dlPotOp.evaluateAtPoints(dirichletData, evaluationPoints,
evaluationOptions))
# Plot data
from bempp import visualization2 as vis
annulus = vis.tvtkStructuredGridData(
evaluationPoints, field, (rCount, thetaCount))
sphere = vis.tvtkGridFunction(dirichletData)
vis.plotScalarData(tvtkGridFunctions=sphere,
tvtkStructuredGridData=annulus)
+ dlPotExt.evaluateAtPoints(uSc, points[:,outside], evalOptions)
+ uIncData(points[:,outside]))
valsInt = ( slPotInt.evaluateAtPoints(uIntDeriv, points[:,inside], evalOptions)
- dlPotInt.evaluateAtPoints(uInt, points[:,inside], evalOptions))
# Combine the results obtained for points inside and outside the scatterer
# in a single array
vals = np.empty(nPointsX * nPointsY, dtype=complex)
np.place(vals, outside, valsExt.ravel())
np.place(vals, inside, valsInt.ravel())
# Display the field plot
from bempp import visualization2 as vis
tvtkU = vis.tvtkStructuredGridData(
points, vals, (nPointsX, nPointsY))
tvtkGrid = vis.tvtkGrid(grid)
vis.plotScalarData(tvtkGrid, None, tvtkU)
# Export the results into a VTK file
from tvtk.api import write_data
write_data(tvtkU, "u.vts")
# PART 6: Evaluate the far-field pattern of the scattered field ################
# Create the necessary potential operators
slFfPot = lib.createHelmholtz3dFarFieldSingleLayerPotentialOperator(context, kExt)
dlFfPot = lib.createHelmholtz3dFarFieldDoubleLayerPotentialOperator(context, kExt)
nPointsZ = nPointsX
x, y, z = np.mgrid[-5:5:nPointsX*1j, 0:0:1j, -5:5:nPointsZ*1j]
points = np.vstack((x.ravel(), y.ravel(), z.ravel()))
# Use Green's representation formula to evaluate the total field
evaluationOptions = createEvaluationOptions()
scatteredField = -(slPotOp.evaluateAtPoints(neumannData, points,
evaluationOptions))
incidentField = evalIncField(points)
field = scatteredField + incidentField
# Display the field plot
from bempp import visualization2 as vis
tvtkField = vis.tvtkStructuredGridData(points, field, (nPointsX, nPointsZ))
tvtkGrid = vis.tvtkGrid(grid)
vis.plotVectorData(tvtkGrids=tvtkGrid, tvtkStructuredGridData=tvtkField)
# from bempp import visualization as vis
# uActor = vis.scalarDataOnRegularGridActor(
# points, fieldMagnitude, (nPointsX, nPointsZ),
# colorRange=(0, 2))
# legendActor = vis.legendActor(uActor)
# gridActor = vis.gridActor(grid)
# vis.plotTvtkActors([uActor, gridActor, legendActor])
# Export the results into a VTK file
from tvtk.api import write_data
write_data(tvtkField, "u.vts")