def steadyStateDirichlet(self):
# -------------------- Find out size of the complete system -------------------------------------
self.nrCtrlPoints = 0
for i in range(self.nrPanelObjects):
self.nrCtrlPoints += self.panelObjects[i].mesh.nrFaces
# Global matrix system to solve, A x = b
A = np.zeros((self.nrCtrlPoints, self.nrCtrlPoints))
b = np.zeros(self.nrCtrlPoints)
# For each panel object, calculate influence matrix
startTime = time.clock()
i_start = 0
for i in range(self.nrPanelObjects):
pCtrl = self.panelObjects[i].mesh.face_center
nCtrl = self.panelObjects[i].mesh.face_n
nrCtrlPoints = self.panelObjects[i].mesh.nrFaces
i_stop = i_start + nrCtrlPoints
j_start = 0
for j in range(self.nrPanelObjects):
panelObject = self.panelObjects[j]
mesh = panelObject.mesh
wake_mesh = panelObject.wake_mesh
j_stop = j_start + mesh.nrFaces
# Calculate influence on current ctrl points from current mesh
A_local = Computation.potentialInfluence(pCtrl, mesh, 'doublet')
A_wake = Computation.potentialInfluence(pCtrl, wake_mesh, 'doublet')
# Combine influence from individual panels to influence from strips
for k in range(nrCtrlPoints):
for l in range(panelObject.nrStrips):
wakeSum = np.sum(A_wake[k, panelObject.wake_stripFaces[l]])
faceIndex = panelObject.stripFaces[l, 0]
n1 = mesh.face_n[faceIndex]
A_local[k, faceIndex] += wakeSum*np.sign(n1[1])
faceIndex = panelObject.stripFaces[l, -1]
n2 = mesh.face_n[faceIndex]
A_local[k, faceIndex] += wakeSum*np.sign(n2[1])
# Put resulting influence matrix into global matrix
A[i_start:i_stop, j_start:j_stop] = A_local
j_start += mesh.nrFaces
# Compute right side of linear system
sigma = Computation.freeStreamNewmann(self.Uinf, nCtrl, nrCtrlPoints)/(4*np.pi)
B = Computation.potentialInfluence(pCtrl, mesh, 'source')
b[i_start:i_stop] = -np.dot(B, sigma)
panelObject.source_strength = sigma
i_start += nrCtrlPoints
stopTime = time.clock()
print('Matrix assembly time:', stopTime - startTime, 's')
# Solve system
startTime = time.clock()
strength = np.linalg.solve(A, b)
stopTime = time.clock()
print('Linear solver time:', stopTime - startTime, 's')
# Transfer global strength values to individual panel objects
i_start = 0
for i in range(self.nrPanelObjects):
panelObject = self.panelObjects[i]
i_stop = i_start + panelObject.mesh.nrFaces
panelObject.doublet_strength = strength[i_start:i_stop]
j_start = 0
for j in range(panelObject.nrStrips):
j_stop = j_start + panelObject.wake_nrPanelsPrStrip
faceIndex1 = panelObject.stripFaces[j, 0]
n1 = self.panelObjects[i].mesh.face_n[faceIndex1]
faceIndex2 = panelObject.stripFaces[j, -1]
n2 = self.panelObjects[i].mesh.face_n[faceIndex2]
stripStrength = panelObject.doublet_strength[faceIndex1]*np.sign(n1[1]) + panelObject.doublet_strength[faceIndex2]*np.sign(n2[1])
panelObject.wake_strength[j_start:j_stop] = stripStrength
j_start += panelObject.wake_nrPanelsPrStrip
i_start += panelObject.mesh.nrFaces
