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simpeg/tests/mesh/test_Mixed_boundaryPoisson.py
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seogi_macbook dcd4fbf973 Implemented mixed B.C. to CC problem. 
Fix bugs in get fuction getxBCyBC_CC
2016-04-24 15:23:14 -07:00

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import numpy as np
import scipy.sparse as sp
import unittest
import matplotlib.pyplot as plt
from SimPEG import *
MESHTYPES = ['uniformTensorMesh']
def getxBCyBC_CC(mesh, alpha, beta, gamma):
# def getxBCyBC(mesh, alpha, beta, gamma):
"""
This is a subfunction generating mixed-boundary condition:
.. math::
\nabla \cdot \vec{j} = -\nabla \cdot \vec{j}_s = q
\rho \vec{j} = -\nabla \phi \phi
\alpha \phi + \beta \frac{\partial \phi}{\partial r} = \gamma \ at \ r = \partial \Omega
xBC = f_1(\alpha, \beta, \gamma)
yBC = f(\alpha, \beta, \gamma)
Computes xBC and yBC for cell-centered discretizations
"""
if mesh.dim == 1: #1D
if (len(alpha) != 2 or len(beta) != 2 or len(gamma) != 2):
raise Exception("Lenght of list, alpha should be 2")
fCCxm,fCCxp = mesh.cellBoundaryInd
nBC = fCCxm.sum()+fCCxp.sum()
h_xm, h_xp = mesh.gridCC[fCCxm], mesh.gridCC[fCCxp]
alpha_xm, beta_xm, gamma_xm = alpha[0], beta[0], gamma[0]
alpha_xp, beta_xp, gamma_xp = alpha[1], beta[1], gamma[1]
# h_xm, h_xp = mesh.gridCC[fCCxm], mesh.gridCC[fCCxp]
h_xm, h_xp = mesh.hx[0], mesh.hx[-1]
a_xm = gamma_xm/(0.5*alpha_xm-beta_xm/h_xm)
b_xm = (0.5*alpha_xm+beta_xm/h_xm)/(0.5*alpha_xm-beta_xm/h_xm)
a_xp = gamma_xp/(0.5*alpha_xp-beta_xp/h_xp)
b_xp = (0.5*alpha_xp+beta_xp/h_xp)/(0.5*alpha_xp-beta_xp/h_xp)
xBC_xm = 0.5*a_xm
xBC_xp = 0.5*a_xp/b_xp
yBC_xm = 0.5*(1.-b_xm)
yBC_xp = 0.5*(1.-1./b_xp)
xBC = np.r_[xBC_xm, xBC_xp]
yBC = np.r_[yBC_xm, yBC_xp]
elif mesh.dim == 2: #2D
if (len(alpha) != 4 or len(beta) != 4 or len(gamma) != 4):
raise Exception("Lenght of list, alpha should be 4")
fxm,fxp,fym,fyp = mesh.faceBoundaryInd
nBC = fxm.sum()+fxp.sum()+fxm.sum()+fxp.sum()
alpha_xm, beta_xm, gamma_xm = alpha[0], beta[0], gamma[0]
alpha_xp, beta_xp, gamma_xp = alpha[1], beta[1], gamma[1]
alpha_ym, beta_ym, gamma_ym = alpha[2], beta[2], gamma[2]
alpha_yp, beta_yp, gamma_yp = alpha[3], beta[3], gamma[3]
# h_xm, h_xp = mesh.gridCC[fCCxm,0], mesh.gridCC[fCCxp,0]
# h_ym, h_yp = mesh.gridCC[fCCym,1], mesh.gridCC[fCCyp,1]
h_xm, h_xp = mesh.hx[0]*np.ones_like(alpha_xm), mesh.hx[-1]*np.ones_like(alpha_xp)
h_ym, h_yp = mesh.hy[0]*np.ones_like(alpha_ym), mesh.hy[-1]*np.ones_like(alpha_yp)
a_xm = gamma_xm/(0.5*alpha_xm-beta_xm/h_xm)
b_xm = (0.5*alpha_xm+beta_xm/h_xm)/(0.5*alpha_xm-beta_xm/h_xm)
a_xp = gamma_xp/(0.5*alpha_xp-beta_xp/h_xp)
b_xp = (0.5*alpha_xp+beta_xp/h_xp)/(0.5*alpha_xp-beta_xp/h_xp)
a_ym = gamma_ym/(0.5*alpha_ym-beta_ym/h_ym)
b_ym = (0.5*alpha_ym+beta_ym/h_ym)/(0.5*alpha_ym-beta_ym/h_ym)
a_yp = gamma_yp/(0.5*alpha_yp-beta_yp/h_yp)
b_yp = (0.5*alpha_yp+beta_yp/h_yp)/(0.5*alpha_yp-beta_yp/h_yp)
xBC_xm = 0.5*a_xm
xBC_xp = 0.5*a_xp/b_xp
yBC_xm = 0.5*(1.-b_xm)
yBC_xp = 0.5*(1.-1./b_xp)
xBC_ym = 0.5*a_ym
xBC_yp = 0.5*a_yp/b_yp
yBC_ym = 0.5*(1.-b_ym)
yBC_yp = 0.5*(1.-1./b_yp)
sortindsfx = np.argsort(np.r_[np.arange(mesh.nFx)[fxm], np.arange(mesh.nFx)[fxp]])
sortindsfy = np.argsort(np.r_[np.arange(mesh.nFy)[fym], np.arange(mesh.nFy)[fyp]])
xBC_x = np.r_[xBC_xm, xBC_xp][sortindsfx]
xBC_y = np.r_[xBC_ym, xBC_yp][sortindsfy]
yBC_x = np.r_[yBC_xm, yBC_xp][sortindsfx]
yBC_y = np.r_[yBC_ym, yBC_yp][sortindsfy]
xBC = np.r_[xBC_x, xBC_y]
yBC = np.r_[yBC_x, yBC_y]
elif mesh.dim == 3: #3D
if (len(alpha) != 6 or len(beta) != 6 or len(gamma) != 6):
raise Exception("Lenght of list, alpha should be 6")
# fCCxm,fCCxp,fCCym,fCCyp,fCCzm,fCCzp = mesh.cellBoundaryInd
fxm,fxp,fym,fyp,fzm,fzp = mesh.faceBoundaryInd
nBC = fxm.sum()+fxp.sum()+fxm.sum()+fxp.sum()
alpha_xm, beta_xm, gamma_xm = alpha[0], beta[0], gamma[0]
alpha_xp, beta_xp, gamma_xp = alpha[1], beta[1], gamma[1]
alpha_ym, beta_ym, gamma_ym = alpha[2], beta[2], gamma[2]
alpha_yp, beta_yp, gamma_yp = alpha[3], beta[3], gamma[3]
alpha_zm, beta_zm, gamma_zm = alpha[4], beta[4], gamma[4]
alpha_zp, beta_zp, gamma_zp = alpha[5], beta[5], gamma[5]
# h_xm, h_xp = mesh.gridCC[fCCxm,0], mesh.gridCC[fCCxp,0]
# h_ym, h_yp = mesh.gridCC[fCCym,1], mesh.gridCC[fCCyp,1]
# h_zm, h_zp = mesh.gridCC[fCCzm,2], mesh.gridCC[fCCzp,2]
h_xm, h_xp = mesh.hx[0]*np.ones_like(alpha_xm), mesh.hx[-1]*np.ones_like(alpha_xp)
h_ym, h_yp = mesh.hy[0]*np.ones_like(alpha_ym), mesh.hy[-1]*np.ones_like(alpha_yp)
h_zm, h_zp = mesh.hz[0]*np.ones_like(alpha_zm), mesh.hz[-1]*np.ones_like(alpha_zp)
a_xm = gamma_xm/(0.5*alpha_xm-beta_xm/h_xm)
b_xm = (0.5*alpha_xm+beta_xm/h_xm)/(0.5*alpha_xm-beta_xm/h_xm)
a_xp = gamma_xp/(0.5*alpha_xp-beta_xp/h_xp)
b_xp = (0.5*alpha_xp+beta_xp/h_xp)/(0.5*alpha_xp-beta_xp/h_xp)
a_ym = gamma_ym/(0.5*alpha_ym-beta_ym/h_ym)
b_ym = (0.5*alpha_ym+beta_ym/h_ym)/(0.5*alpha_ym-beta_ym/h_ym)
a_yp = gamma_yp/(0.5*alpha_yp-beta_yp/h_yp)
b_yp = (0.5*alpha_yp+beta_yp/h_yp)/(0.5*alpha_yp-beta_yp/h_yp)
a_zm = gamma_zm/(0.5*alpha_zm-beta_zm/h_zm)
b_zm = (0.5*alpha_zm+beta_zm/h_zm)/(0.5*alpha_zm-beta_zm/h_zm)
a_zp = gamma_zp/(0.5*alpha_zp-beta_zp/h_zp)
b_zp = (0.5*alpha_zp+beta_zp/h_zp)/(0.5*alpha_zp-beta_zp/h_zp)
xBC_xm = 0.5*a_xm
xBC_xp = 0.5*a_xp/b_xp
yBC_xm = 0.5*(1.-b_xm)
yBC_xp = 0.5*(1.-1./b_xp)
xBC_ym = 0.5*a_ym
xBC_yp = 0.5*a_yp/b_yp
yBC_ym = 0.5*(1.-b_ym)
yBC_yp = 0.5*(1.-1./b_yp)
xBC_zm = 0.5*a_zm
xBC_zp = 0.5*a_zp/b_zp
yBC_zm = 0.5*(1.-b_zm)
yBC_zp = 0.5*(1.-1./b_zp)
sortindsfx = np.argsort(np.r_[np.arange(mesh.nFx)[fxm], np.arange(mesh.nFx)[fxp]])
sortindsfy = np.argsort(np.r_[np.arange(mesh.nFy)[fym], np.arange(mesh.nFy)[fyp]])
sortindsfz = np.argsort(np.r_[np.arange(mesh.nFz)[fzm], np.arange(mesh.nFz)[fzp]])
xBC_x = np.r_[xBC_xm, xBC_xp][sortindsfx]
xBC_y = np.r_[xBC_ym, xBC_yp][sortindsfy]
xBC_z = np.r_[xBC_zm, xBC_zp][sortindsfz]
yBC_x = np.r_[yBC_xm, yBC_xp][sortindsfx]
yBC_y = np.r_[yBC_ym, yBC_yp][sortindsfy]
yBC_z = np.r_[yBC_zm, yBC_zp][sortindsfz]
xBC = np.r_[xBC_x, xBC_y, xBC_z]
yBC = np.r_[yBC_x, yBC_y, yBC_z]
return xBC, yBC
class Test1D_InhomogeneousMixed(Tests.OrderTest):
name = "1D - Mixed"
meshTypes = MESHTYPES
meshDimension = 1
expectedOrders = 2
meshSizes = [4, 8, 16, 32]
def getError(self):
#Test function
phi_fun = lambda x: np.cos(np.pi*x)
j_fun = lambda x: np.pi*np.sin(np.pi*x)
phi_deriv = lambda x: -j_fun(x)
q_fun = lambda x: (np.pi**2)*np.cos(np.pi*x)
xc_ana = phi_fun(self.M.gridCC)
q_ana = q_fun(self.M.gridCC)
j_ana = j_fun(self.M.gridFx)
# Get boundary locations
vecN = self.M.vectorNx
vecC = self.M.vectorCCx
# Setup Mixed B.C (alpha, beta, gamma)
alpha_xm, alpha_xp = 1., 1.
beta_xm, beta_xp = 1., 1.
alpha = np.r_[alpha_xm, alpha_xp]
beta = np.r_[beta_xm, beta_xp]
vecN = self.M.vectorNx
vecC = self.M.vectorCCx
phi_bc = phi_fun(vecN[[0,-1]])
phi_deriv_bc = phi_deriv(vecN[[0,-1]])
gamma = alpha*phi_bc + beta*phi_deriv_bc
x_BC, y_BC = getxBCyBC_CC(self.M, alpha, beta, gamma)
sigma = np.ones(self.M.nC)
Mfrho = self.M.getFaceInnerProduct(1./sigma)
MfrhoI = self.M.getFaceInnerProduct(1./sigma, invMat=True)
V = Utils.sdiag(self.M.vol)
Div = V*self.M.faceDiv
P_BC, B = self.M.getBCProjWF_simple()
q = q_fun(self.M.gridCC)
M = B*self.M.aveCC2F
G = Div.T - P_BC*Utils.sdiag(y_BC)*M
# Mrhoj = D.T V phi + P_BC*Utils.sdiag(y_BC)*M phi - P_BC*x_BC
rhs = V*q + Div*MfrhoI*P_BC*x_BC
A = Div*MfrhoI*G
if self.myTest == 'xc':
#TODO: fix the null space
Ainv = Solver(A)
xc = Ainv*rhs
err = np.linalg.norm((xc-xc_ana), np.inf)
else:
NotImplementedError
return err
def test_order(self):
print "==== Testing Mixed boudary conduction for CC-problem ===="
self.name = "1D"
self.myTest = 'xc'
self.orderTest()
class Test2D_InhomogeneousMixed(Tests.OrderTest):
name = "2D - Mixed"
meshTypes = MESHTYPES
meshDimension = 2
expectedOrders = 2
meshSizes = [4, 8, 16, 32]
def getError(self):
#Test function
phi_fun = lambda x: np.cos(np.pi*x[:,0])*np.cos(np.pi*x[:,1])
j_funX = lambda x: +np.pi*np.sin(np.pi*x[:,0])*np.cos(np.pi*x[:,1])
j_funY = lambda x: +np.pi*np.cos(np.pi*x[:,0])*np.sin(np.pi*x[:,1])
phideriv_funX = lambda x: -j_funX(x)
phideriv_funY = lambda x: -j_funY(x)
q_fun = lambda x: +2*(np.pi**2)*phi_fun(x)
xc_ana = phi_fun(self.M.gridCC)
q_ana = q_fun(self.M.gridCC)
jX_ana = j_funX(self.M.gridFx)
jY_ana = j_funY(self.M.gridFy)
j_ana = np.r_[jX_ana,jY_ana]
# Get boundary locations
fxm,fxp,fym,fyp = self.M.faceBoundaryInd
gBFxm = self.M.gridFx[fxm,:]
gBFxp = self.M.gridFx[fxp,:]
gBFym = self.M.gridFy[fym,:]
gBFyp = self.M.gridFy[fyp,:]
# Setup Mixed B.C (alpha, beta, gamma)
alpha_xm, alpha_xp = np.ones_like(gBFxm[:,0]), np.ones_like(gBFxp[:,0])
beta_xm, beta_xp = np.ones_like(gBFxm[:,0]), np.ones_like(gBFxp[:,0])
alpha_ym, alpha_yp = np.ones_like(gBFym[:,1]), np.ones_like(gBFyp[:,1])
beta_ym, beta_yp = np.ones_like(gBFym[:,1]), np.ones_like(gBFyp[:,1])
phi_bc_xm, phi_bc_xp = phi_fun(gBFxm), phi_fun(gBFxp)
phi_bc_ym, phi_bc_yp = phi_fun(gBFym), phi_fun(gBFyp)
phiderivX_bc_xm, phiderivX_bc_xp = phideriv_funX(gBFxm), phideriv_funX(gBFxp)
phiderivY_bc_ym, phiderivY_bc_yp = phideriv_funY(gBFym), phideriv_funY(gBFyp)
gamma_fun = lambda alpha, beta, phi, phi_deriv: alpha*phi + beta*phi_deriv
gamma_xm = gamma_fun(alpha_xm, beta_xm, phi_bc_xm, phiderivX_bc_xm)
gamma_xp = gamma_fun(alpha_xp, beta_xp, phi_bc_xp, phiderivX_bc_xp)
gamma_ym = gamma_fun(alpha_ym, beta_ym, phi_bc_ym, phiderivY_bc_ym)
gamma_yp = gamma_fun(alpha_yp, beta_yp, phi_bc_yp, phiderivY_bc_yp)
alpha = [alpha_xm, alpha_xp, alpha_ym, alpha_yp]
beta = [beta_xm, beta_xp, beta_ym, beta_yp]
gamma = [gamma_xm, gamma_xp, gamma_ym, gamma_yp]
x_BC, y_BC = getxBCyBC_CC(self.M, alpha, beta, gamma)
sigma = np.ones(self.M.nC)
Mfrho = self.M.getFaceInnerProduct(1./sigma)
MfrhoI = self.M.getFaceInnerProduct(1./sigma, invMat=True)
V = Utils.sdiag(self.M.vol)
Div = V*self.M.faceDiv
P_BC, B = self.M.getBCProjWF_simple()
q = q_fun(self.M.gridCC)
M = B*self.M.aveCC2F
G = Div.T - P_BC*Utils.sdiag(y_BC)*M
rhs = V*q + Div*MfrhoI*P_BC*x_BC
A = Div*MfrhoI*G
if self.myTest == 'xc':
Ainv = Solver(A)
xc = Ainv*rhs
err = np.linalg.norm((xc-xc_ana), np.inf)
else:
NotImplementedError
return err
def test_order(self):
print "==== Testing Mixed boudary conduction for CC-problem ===="
self.name = "2D"
self.myTest = 'xc'
self.orderTest()
class Test3D_InhomogeneousMixed(Tests.OrderTest):
name = "3D - Mixed"
meshTypes = MESHTYPES
meshDimension = 3
expectedOrders = 2
meshSizes = [4, 8, 16]
def getError(self):
#Test function
phi_fun = lambda x: np.cos(np.pi*x[:,0])*np.cos(np.pi*x[:,1])*np.cos(np.pi*x[:,2])
j_funX = lambda x: +np.pi*np.sin(np.pi*x[:,0])*np.cos(np.pi*x[:,1])*np.cos(np.pi*x[:,2])
j_funY = lambda x: +np.pi*np.cos(np.pi*x[:,0])*np.sin(np.pi*x[:,1])*np.cos(np.pi*x[:,2])
j_funZ = lambda x: +np.pi*np.cos(np.pi*x[:,0])*np.cos(np.pi*x[:,1])*np.sin(np.pi*x[:,2])
phideriv_funX = lambda x: -j_funX(x)
phideriv_funY = lambda x: -j_funY(x)
phideriv_funZ = lambda x: -j_funZ(x)
q_fun = lambda x: 3*(np.pi**2)*phi_fun(x)
xc_ana = phi_fun(self.M.gridCC)
q_ana = q_fun(self.M.gridCC)
jX_ana = j_funX(self.M.gridFx)
jY_ana = j_funY(self.M.gridFy)
j_ana = np.r_[jX_ana,jY_ana,jY_ana]
# Get boundary locations
fxm,fxp,fym,fyp,fzm,fzp = self.M.faceBoundaryInd
gBFxm = self.M.gridFx[fxm,:]
gBFxp = self.M.gridFx[fxp,:]
gBFym = self.M.gridFy[fym,:]
gBFyp = self.M.gridFy[fyp,:]
gBFzm = self.M.gridFz[fzm,:]
gBFzp = self.M.gridFz[fzp,:]
# Setup Mixed B.C (alpha, beta, gamma)
alpha_xm, alpha_xp = np.ones_like(gBFxm[:,0]), np.ones_like(gBFxp[:,0])
beta_xm, beta_xp = np.ones_like(gBFxm[:,0]), np.ones_like(gBFxp[:,0])
alpha_ym, alpha_yp = np.ones_like(gBFym[:,1]), np.ones_like(gBFyp[:,1])
beta_ym, beta_yp = np.ones_like(gBFym[:,1]), np.ones_like(gBFyp[:,1])
alpha_zm, alpha_zp = np.ones_like(gBFzm[:,2]), np.ones_like(gBFzp[:,2])
beta_zm, beta_zp = np.ones_like(gBFzm[:,2]), np.ones_like(gBFzp[:,2])
phi_bc_xm, phi_bc_xp = phi_fun(gBFxm), phi_fun(gBFxp)
phi_bc_ym, phi_bc_yp = phi_fun(gBFym), phi_fun(gBFyp)
phi_bc_zm, phi_bc_zp = phi_fun(gBFzm), phi_fun(gBFzp)
phiderivX_bc_xm, phiderivX_bc_xp = phideriv_funX(gBFxm), phideriv_funX(gBFxp)
phiderivY_bc_ym, phiderivY_bc_yp = phideriv_funY(gBFym), phideriv_funY(gBFyp)
phiderivY_bc_zm, phiderivY_bc_zp = phideriv_funZ(gBFzm), phideriv_funZ(gBFzp)
gamma_fun = lambda alpha, beta, phi, phi_deriv: alpha*phi + beta*phi_deriv
gamma_xm = gamma_fun(alpha_xm, beta_xm, phi_bc_xm, phiderivX_bc_xm)
gamma_xp = gamma_fun(alpha_xp, beta_xp, phi_bc_xp, phiderivX_bc_xp)
gamma_ym = gamma_fun(alpha_ym, beta_ym, phi_bc_ym, phiderivY_bc_ym)
gamma_yp = gamma_fun(alpha_yp, beta_yp, phi_bc_yp, phiderivY_bc_yp)
gamma_zm = gamma_fun(alpha_zm, beta_zm, phi_bc_zm, phiderivY_bc_zm)
gamma_zp = gamma_fun(alpha_zp, beta_zp, phi_bc_zp, phiderivY_bc_zp)
alpha = [alpha_xm, alpha_xp, alpha_ym, alpha_yp, alpha_zm, alpha_zp]
beta = [beta_xm, beta_xp, beta_ym, beta_yp, beta_zm, beta_zp]
gamma = [gamma_xm, gamma_xp, gamma_ym, gamma_yp, gamma_zm, gamma_zp]
x_BC, y_BC = getxBCyBC_CC(self.M, alpha, beta, gamma)
sigma = np.ones(self.M.nC)
Mfrho = self.M.getFaceInnerProduct(1./sigma)
MfrhoI = self.M.getFaceInnerProduct(1./sigma, invMat=True)
V = Utils.sdiag(self.M.vol)
Div = V*self.M.faceDiv
P_BC, B = self.M.getBCProjWF_simple()
q = q_fun(self.M.gridCC)
M = B*self.M.aveCC2F
G = Div.T - P_BC*Utils.sdiag(y_BC)*M
rhs = V*q + Div*MfrhoI*P_BC*x_BC
A = Div*MfrhoI*G
if self.myTest == 'xc':
#TODO: fix the null space
Ainv = Solver(A)
xc = Ainv*rhs
err = np.linalg.norm((xc-xc_ana), np.inf)
else:
NotImplementedError
return err
def test_order(self):
print "==== Testing Mixed boudary conduction for CC-problem ===="
self.name = "3D"
self.myTest = 'xc'
self.orderTest()
if __name__ == '__main__':
unittest.main()
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