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