mirror of
https://github.com/wassname/simpeg.git
synced 2026-06-28 03:51:17 +08:00
Brendan Smithyman
507 lines
16 KiB
Python
507 lines
16 KiB
Python
from __future__ import print_function
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from __future__ import unicode_literals
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from __future__ import division
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from __future__ import absolute_import
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from future import standard_library
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standard_library.install_aliases()
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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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class Test1D_InhomogeneousDirichlet(Tests.OrderTest):
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name = "1D - Dirichlet"
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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, 64, 128]
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def getError(self):
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#Test function
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phi = 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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q_fun = lambda x: -(np.pi**2)*np.cos(np.pi*x)
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xc_ana = phi(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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#TODO: Check where our boundary conditions are CCx or Nx
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# vec = self.M.vectorNx
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vec = self.M.vectorCCx
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phi_bc = phi(vec[[0,-1]])
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j_bc = j_fun(vec[[0,-1]])
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P, Pin, Pout = self.M.getBCProjWF([['dirichlet', 'dirichlet']])
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Mc = self.M.getFaceInnerProduct()
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McI = Utils.sdInv(self.M.getFaceInnerProduct())
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V = Utils.sdiag(self.M.vol)
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G = -Pin.T*Pin*self.M.faceDiv.T * V
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D = self.M.faceDiv
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j = McI*(G*xc_ana + P*phi_bc)
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q = V*D*Pin.T*Pin*j + V*D*Pout.T*j_bc
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# Rearrange if we know q to solve for x
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A = V*D*Pin.T*Pin*McI*G
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rhs = V*q_ana - V*D*Pin.T*Pin*McI*P*phi_bc - V*D*Pout.T*j_bc
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# A = D*McI*G
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# rhs = q_ana - D*McI*P*phi_bc
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if self.myTest == 'j':
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err = np.linalg.norm((j-j_ana), np.inf)
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elif self.myTest == 'q':
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err = np.linalg.norm((q-V*q_ana), np.inf)
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elif self.myTest == 'xc':
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#TODO: fix the null space
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solver = SolverCG(A, maxiter=1000)
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xc = solver * (rhs)
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print('ACCURACY', np.linalg.norm(Utils.mkvc(A*xc) - rhs))
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err = np.linalg.norm((xc-xc_ana), np.inf)
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elif self.myTest == 'xcJ':
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#TODO: fix the null space
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xc = Solver(A) * (rhs)
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print(np.linalg.norm(Utils.mkvc(A*xc) - rhs))
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j = McI*(G*xc + P*phi_bc)
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err = np.linalg.norm((j-j_ana), np.inf)
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return err
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def test_orderJ(self):
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self.name = "1D - InhomogeneousDirichlet_Forward j"
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self.myTest = 'j'
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self.orderTest()
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def test_orderQ(self):
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self.name = "1D - InhomogeneousDirichlet_Forward q"
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self.myTest = 'q'
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self.orderTest()
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def test_orderX(self):
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self.name = "1D - InhomogeneousDirichlet_Inverse"
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self.myTest = 'xc'
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self.orderTest()
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def test_orderXJ(self):
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self.name = "1D - InhomogeneousDirichlet_Inverse J"
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self.myTest = 'xcJ'
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self.orderTest()
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class Test2D_InhomogeneousDirichlet(Tests.OrderTest):
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name = "2D - Dirichlet"
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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 = 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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q_fun = lambda x: -2*(np.pi**2)*phi(x)
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xc_ana = phi(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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#TODO: Check where our boundary conditions are CCx or Nx
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# fxm,fxp,fym,fyp = self.M.faceBoundaryInd
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# gBFx = self.M.gridFx[(fxm|fxp),:]
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# gBFy = self.M.gridFy[(fym|fyp),:]
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fxm,fxp,fym,fyp = self.M.cellBoundaryInd
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gBFx = self.M.gridCC[(fxm|fxp),:]
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gBFy = self.M.gridCC[(fym|fyp),:]
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bc = phi(np.r_[gBFx,gBFy])
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# P = sp.csr_matrix(([-1,1],([0,self.M.nF-1],[0,1])), shape=(self.M.nF, 2))
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P, Pin, Pout = self.M.getBCProjWF('dirichlet')
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Mc = self.M.getFaceInnerProduct()
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McI = Utils.sdInv(self.M.getFaceInnerProduct())
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G = -self.M.faceDiv.T * Utils.sdiag(self.M.vol)
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D = self.M.faceDiv
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j = McI*(G*xc_ana + P*bc)
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q = D*j
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# self.M.plotImage(j, 'FxFy', showIt=True)
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# Rearrange if we know q to solve for x
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A = D*McI*G
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rhs = q_ana - D*McI*P*bc
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if self.myTest == 'j':
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err = np.linalg.norm((j-j_ana), np.inf)
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elif self.myTest == 'q':
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err = np.linalg.norm((q-q_ana), np.inf)
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elif self.myTest == 'xc':
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xc = Solver(A) * (rhs)
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err = np.linalg.norm((xc-xc_ana), np.inf)
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elif self.myTest == 'xcJ':
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xc = Solver(A) * (rhs)
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j = McI*(G*xc + P*bc)
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err = np.linalg.norm((j-j_ana), np.inf)
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return err
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def test_orderJ(self):
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self.name = "2D - InhomogeneousDirichlet_Forward j"
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self.myTest = 'j'
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self.orderTest()
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def test_orderQ(self):
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self.name = "2D - InhomogeneousDirichlet_Forward q"
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self.myTest = 'q'
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self.orderTest()
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def test_orderX(self):
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self.name = "2D - InhomogeneousDirichlet_Inverse"
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self.myTest = 'xc'
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self.orderTest()
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def test_orderXJ(self):
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self.name = "2D - InhomogeneousDirichlet_Inverse J"
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self.myTest = 'xcJ'
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self.orderTest()
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class Test1D_InhomogeneousNeumann(Tests.OrderTest):
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name = "1D - Neumann"
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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, 64, 128]
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def getError(self):
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#Test function
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phi = lambda x: np.sin(np.pi*x)
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j_fun = lambda x: np.pi*np.cos(np.pi*x)
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q_fun = lambda x: -(np.pi**2)*np.sin(np.pi*x)
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xc_ana = phi(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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#TODO: Check where our boundary conditions are CCx or Nx
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vecN = self.M.vectorNx
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vecC = self.M.vectorCCx
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phi_bc = phi(vecC[[0,-1]])
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j_bc = j_fun(vecN[[0,-1]])
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P, Pin, Pout = self.M.getBCProjWF([['neumann', 'neumann']])
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Mc = self.M.getFaceInnerProduct()
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McI = Utils.sdInv(self.M.getFaceInnerProduct())
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V = Utils.sdiag(self.M.vol)
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G = -Pin.T*Pin*self.M.faceDiv.T * V
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D = self.M.faceDiv
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j = McI*(G*xc_ana + P*phi_bc)
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q = V*D*Pin.T*Pin*j + V*D*Pout.T*j_bc
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# Rearrange if we know q to solve for x
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A = V*D*Pin.T*Pin*McI*G
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rhs = V*q_ana - V*D*Pin.T*Pin*McI*P*phi_bc - V*D*Pout.T*j_bc
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# A = D*McI*G
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# rhs = q_ana - D*McI*P*phi_bc
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if self.myTest == 'j':
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err = np.linalg.norm((Pin*j-Pin*j_ana), np.inf)
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elif self.myTest == 'q':
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err = np.linalg.norm((q-V*q_ana), np.inf)
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elif self.myTest == 'xc':
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#TODO: fix the null space
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xc, info = sp.linalg.minres(A, rhs, tol = 1e-6)
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err = np.linalg.norm((xc-xc_ana), np.inf)
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if info > 0:
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print('Solve does not work well')
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print('ACCURACY', np.linalg.norm(Utils.mkvc(A*xc) - rhs))
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elif self.myTest == 'xcJ':
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#TODO: fix the null space
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xc, info = sp.linalg.minres(A, rhs, tol = 1e-6)
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j = McI*(G*xc + P*phi_bc)
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err = np.linalg.norm((Pin*j-Pin*j_ana), np.inf)
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if info > 0:
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print('Solve does not work well')
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print('ACCURACY', np.linalg.norm(Utils.mkvc(A*xc) - rhs))
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return err
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def test_orderJ(self):
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self.name = "1D - InhomogeneousNeumann_Forward j"
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self.myTest = 'j'
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self.orderTest()
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def test_orderQ(self):
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self.name = "1D - InhomogeneousNeumann_Forward q"
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self.myTest = 'q'
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self.orderTest()
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def test_orderXJ(self):
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self.name = "1D - InhomogeneousNeumann_Inverse J"
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self.myTest = 'xcJ'
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self.orderTest()
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class Test2D_InhomogeneousNeumann(Tests.OrderTest):
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name = "2D - Neumann"
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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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# meshSizes = [4]
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def getError(self):
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#Test function
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phi = lambda x: np.sin(np.pi*x[:,0])*np.sin(np.pi*x[:,1])
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j_funX = lambda x: np.pi*np.cos(np.pi*x[:,0])*np.sin(np.pi*x[:,1])
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j_funY = lambda x: np.pi*np.sin(np.pi*x[:,0])*np.cos(np.pi*x[:,1])
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q_fun = lambda x: -2*(np.pi**2)*phi(x)
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xc_ana = phi(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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#TODO: Check where our boundary conditions are CCx or Nx
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cxm,cxp,cym,cyp = self.M.cellBoundaryInd
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fxm,fxp,fym,fyp = self.M.faceBoundaryInd
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gBFx = self.M.gridFx[(fxm|fxp),:]
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gBFy = self.M.gridFy[(fym|fyp),:]
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gBCx = self.M.gridCC[(cxm|cxp),:]
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gBCy = self.M.gridCC[(cym|cyp),:]
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phi_bc = phi(np.r_[gBFx,gBFy])
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j_bc = np.r_[j_funX(gBFx), j_funY(gBFy)]
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# P = sp.csr_matrix(([-1,1],([0,self.M.nF-1],[0,1])), shape=(self.M.nF, 2))
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P, Pin, Pout = self.M.getBCProjWF('neumann')
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Mc = self.M.getFaceInnerProduct()
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McI = Utils.sdInv(self.M.getFaceInnerProduct())
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V = Utils.sdiag(self.M.vol)
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G = -Pin.T*Pin*self.M.faceDiv.T * V
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D = self.M.faceDiv
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j = McI*(G*xc_ana + P*phi_bc)
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q = V*D*Pin.T*Pin*j + V*D*Pout.T*j_bc
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# Rearrange if we know q to solve for x
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A = V*D*Pin.T*Pin*McI*G
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rhs = V*q_ana - V*D*Pin.T*Pin*McI*P*phi_bc - V*D*Pout.T*j_bc
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if self.myTest == 'j':
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err = np.linalg.norm((Pin*j-Pin*j_ana), np.inf)
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elif self.myTest == 'q':
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err = np.linalg.norm((q-V*q_ana), np.inf)
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elif self.myTest == 'xc':
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#TODO: fix the null space
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xc, info = sp.linalg.minres(A, rhs, tol = 1e-6)
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err = np.linalg.norm((xc-xc_ana), np.inf)
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if info > 0:
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print('Solve does not work well')
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print('ACCURACY', np.linalg.norm(Utils.mkvc(A*xc) - rhs))
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elif self.myTest == 'xcJ':
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#TODO: fix the null space
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xc, info = sp.linalg.minres(A, rhs, tol = 1e-6)
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j = McI*(G*xc + P*phi_bc)
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err = np.linalg.norm((Pin*j-Pin*j_ana), np.inf)
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if info > 0:
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print('Solve does not work well')
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print('ACCURACY', np.linalg.norm(Utils.mkvc(A*xc) - rhs))
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return err
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def test_orderJ(self):
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self.name = "2D - InhomogeneousNeumann_Forward j"
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self.myTest = 'j'
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self.orderTest()
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def test_orderQ(self):
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self.name = "2D - InhomogeneousNeumann_Forward q"
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self.myTest = 'q'
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self.orderTest()
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def test_orderXJ(self):
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self.name = "2D - InhomogeneousNeumann_Inverse J"
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self.myTest = 'xcJ'
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self.orderTest()
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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, 64, 128]
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def getError(self):
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#Test function
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phi = lambda x: np.cos(0.5*np.pi*x)
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j_fun = lambda x: -0.5*np.pi*np.sin(0.5*np.pi*x)
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q_fun = lambda x: -0.25*(np.pi**2)*np.cos(0.5*np.pi*x)
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xc_ana = phi(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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#TODO: Check where our boundary conditions are CCx or Nx
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vecN = self.M.vectorNx
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vecC = self.M.vectorCCx
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phi_bc = phi(vecC[[0,-1]])
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j_bc = j_fun(vecN[[0,-1]])
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P, Pin, Pout = self.M.getBCProjWF([['dirichlet', 'neumann']])
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Mc = self.M.getFaceInnerProduct()
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McI = Utils.sdInv(self.M.getFaceInnerProduct())
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V = Utils.sdiag(self.M.vol)
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G = -Pin.T*Pin*self.M.faceDiv.T * V
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D = self.M.faceDiv
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j = McI*(G*xc_ana + P*phi_bc)
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q = V*D*Pin.T*Pin*j + V*D*Pout.T*j_bc
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# Rearrange if we know q to solve for x
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A = V*D*Pin.T*Pin*McI*G
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rhs = V*q_ana - V*D*Pin.T*Pin*McI*P*phi_bc - V*D*Pout.T*j_bc
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# A = D*McI*G
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# rhs = q_ana - D*McI*P*phi_bc
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if self.myTest == 'j':
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err = np.linalg.norm((Pin*j-Pin*j_ana), np.inf)
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elif self.myTest == 'q':
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err = np.linalg.norm((q-V*q_ana), np.inf)
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elif self.myTest == 'xc':
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#TODO: fix the null space
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xc, info = sp.linalg.minres(A, rhs, tol = 1e-6)
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err = np.linalg.norm((xc-xc_ana), np.inf)
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if info > 0:
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print('Solve does not work well')
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print('ACCURACY', np.linalg.norm(Utils.mkvc(A*xc) - rhs))
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elif self.myTest == 'xcJ':
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#TODO: fix the null space
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xc, info = sp.linalg.minres(A, rhs, tol = 1e-6)
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j = McI*(G*xc + P*phi_bc)
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err = np.linalg.norm((Pin*j-Pin*j_ana), np.inf)
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if info > 0:
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print('Solve does not work well')
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print('ACCURACY', np.linalg.norm(Utils.mkvc(A*xc) - rhs))
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return err
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def test_orderJ(self):
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self.name = "1D - InhomogeneousMixed_Forward j"
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self.myTest = 'j'
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self.orderTest()
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def test_orderQ(self):
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self.name = "1D - InhomogeneousMixed_Forward q"
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self.myTest = 'q'
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self.orderTest()
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def test_orderXJ(self):
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self.name = "1D - InhomogeneousMixed_Inverse J"
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self.myTest = 'xcJ'
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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 = [2, 4, 8, 16]
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# meshSizes = [4]
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def getError(self):
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#Test function
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phi = lambda x: np.cos(0.5*np.pi*x[:,0])*np.cos(0.5*np.pi*x[:,1])
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j_funX = lambda x: -0.5*np.pi*np.sin(0.5*np.pi*x[:,0])*np.cos(0.5*np.pi*x[:,1])
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j_funY = lambda x: -0.5*np.pi*np.cos(0.5*np.pi*x[:,0])*np.sin(0.5*np.pi*x[:,1])
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q_fun = lambda x: -2*((0.5*np.pi)**2)*phi(x)
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xc_ana = phi(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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#TODO: Check where our boundary conditions are CCx or Nx
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cxm,cxp,cym,cyp = self.M.cellBoundaryInd
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fxm,fxp,fym,fyp = self.M.faceBoundaryInd
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gBFx = self.M.gridFx[(fxm|fxp),:]
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gBFy = self.M.gridFy[(fym|fyp),:]
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gBCx = self.M.gridCC[(cxm|cxp),:]
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gBCy = self.M.gridCC[(cym|cyp),:]
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phi_bc = phi(np.r_[gBCx,gBCy])
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j_bc = np.r_[j_funX(gBFx), j_funY(gBFy)]
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# P = sp.csr_matrix(([-1,1],([0,self.M.nF-1],[0,1])), shape=(self.M.nF, 2))
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P, Pin, Pout = self.M.getBCProjWF([['dirichlet', 'neumann'], ['dirichlet', 'neumann']])
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Mc = self.M.getFaceInnerProduct()
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McI = Utils.sdInv(self.M.getFaceInnerProduct())
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V = Utils.sdiag(self.M.vol)
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G = -Pin.T*Pin*self.M.faceDiv.T * V
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D = self.M.faceDiv
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j = McI*(G*xc_ana + P*phi_bc)
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q = V*D*Pin.T*Pin*j + V*D*Pout.T*j_bc
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# Rearrange if we know q to solve for x
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A = V*D*Pin.T*Pin*McI*G
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rhs = V*q_ana - V*D*Pin.T*Pin*McI*P*phi_bc - V*D*Pout.T*j_bc
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if self.myTest == 'j':
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err = np.linalg.norm((Pin*j-Pin*j_ana), np.inf)
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elif self.myTest == 'q':
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err = np.linalg.norm((q-V*q_ana), np.inf)
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elif self.myTest == 'xc':
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#TODO: fix the null space
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xc, info = sp.linalg.minres(A, rhs, tol = 1e-6)
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err = np.linalg.norm((xc-xc_ana), np.inf)
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if info > 0:
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print('Solve does not work well')
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print('ACCURACY', np.linalg.norm(Utils.mkvc(A*xc) - rhs))
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elif self.myTest == 'xcJ':
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#TODO: fix the null space
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xc, info = sp.linalg.minres(A, rhs, tol = 1e-6)
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j = McI*(G*xc + P*phi_bc)
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err = np.linalg.norm((Pin*j-Pin*j_ana), np.inf)
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if info > 0:
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print('Solve does not work well')
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print('ACCURACY', np.linalg.norm(Utils.mkvc(A*xc) - rhs))
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return err
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def test_orderJ(self):
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self.name = "2D - InhomogeneousMixed_Forward j"
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self.myTest = 'j'
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self.orderTest()
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def test_orderQ(self):
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self.name = "2D - InhomogeneousMixed_Forward q"
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self.myTest = 'q'
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self.orderTest()
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|
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def test_orderXJ(self):
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self.name = "2D - InhomogeneousMixed_Inverse J"
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self.myTest = 'xcJ'
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|
self.orderTest()
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if __name__ == '__main__':
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unittest.main()
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