mirror of
https://github.com/wassname/simpeg.git
synced 2026-06-28 04:55:25 +08:00
Rowan Cockett
484 lines
16 KiB
Python
484 lines
16 KiB
Python
import numpy as np
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import unittest
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from SimPEG.Tests import OrderTest
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import matplotlib.pyplot as plt
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#TODO: 'randomTensorMesh'
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MESHTYPES = ['uniformTensorMesh', 'uniformCurv', 'rotateCurv']
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call2 = lambda fun, xyz: fun(xyz[:, 0], xyz[:, 1])
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call3 = lambda fun, xyz: fun(xyz[:, 0], xyz[:, 1], xyz[:, 2])
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cart_row2 = lambda g, xfun, yfun: np.c_[call2(xfun, g), call2(yfun, g)]
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cart_row3 = lambda g, xfun, yfun, zfun: np.c_[call3(xfun, g), call3(yfun, g), call3(zfun, g)]
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cartF2 = lambda M, fx, fy: np.vstack((cart_row2(M.gridFx, fx, fy), cart_row2(M.gridFy, fx, fy)))
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cartE2 = lambda M, ex, ey: np.vstack((cart_row2(M.gridEx, ex, ey), cart_row2(M.gridEy, ex, ey)))
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cartF3 = lambda M, fx, fy, fz: np.vstack((cart_row3(M.gridFx, fx, fy, fz), cart_row3(M.gridFy, fx, fy, fz), cart_row3(M.gridFz, fx, fy, fz)))
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cartE3 = lambda M, ex, ey, ez: np.vstack((cart_row3(M.gridEx, ex, ey, ez), cart_row3(M.gridEy, ex, ey, ez), cart_row3(M.gridEz, ex, ey, ez)))
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class TestCurl(OrderTest):
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name = "Curl"
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meshTypes = MESHTYPES
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def getError(self):
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# fun: i (cos(y)) + j (cos(z)) + k (cos(x))
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# sol: i (sin(z)) + j (sin(x)) + k (sin(y))
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funX = lambda x, y, z: np.cos(2*np.pi*y)
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funY = lambda x, y, z: np.cos(2*np.pi*z)
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funZ = lambda x, y, z: np.cos(2*np.pi*x)
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solX = lambda x, y, z: 2*np.pi*np.sin(2*np.pi*z)
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solY = lambda x, y, z: 2*np.pi*np.sin(2*np.pi*x)
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solZ = lambda x, y, z: 2*np.pi*np.sin(2*np.pi*y)
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Ec = cartE3(self.M, funX, funY, funZ)
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E = self.M.projectEdgeVector(Ec)
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Fc = cartF3(self.M, solX, solY, solZ)
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curlE_ana = self.M.projectFaceVector(Fc)
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curlE = self.M.edgeCurl.dot(E)
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if self._meshType == 'rotateCurv':
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# Really it is the integration we should be caring about:
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# So, let us look at the l2 norm.
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err = np.linalg.norm(self.M.area*(curlE - curlE_ana), 2)
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else:
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err = np.linalg.norm((curlE - curlE_ana), np.inf)
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return err
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def test_order(self):
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self.orderTest()
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class TestCurl2D(OrderTest):
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name = "Cell Grad 2D - Dirichlet"
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meshTypes = ['uniformTensorMesh']
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meshDimension = 2
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meshSizes = [8, 16, 32, 64]
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def getError(self):
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#Test function
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ex = lambda x, y: np.cos(y)
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ey = lambda x, y: np.cos(x)
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sol = lambda x, y: -np.sin(x)+np.sin(y)
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sol_curl2d = call2(sol, self.M.gridCC)
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Ec = cartE2(self.M, ex, ey)
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sol_ana = self.M.edgeCurl*self.M.projectFaceVector(Ec)
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err = np.linalg.norm((sol_curl2d-sol_ana), np.inf)
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return err
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def test_order(self):
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self.orderTest()
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class TestCellGrad1D_InhomogeneousDirichlet(OrderTest):
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name = "Cell Grad 1D - Dirichlet"
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meshTypes = ['uniformTensorMesh']
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meshDimension = 1
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expectedOrders = 1 # because of the averaging involved in the ghost point. u_b = (u_n + u_g)/2
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meshSizes = [8, 16, 32, 64]
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def getError(self):
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#Test function
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fx = lambda x: -2*np.pi*np.sin(2*np.pi*x)
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sol = lambda x: np.cos(2*np.pi*x)
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xc = sol(self.M.gridCC)
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gradX_ana = fx(self.M.gridFx)
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bc = np.array([1,1])
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self.M.setCellGradBC('dirichlet')
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gradX = self.M.cellGrad.dot(xc) + self.M.cellGradBC*bc
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err = np.linalg.norm((gradX-gradX_ana), np.inf)
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return err
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def test_order(self):
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self.orderTest()
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class TestCellGrad2D_Dirichlet(OrderTest):
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name = "Cell Grad 2D - Dirichlet"
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meshTypes = ['uniformTensorMesh']
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meshDimension = 2
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meshSizes = [8, 16, 32, 64]
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def getError(self):
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#Test function
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fx = lambda x, y: 2*np.pi*np.cos(2*np.pi*x)*np.sin(2*np.pi*y)
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fy = lambda x, y: 2*np.pi*np.cos(2*np.pi*y)*np.sin(2*np.pi*x)
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sol = lambda x, y: np.sin(2*np.pi*x)*np.sin(2*np.pi*y)
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xc = call2(sol, self.M.gridCC)
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Fc = cartF2(self.M, fx, fy)
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gradX_ana = self.M.projectFaceVector(Fc)
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self.M.setCellGradBC('dirichlet')
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gradX = self.M.cellGrad.dot(xc)
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err = np.linalg.norm((gradX-gradX_ana), np.inf)
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return err
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def test_order(self):
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self.orderTest()
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class TestCellGrad3D_Dirichlet(OrderTest):
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name = "Cell Grad 3D - Dirichlet"
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meshTypes = ['uniformTensorMesh']
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meshDimension = 3
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meshSizes = [8, 16, 32]
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def getError(self):
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#Test function
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fx = lambda x, y, z: 2*np.pi*np.cos(2*np.pi*x)*np.sin(2*np.pi*y)*np.sin(2*np.pi*z)
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fy = lambda x, y, z: 2*np.pi*np.sin(2*np.pi*x)*np.cos(2*np.pi*y)*np.sin(2*np.pi*z)
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fz = lambda x, y, z: 2*np.pi*np.sin(2*np.pi*x)*np.sin(2*np.pi*y)*np.cos(2*np.pi*z)
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sol = lambda x, y, z: np.sin(2*np.pi*x)*np.sin(2*np.pi*y)*np.sin(2*np.pi*z)
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xc = call3(sol, self.M.gridCC)
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Fc = cartF3(self.M, fx, fy, fz)
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gradX_ana = self.M.projectFaceVector(Fc)
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self.M.setCellGradBC('dirichlet')
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gradX = self.M.cellGrad.dot(xc)
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err = np.linalg.norm((gradX-gradX_ana), np.inf)
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return err
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def test_order(self):
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self.orderTest()
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class TestCellGrad2D_Neumann(OrderTest):
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name = "Cell Grad 2D - Neumann"
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meshTypes = ['uniformTensorMesh']
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meshDimension = 2
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meshSizes = [8, 16, 32, 64]
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def getError(self):
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#Test function
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fx = lambda x, y: -2*np.pi*np.sin(2*np.pi*x)*np.cos(2*np.pi*y)
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fy = lambda x, y: -2*np.pi*np.sin(2*np.pi*y)*np.cos(2*np.pi*x)
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sol = lambda x, y: np.cos(2*np.pi*x)*np.cos(2*np.pi*y)
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xc = call2(sol, self.M.gridCC)
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Fc = cartF2(self.M, fx, fy)
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gradX_ana = self.M.projectFaceVector(Fc)
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self.M.setCellGradBC('neumann')
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gradX = self.M.cellGrad.dot(xc)
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err = np.linalg.norm((gradX-gradX_ana), np.inf)
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return err
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def test_order(self):
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self.orderTest()
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class TestCellGrad3D_Neumann(OrderTest):
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name = "Cell Grad 3D - Neumann"
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meshTypes = ['uniformTensorMesh']
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meshDimension = 3
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meshSizes = [8, 16, 32]
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def getError(self):
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#Test function
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fx = lambda x, y, z: -2*np.pi*np.sin(2*np.pi*x)*np.cos(2*np.pi*y)*np.cos(2*np.pi*z)
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fy = lambda x, y, z: -2*np.pi*np.cos(2*np.pi*x)*np.sin(2*np.pi*y)*np.cos(2*np.pi*z)
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fz = lambda x, y, z: -2*np.pi*np.cos(2*np.pi*x)*np.cos(2*np.pi*y)*np.sin(2*np.pi*z)
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sol = lambda x, y, z: np.cos(2*np.pi*x)*np.cos(2*np.pi*y)*np.cos(2*np.pi*z)
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xc = call3(sol, self.M.gridCC)
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Fc = cartF3(self.M, fx, fy, fz)
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gradX_ana = self.M.projectFaceVector(Fc)
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self.M.setCellGradBC('neumann')
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gradX = self.M.cellGrad.dot(xc)
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err = np.linalg.norm((gradX-gradX_ana), np.inf)
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return err
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def test_order(self):
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self.orderTest()
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class TestFaceDiv3D(OrderTest):
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name = "Face Divergence 3D"
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meshTypes = MESHTYPES
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meshSizes = [8, 16, 32]
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def getError(self):
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#Test function
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fx = lambda x, y, z: np.sin(2*np.pi*x)
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fy = lambda x, y, z: np.sin(2*np.pi*y)
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fz = lambda x, y, z: np.sin(2*np.pi*z)
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sol = lambda x, y, z: (2*np.pi*np.cos(2*np.pi*x)+2*np.pi*np.cos(2*np.pi*y)+2*np.pi*np.cos(2*np.pi*z))
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Fc = cartF3(self.M, fx, fy, fz)
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F = self.M.projectFaceVector(Fc)
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divF = self.M.faceDiv.dot(F)
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divF_ana = call3(sol, self.M.gridCC)
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if self._meshType == 'rotateCurv':
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# Really it is the integration we should be caring about:
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# So, let us look at the l2 norm.
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err = np.linalg.norm(self.M.vol*(divF-divF_ana), 2)
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else:
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err = np.linalg.norm((divF-divF_ana), np.inf)
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return err
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def test_order(self):
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self.orderTest()
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class TestFaceDiv2D(OrderTest):
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name = "Face Divergence 2D"
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meshTypes = MESHTYPES
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meshDimension = 2
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meshSizes = [8, 16, 32, 64]
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def getError(self):
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#Test function
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fx = lambda x, y: np.sin(2*np.pi*x)
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fy = lambda x, y: np.sin(2*np.pi*y)
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sol = lambda x, y: 2*np.pi*(np.cos(2*np.pi*x)+np.cos(2*np.pi*y))
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Fc = cartF2(self.M, fx, fy)
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F = self.M.projectFaceVector(Fc)
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divF = self.M.faceDiv.dot(F)
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divF_ana = call2(sol, self.M.gridCC)
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err = np.linalg.norm((divF-divF_ana), np.inf)
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return err
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def test_order(self):
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self.orderTest()
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class TestNodalGrad(OrderTest):
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name = "Nodal Gradient"
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meshTypes = MESHTYPES
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def getError(self):
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#Test function
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fun = lambda x, y, z: (np.cos(x)+np.cos(y)+np.cos(z))
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# i (sin(x)) + j (sin(y)) + k (sin(z))
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solX = lambda x, y, z: -np.sin(x)
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solY = lambda x, y, z: -np.sin(y)
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solZ = lambda x, y, z: -np.sin(z)
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phi = call3(fun, self.M.gridN)
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gradE = self.M.nodalGrad.dot(phi)
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Ec = cartE3(self.M, solX, solY, solZ)
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gradE_ana = self.M.projectEdgeVector(Ec)
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err = np.linalg.norm((gradE-gradE_ana), np.inf)
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return err
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def test_order(self):
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self.orderTest()
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class TestNodalGrad2D(OrderTest):
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name = "Nodal Gradient 2D"
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meshTypes = MESHTYPES
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meshDimension = 2
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def getError(self):
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#Test function
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fun = lambda x, y: (np.cos(x)+np.cos(y))
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# i (sin(x)) + j (sin(y)) + k (sin(z))
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solX = lambda x, y: -np.sin(x)
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solY = lambda x, y: -np.sin(y)
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phi = call2(fun, self.M.gridN)
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gradE = self.M.nodalGrad.dot(phi)
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Ec = cartE2(self.M, solX, solY)
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gradE_ana = self.M.projectEdgeVector(Ec)
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err = np.linalg.norm((gradE-gradE_ana), np.inf)
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return err
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def test_order(self):
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self.orderTest()
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class TestAveraging2D(OrderTest):
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name = "Averaging 2D"
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meshTypes = MESHTYPES
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meshDimension = 2
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def getError(self):
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num = self.getAve(self.M) * self.getHere(self.M)
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err = np.linalg.norm((self.getThere(self.M)-num), np.inf)
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return err
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def test_orderN2CC(self):
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self.name = "Averaging 2D: N2CC"
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fun = lambda x, y: (np.cos(x)+np.sin(y))
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self.getHere = lambda M: call2(fun, M.gridN)
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self.getThere = lambda M: call2(fun, M.gridCC)
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self.getAve = lambda M: M.aveN2CC
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self.orderTest()
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def test_orderN2F(self):
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self.name = "Averaging 2D: N2F"
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fun = lambda x, y: (np.cos(x)+np.sin(y))
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self.getHere = lambda M: call2(fun, M.gridN)
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self.getThere = lambda M: np.r_[call2(fun, M.gridFx), call2(fun, M.gridFy)]
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self.getAve = lambda M: M.aveN2F
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self.orderTest()
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def test_orderN2E(self):
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self.name = "Averaging 2D: N2E"
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fun = lambda x, y: (np.cos(x)+np.sin(y))
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self.getHere = lambda M: call2(fun, M.gridN)
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self.getThere = lambda M: np.r_[call2(fun, M.gridEx), call2(fun, M.gridEy)]
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self.getAve = lambda M: M.aveN2E
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self.orderTest()
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def test_orderF2CC(self):
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self.name = "Averaging 2D: F2CC"
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fun = lambda x, y: (np.cos(x)+np.sin(y))
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self.getHere = lambda M: np.r_[call2(fun, M.gridFx), call2(fun, M.gridFy)]
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self.getThere = lambda M: call2(fun, M.gridCC)
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self.getAve = lambda M: M.aveF2CC
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self.orderTest()
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def test_orderF2CCV(self):
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self.name = "Averaging 2D: F2CCV"
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funX = lambda x, y: (np.cos(x)+np.sin(y))
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funY = lambda x, y: (np.cos(y)*np.sin(x))
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self.getHere = lambda M: np.r_[call2(funX, M.gridFx), call2(funY, M.gridFy)]
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self.getThere = lambda M: np.r_[call2(funX, M.gridCC), call2(funY, M.gridCC)]
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self.getAve = lambda M: M.aveF2CCV
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self.orderTest()
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def test_orderCC2F(self):
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self.name = "Averaging 2D: CC2F"
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fun = lambda x, y: (np.cos(x)+np.sin(y))
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self.getHere = lambda M: call2(fun, M.gridCC)
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self.getThere = lambda M: np.r_[call2(fun, M.gridFx), call2(fun, M.gridFy)]
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self.getAve = lambda M: M.aveCC2F
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self.expectedOrders = 1
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self.orderTest()
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self.expectedOrders = 2
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def test_orderE2CC(self):
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self.name = "Averaging 2D: E2CC"
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fun = lambda x, y: (np.cos(x)+np.sin(y))
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self.getHere = lambda M: np.r_[call2(fun, M.gridEx), call2(fun, M.gridEy)]
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self.getThere = lambda M: call2(fun, M.gridCC)
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self.getAve = lambda M: M.aveE2CC
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self.orderTest()
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def test_orderE2CCV(self):
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self.name = "Averaging 2D: E2CCV"
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funX = lambda x, y: (np.cos(x)+np.sin(y))
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funY = lambda x, y: (np.cos(y)*np.sin(x))
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self.getHere = lambda M: np.r_[call2(funX, M.gridEx), call2(funY, M.gridEy)]
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self.getThere = lambda M: np.r_[call2(funX, M.gridCC), call2(funY, M.gridCC)]
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self.getAve = lambda M: M.aveE2CCV
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self.orderTest()
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class TestAveraging3D(OrderTest):
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name = "Averaging 3D"
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meshTypes = MESHTYPES
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meshDimension = 3
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def getError(self):
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num = self.getAve(self.M) * self.getHere(self.M)
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err = np.linalg.norm((self.getThere(self.M)-num), np.inf)
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return err
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def test_orderN2CC(self):
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self.name = "Averaging 3D: N2CC"
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fun = lambda x, y, z: (np.cos(x)+np.sin(y)+np.exp(z))
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self.getHere = lambda M: call3(fun, M.gridN)
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self.getThere = lambda M: call3(fun, M.gridCC)
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self.getAve = lambda M: M.aveN2CC
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self.orderTest()
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def test_orderN2F(self):
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self.name = "Averaging 3D: N2F"
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fun = lambda x, y, z: (np.cos(x)+np.sin(y)+np.exp(z))
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self.getHere = lambda M: call3(fun, M.gridN)
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self.getThere = lambda M: np.r_[call3(fun, M.gridFx), call3(fun, M.gridFy), call3(fun, M.gridFz)]
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self.getAve = lambda M: M.aveN2F
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self.orderTest()
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def test_orderN2E(self):
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self.name = "Averaging 3D: N2E"
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fun = lambda x, y, z: (np.cos(x)+np.sin(y)+np.exp(z))
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self.getHere = lambda M: call3(fun, M.gridN)
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self.getThere = lambda M: np.r_[call3(fun, M.gridEx), call3(fun, M.gridEy), call3(fun, M.gridEz)]
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self.getAve = lambda M: M.aveN2E
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self.orderTest()
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def test_orderF2CC(self):
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self.name = "Averaging 3D: F2CC"
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fun = lambda x, y, z: (np.cos(x)+np.sin(y)+np.exp(z))
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self.getHere = lambda M: np.r_[call3(fun, M.gridFx), call3(fun, M.gridFy), call3(fun, M.gridFz)]
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self.getThere = lambda M: call3(fun, M.gridCC)
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self.getAve = lambda M: M.aveF2CC
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self.orderTest()
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|
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def test_orderF2CCV(self):
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self.name = "Averaging 3D: F2CCV"
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funX = lambda x, y, z: (np.cos(x)+np.sin(y)+np.exp(z))
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funY = lambda x, y, z: (np.cos(x)+np.sin(y)*np.exp(z))
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funZ = lambda x, y, z: (np.cos(x)*np.sin(y)+np.exp(z))
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self.getHere = lambda M: np.r_[call3(funX, M.gridFx), call3(funY, M.gridFy), call3(funZ, M.gridFz)]
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self.getThere = lambda M: np.r_[call3(funX, M.gridCC), call3(funY, M.gridCC), call3(funZ, M.gridCC)]
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self.getAve = lambda M: M.aveF2CCV
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|
self.orderTest()
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|
|
|
def test_orderE2CC(self):
|
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self.name = "Averaging 3D: E2CC"
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fun = lambda x, y, z: (np.cos(x)+np.sin(y)+np.exp(z))
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self.getHere = lambda M: np.r_[call3(fun, M.gridEx), call3(fun, M.gridEy), call3(fun, M.gridEz)]
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|
self.getThere = lambda M: call3(fun, M.gridCC)
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|
self.getAve = lambda M: M.aveE2CC
|
|
self.orderTest()
|
|
|
|
def test_orderE2CCV(self):
|
|
self.name = "Averaging 3D: E2CCV"
|
|
funX = lambda x, y, z: (np.cos(x)+np.sin(y)+np.exp(z))
|
|
funY = lambda x, y, z: (np.cos(x)+np.sin(y)*np.exp(z))
|
|
funZ = lambda x, y, z: (np.cos(x)*np.sin(y)+np.exp(z))
|
|
self.getHere = lambda M: np.r_[call3(funX, M.gridEx), call3(funY, M.gridEy), call3(funZ, M.gridEz)]
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|
self.getThere = lambda M: np.r_[call3(funX, M.gridCC), call3(funY, M.gridCC), call3(funZ, M.gridCC)]
|
|
self.getAve = lambda M: M.aveE2CCV
|
|
self.orderTest()
|
|
|
|
def test_orderCC2F(self):
|
|
self.name = "Averaging 3D: CC2F"
|
|
fun = lambda x, y, z: (np.cos(x)+np.sin(y)+np.exp(z))
|
|
self.getHere = lambda M: call3(fun, M.gridCC)
|
|
self.getThere = lambda M: np.r_[call3(fun, M.gridFx), call3(fun, M.gridFy), call3(fun, M.gridFz)]
|
|
self.getAve = lambda M: M.aveCC2F
|
|
self.expectedOrders = 1
|
|
self.orderTest()
|
|
self.expectedOrders = 2
|
|
|
|
|
|
|
|
if __name__ == '__main__':
|
|
unittest.main()
|