edgeCurl is O(h) not O(h^2) ????

2026-07-13 17:45:30 +08:00 · 2015-11-09 19:51:46 -08:00
parent 94a79298bd
commit da7fbbb461
4 changed files with 397 additions and 96 deletions
@@ -0,0 +1,103 @@
+import numpy as np
+import unittest
+from SimPEG.Tests import OrderTest
+import matplotlib.pyplot as plt
+
+#TODO: 'randomTensorMesh'
+MESHTYPES = ['uniformTree'] #['randomTree', 'uniformTree']
+call2 = lambda fun, xyz: fun(xyz[:, 0], xyz[:, 1])
+call3 = lambda fun, xyz: fun(xyz[:, 0], xyz[:, 1], xyz[:, 2])
+cart_row2 = lambda g, xfun, yfun: np.c_[call2(xfun, g), call2(yfun, g)]
+cart_row3 = lambda g, xfun, yfun, zfun: np.c_[call3(xfun, g), call3(yfun, g), call3(zfun, g)]
+cartF2 = lambda M, fx, fy: np.vstack((cart_row2(M.gridFx, fx, fy), cart_row2(M.gridFy, fx, fy)))
+cartE2 = lambda M, ex, ey: np.vstack((cart_row2(M.gridEx, ex, ey), cart_row2(M.gridEy, ex, ey)))
+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)))
+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)))
+
+
+class TestFaceDiv2D(OrderTest):
+    name = "Face Divergence 2D"
+    meshTypes = MESHTYPES
+    meshDimension = 2
+    meshSizes = [16, 32]
+
+    def getError(self):
+        #Test function
+        fx = lambda x, y: np.sin(2*np.pi*x)
+        fy = lambda x, y: np.sin(2*np.pi*y)
+        sol = lambda x, y: 2*np.pi*(np.cos(2*np.pi*x)+np.cos(2*np.pi*y))
+
+        Fc = cartF2(self.M, fx, fy)
+        F = self.M.projectFaceVector(Fc)
+
+        divF = self.M.faceDiv.dot(F)
+        divF_ana = call2(sol, self.M.gridCC)
+
+        err = np.linalg.norm((divF-divF_ana), np.inf)
+
+        # self.M.plotImage(divF-divF_ana, showIt=True)
+
+        return err
+
+    def test_order(self):
+        self.orderTest()
+
+class TestFaceDiv3D(OrderTest):
+    name = "Face Divergence 3D"
+    meshTypes = MESHTYPES
+    meshSizes = [8, 16]
+
+    def getError(self):
+        #Test function
+        fx = lambda x, y, z: np.sin(2*np.pi*x)
+        fy = lambda x, y, z: np.sin(2*np.pi*y)
+        fz = lambda x, y, z: np.sin(2*np.pi*z)
+        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))
+
+        Fc = cartF3(self.M, fx, fy, fz)
+        F = self.M.projectFaceVector(Fc)
+
+        divF = self.M.faceDiv.dot(F)
+        divF_ana = call3(sol, self.M.gridCC)
+
+        return np.linalg.norm((divF-divF_ana), np.inf)
+
+
+    def test_order(self):
+        self.orderTest()
+
+
+class TestCurl(OrderTest):
+    name = "Curl"
+    meshTypes = MESHTYPES
+    meshSizes = [4, 8, 16, 32]
+
+    def getError(self):
+        # fun: i (cos(y)) + j (cos(z)) + k (cos(x))
+        # sol: i (sin(z)) + j (sin(x)) + k (sin(y))
+
+        funX = lambda x, y, z: np.cos(2*np.pi*y)
+        funY = lambda x, y, z: np.cos(2*np.pi*z)
+        funZ = lambda x, y, z: np.cos(2*np.pi*x)
+
+        solX = lambda x, y, z: 2*np.pi*np.sin(2*np.pi*z)
+        solY = lambda x, y, z: 2*np.pi*np.sin(2*np.pi*x)
+        solZ = lambda x, y, z: 2*np.pi*np.sin(2*np.pi*y)
+
+        Ec = cartE3(self.M, funX, funY, funZ)
+        E = self.M.projectEdgeVector(Ec)
+
+        Fc = cartF3(self.M, solX, solY, solZ)
+        curlE_ana = self.M.projectFaceVector(Fc)
+
+        curlE = self.M.edgeCurl.dot(E)
+
+        err = np.linalg.norm((curlE - curlE_ana), np.inf)
+
+        return err
+
+    def test_order(self):
+        self.orderTest()
+
+if __name__ == '__main__':
+    unittest.main()