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https://github.com/wassname/simpeg.git
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MagForwrad secondary and total
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SEOGI KANG committed
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@@ -12,7 +12,7 @@
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"collapsed": false,
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"input": [
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"from SimPEG import *\n",
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"from test_boundary import spheremodel, MagSphereAnalFun\n",
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"from MagAnalytics import spheremodel, MagSphereAnalFun, CongruousMagBC\n",
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"%pylab inline"
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],
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"language": "python",
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@@ -32,14 +32,7 @@
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"stream": "stdout",
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"text": [
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"\n",
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"Populating the interactive namespace from numpy and matplotlib"
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]
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},
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{
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"output_type": "stream",
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"stream": "stdout",
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"text": [
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"\n"
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"Populating the interactive namespace from numpy and matplotlib\n"
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]
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}
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],
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@@ -49,77 +42,40 @@
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Step:1 Generating mesh and operators"
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"# Writing magnetostatic problem with secondary field formulation\n",
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"\n",
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"## - Here we focus on cell-centered system with FVM-Weak form"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Step:1 Generating mesh and operators"
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]
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},
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{
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"cell_type": "code",
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"collapsed": false,
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"input": [
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"hxind = ((10,25,1.3),(41, 12.5),(5,25,1.3))\n",
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"hyind = ((10,25,1.3),(41, 12.5),(5,25,1.3))\n",
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"hzind = ((10,25,1.3),(40, 12.5),(1,25,1.3))\n",
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"hxind = ((5,25,1.3),(41, 12.5),(5,25,1.3))\n",
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"hyind = ((5,25,1.3),(41, 12.5),(5,25,1.3))\n",
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"hzind = ((5,25,1.3),(40, 12.5),(1,25,1.3))\n",
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"hx, hy, hz = Utils.meshTensors(hxind, hyind, hzind)\n",
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"M3 = Mesh.TensorMesh([hx, hy, hz], [-sum(hx)/2,-sum(hy)/2,-sum(hz)/2])"
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],
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"language": "python",
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"metadata": {},
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"outputs": [],
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"prompt_number": 46
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"prompt_number": 2
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Step2: Compute Boundary indicies and set $\\mathbf{B}_{sBC}$"
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]
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},
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{
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"cell_type": "code",
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"collapsed": false,
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"input": [
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"BC = [['neumann', 'neumann'], ['neumann', 'neumann'], ['neumann', 'neumann']]\n",
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"indxd, indxu, indyd, indyu, indzd, indzu = M3.faceBoundaryInd\n",
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"ind = np.r_[(indxd | indxu), (indyd | indyu), (indzd | indzu)]"
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],
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"language": "python",
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"metadata": {},
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"outputs": [],
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"prompt_number": 47
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},
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{
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"cell_type": "code",
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"collapsed": false,
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"input": [
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"Box = 1 # Primary field in x-direction (background)\n",
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"Boy = 0 # Primary field in y-direction (background)\n",
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"Boz = 0 # Primary field in z-direction (background)\n",
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"B0 = np.r_[Box*np.ones(np.prod(M3.nFx)), Boy*np.ones(np.prod(M3.nFy)), Boz*np.ones(np.prod(M3.nFz))]\n",
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"Bbcx = np.zeros(np.prod(M3.nFx))\n",
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"Bbcy = np.zeros(np.prod(M3.nFy))\n",
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"Bbcz = np.zeros(np.prod(M3.nFz))\n",
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"## Step2: Generating model $\\mu$\n",
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"\n",
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"Bbcx[indxd] = 0\n",
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"Bbcx[indxu] = 0\n",
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"Bbcy[indyd] = Boy\n",
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"Bbcy[indyu] = Boy\n",
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"Bbcz[indzd] = Boz\n",
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"Bbcz[indzu] = Boz\n",
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"\n",
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"Bbc = np.r_[Bbcx, Bbcy, Bbcz]"
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],
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"language": "python",
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"metadata": {},
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"outputs": [],
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"prompt_number": 48
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Step3: Generating model $\\mu$\n",
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"\n",
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"$\\mu = \\mu_0(1+\\chi)$"
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"### $\\mu = \\mu_0(1+\\chi)$"
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]
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},
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{
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@@ -134,78 +90,82 @@
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"language": "python",
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"metadata": {},
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"outputs": [],
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"prompt_number": 49
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"prompt_number": 3
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},
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{
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"cell_type": "code",
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"collapsed": false,
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"input": [
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"sph_ind = spheremodel(M3, 0, 0, 0, 100)\n",
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"sph_ind = spheremodel(M3, 0., 0., 0., 100)\n",
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"chi[sph_ind] = chiblk\n",
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"mu = (1.+chi)*mu0"
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],
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"language": "python",
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"metadata": {},
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"outputs": [],
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"prompt_number": 50
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"prompt_number": 4
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Additional: Congrous sphere method (for boudary condition)"
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"## Step3: Compute Boundary condition $\\mathbf{B}_{sBC}$ using congruous sphere method"
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]
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},
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{
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"cell_type": "code",
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"collapsed": false,
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"input": [
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"V = M3.vol[sph_ind].sum()\n",
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"gamma = 1/V*(chiblk*M3.vol).sum()\n",
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"mom = 1/mu0*gamma*V/(1+gamma/3)"
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"BC = [['neumann', 'neumann'], ['neumann', 'neumann'], ['neumann', 'neumann']]\n",
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"Box = 1 # Primary field in x-direction (background)\n",
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"Boy = 0 # Primary field in y-direction (background)\n",
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"Boz = 0 # Primary field in z-direction (background)\n",
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"B0 = np.r_[Box*np.ones(np.prod(M3.nFx)), Boy*np.ones(np.prod(M3.nFy)), Boz*np.ones(np.prod(M3.nFz))]"
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],
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"language": "python",
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"metadata": {},
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"outputs": [],
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"prompt_number": 72
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},
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{
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"cell_type": "code",
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"collapsed": false,
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"input": [],
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"language": "python",
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"metadata": {},
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"outputs": [
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{
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"output_type": "stream",
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"stream": "stdout",
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"text": [
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"4109375.0\n"
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]
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}
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],
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"prompt_number": 70
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"prompt_number": 5
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},
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{
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"cell_type": "code",
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"collapsed": false,
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"input": [
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"# figsize(10,10)\n",
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"# M3.plotGrid()"
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"Bbc = CongruousMagBC(M3, np.array([Box, Boy, Boz]), chi)"
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],
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"language": "python",
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"metadata": {},
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"outputs": [],
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"prompt_number": 6
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},
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{
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"cell_type": "code",
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"collapsed": false,
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"input": [
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"figsize(10,10)\n",
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"M3.plotGrid()"
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],
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"language": "python",
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"metadata": {},
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"outputs": [
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{
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"output_type": "stream",
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"stream": "stderr",
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"text": [
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"C:\\Users\\SEOGI\\AppData\\Local\\Enthought\\Canopy\\App\\appdata\\canopy-1.0.1.1189.win-x86_64\\lib\\site-packages\\matplotlib\\lines.py:483: RuntimeWarning: invalid value encountered in greater_equal\n",
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" return np.alltrue(x[1:]-x[0:-1]>=0)\n"
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]
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},
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{
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"metadata": {},
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"output_type": "display_data",
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|
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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x231e8588>"
|
||||
"<matplotlib.figure.Figure at 0xa21a860>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 51
|
||||
"prompt_number": 7
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
@@ -219,54 +179,52 @@
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "pyout",
|
||||
"prompt_number": 52,
|
||||
"prompt_number": 8,
|
||||
"text": [
|
||||
"<matplotlib.collections.QuadMesh at 0x1f145d68>"
|
||||
"<matplotlib.collections.QuadMesh at 0xa646390>"
|
||||
]
|
||||
},
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x1eef3e48>"
|
||||
"<matplotlib.figure.Figure at 0xa18f8d0>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 52
|
||||
"prompt_number": 8
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"### Step4: get system matrix $\\mathbf{A}$ and right handside\n",
|
||||
"#### 4.1 Backgrounds: Weak formulation for Poisson equation with cell-centered system\n",
|
||||
"## Step4: get system matrix $\\mathbf{A}$ and right handside\n",
|
||||
"### 4.1 Backgrounds: Weak formulation for Poisson equation with cell-centered system\n",
|
||||
"\n",
|
||||
"$$\\frac{1}{\\mu}\\mathbf{B}_s = (\\frac{1}{\\mu}_0-\\frac{1}{\\mu})\\mathbf{B}_0+\\nabla\\phi_s$$\n",
|
||||
"### $$\\frac{1}{\\mu}\\mathbf{B}_s = (\\frac{1}{\\mu}_0-\\frac{1}{\\mu})\\mathbf{B}_0+\\nabla\\phi_s$$\n",
|
||||
"\n",
|
||||
"$$\\nabla \\cdot \\mathbf{B}_s = 0 $$\n",
|
||||
"### $$\\nabla \\cdot \\mathbf{B}_s = 0 $$\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"$$ (\\mathbf{B}_s\\cdot{\\bar{\\mathbf{n}}})_{\\partial\\Omega} = B_{sBC}$$\n",
|
||||
"### $$ (\\mathbf{B}_s\\cdot{\\bar{\\mathbf{n}}})_{\\partial\\Omega} = B_{sBC}$$\n",
|
||||
"\n",
|
||||
"In discretized form we have \n",
|
||||
"### In discretized form we have \n",
|
||||
"\n",
|
||||
"$$\\mathbf{diag(v)}\\mathbf{D}\\mathbf{P}_{in}^T \\mathbf{P}_{in}\\mathbf{B}_s + \\mathbf{diag(v)}\\mathbf{D} \\mathbf{P}_{out}^T B_{sBC}=0$$\n",
|
||||
"### $$\\mathbf{diag(v)}\\mathbf{D}\\mathbf{P}_{in}^T \\mathbf{P}_{in}\\mathbf{B}_s + \\mathbf{diag(v)}\\mathbf{D} \\mathbf{P}_{out}^T B_{sBC}=0$$\n",
|
||||
"\n",
|
||||
"$$\\mathbf{M}^f_{\\frac{1}{\\mu}}\\mathbf{B}_s = \\mathbf{M}^f_{\\frac{1}{\\mu_0}}\\mathbf{B}_0-\\mathbf{M}^f_{\\frac{1}{\\mu}}\\mathbf{B}_0\n",
|
||||
"-\\mathbf{P}_{in}\\mathbf{P}_{in}^T\\mathbf{D}^T\\mathbf{diag(v)}\\phi_s$$\n",
|
||||
"### $$\\mathbf{M}^f_{\\frac{1}{\\mu}}\\mathbf{B}_s = \\mathbf{M}^f_{\\frac{1}{\\mu_0}}\\mathbf{B}_0-\\mathbf{M}^f_{\\frac{1}{\\mu}}\\mathbf{B}_0 -\\mathbf{P}_{in}\\mathbf{P}_{in}^T\\mathbf{D}^T\\mathbf{diag(v)}\\phi_s$$\n",
|
||||
"\n",
|
||||
"$$ \\mathbf{Div} = \\mathbf{diag(v)}\\mathbf{D}\\mathbf{P}_{in}^T \\mathbf{P}_{in}$$\n",
|
||||
"### $$ \\mathbf{Div} = \\mathbf{diag(v)}\\mathbf{D}\\mathbf{P}_{in}^T \\mathbf{P}_{in}$$\n",
|
||||
"\n",
|
||||
"$$ \\mathbf{Div}\\mathbf{B}_s + \\mathbf{diag(v)}\\mathbf{D} \\mathbf{P}_{out}^T B_{sBC}=0$$\n",
|
||||
"### $$ \\mathbf{Div}\\mathbf{B}_s + \\mathbf{diag(v)}\\mathbf{D} \\mathbf{P}_{out}^T B_{sBC}=0$$\n",
|
||||
"\n",
|
||||
"$$\\mathbf{B}_s = (\\mathbf{M}^f_{\\frac{1}{\\mu}})^{-1}\\mathbf{M}^f_{\\frac{1}{\\mu_0}}\\mathbf{B}_0-\\mathbf{B}_0\n",
|
||||
"-(\\mathbf{M}^f_{\\frac{1}{\\mu}})^{-1}\\mathbf{Div}^T\\phi_s$$\n",
|
||||
"### $$\\mathbf{B}_s = (\\mathbf{M}^f_{\\frac{1}{\\mu}})^{-1}\\mathbf{M}^f_{\\frac{1}{\\mu_0}}\\mathbf{B}_0-\\mathbf{B}_0 -(\\mathbf{M}^f_{\\frac{1}{\\mu}})^{-1}\\mathbf{Div}^T\\phi_s$$\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"$$\\mathbf{A} = - \\mathbf{Div}(\\mathbf{M}^f_{\\frac{1}{\\mu}})^{-1}\\mathbf{Div}^{T}$$\n",
|
||||
"### $$\\mathbf{A} = - \\mathbf{Div}(\\mathbf{M}^f_{\\frac{1}{\\mu}})^{-1}\\mathbf{Div}^{T}$$\n",
|
||||
"\n",
|
||||
"$$\\mathbf{rhs} = - \\mathbf{Div}(\\mathbf{M}^f_{\\frac{1}{\\mu}})^{-1}\\mathbf{M}^f_{\\frac{1}{\\mu_0}}\\mathbf{B}_0 + \\mathbf{Div}\\mathbf{B}_0-\\mathbf{diag}(v)\\mathbf{D} \\mathbf{P}_{out}^T B_{sBC}$$"
|
||||
"### $$\\mathbf{rhs} = - \\mathbf{Div}(\\mathbf{M}^f_{\\frac{1}{\\mu}})^{-1}\\mathbf{M}^f_{\\frac{1}{\\mu_0}}\\mathbf{B}_0 + \\mathbf{Div}\\mathbf{B}_0-\\mathbf{diag}(v)\\mathbf{D} \\mathbf{P}_{out}^T B_{sBC}$$"
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -280,12 +238,12 @@
|
||||
"MfmuI = Utils.sdiag(1/M3.getFaceInnerProduct(mu = 1/mu).diagonal())\n",
|
||||
"Mfmu0 = 1/mu0*M3.getFaceInnerProduct()\n",
|
||||
"A = -Div*MfmuI*Div.T\n",
|
||||
"rhs = -Div*MfmuI*Mfmu0*B0 + Div*B0 - Mc*Dface*Pout.T*Bbc[ind]"
|
||||
"rhs = -Div*MfmuI*Mfmu0*B0 + Div*B0 - Mc*Dface*Pout.T*Bbc"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 53
|
||||
"prompt_number": 9
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
@@ -300,11 +258,11 @@
|
||||
"output_type": "stream",
|
||||
"stream": "stdout",
|
||||
"text": [
|
||||
"(397851, 397851) (397851, 130050)\n"
|
||||
"(366231, 366231) (366231, 119646)\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 54
|
||||
"prompt_number": 10
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
@@ -323,7 +281,7 @@
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 55
|
||||
"prompt_number": 11
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
@@ -338,7 +296,7 @@
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 56
|
||||
"prompt_number": 12
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
@@ -364,7 +322,7 @@
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 57
|
||||
"prompt_number": 13
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
@@ -384,11 +342,11 @@
|
||||
"output_type": "stream",
|
||||
"stream": "stdout",
|
||||
"text": [
|
||||
"Wall time: 1.31 s\n"
|
||||
"Wall time: 1.33 s\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 58
|
||||
"prompt_number": 14
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
@@ -405,11 +363,11 @@
|
||||
"stream": "stdout",
|
||||
"text": [
|
||||
"0\n",
|
||||
"130050\n"
|
||||
"119646\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 59
|
||||
"prompt_number": 15
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
@@ -428,11 +386,11 @@
|
||||
"stream": "stdout",
|
||||
"text": [
|
||||
"0\n",
|
||||
"9.95677949419e-07\n"
|
||||
"8.8645586939e-07\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 60
|
||||
"prompt_number": 16
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
@@ -454,56 +412,57 @@
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x1f138828>"
|
||||
"<matplotlib.figure.Figure at 0x9e95b70>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 61
|
||||
"prompt_number": 19
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"### Step4: Compute analytic function (sphere in whole space)\n",
|
||||
"Outside of the sphere $(r>R)$\n",
|
||||
"## Step4: Compute analytic function (sphere in whole space)\n",
|
||||
"\n",
|
||||
"$$\\mathbf{H}_1 = H_0 \\hat{x} + H_0\\frac{R}{r^5}\\frac{\\mu_2-\\mu_1}{\\mu_2+2\\mu_1}[(2x^2-y^2-z^2)\\hat{x}+(3xy)\\hat{y}+(3xz)\\hat{z}]$$\n",
|
||||
"### Outside of the sphere $(r>R)$\n",
|
||||
"\n",
|
||||
"$$H_{x1} = H_0 + H_0\\frac{R}{r^5}\\frac{\\mu_2-\\mu_1}{\\mu_2+2\\mu_1}(2x^2-y^2-z^2)$$\n",
|
||||
"### $$\\mathbf{H}_1 = H_0 \\hat{x} + H_0\\frac{R}{r^5}\\frac{\\mu_2-\\mu_1}{\\mu_2+2\\mu_1}[(2x^2-y^2-z^2)\\hat{x}+(3xy)\\hat{y}+(3xz)\\hat{z}]$$\n",
|
||||
"\n",
|
||||
"$$H_{y1} = H_0\\frac{R}{r^5}\\frac{\\mu_2-\\mu_1}{\\mu_2+2\\mu_1}(3xy)$$\n",
|
||||
"### $$H_{x1} = H_0 + H_0\\frac{R}{r^5}\\frac{\\mu_2-\\mu_1}{\\mu_2+2\\mu_1}(2x^2-y^2-z^2)$$\n",
|
||||
"\n",
|
||||
"$$H_{z1} = H_0\\frac{R}{r^5}\\frac{\\mu_2-\\mu_1}{\\mu_2+2\\mu_1}(3xz)$$\n",
|
||||
"### $$H_{y1} = H_0\\frac{R}{r^5}\\frac{\\mu_2-\\mu_1}{\\mu_2+2\\mu_1}(3xy)$$\n",
|
||||
"\n",
|
||||
"Inside of the sphere $(r\\le R)$\n",
|
||||
"### $$H_{z1} = H_0\\frac{R}{r^5}\\frac{\\mu_2-\\mu_1}{\\mu_2+2\\mu_1}(3xz)$$\n",
|
||||
"\n",
|
||||
"$$\\mathbf{H}_2 = H_0\\frac{3\\mu_1}{\\mu_2+2\\mu_1}\\hat{x}$$\n",
|
||||
"### Inside of the sphere $(r\\le R)$\n",
|
||||
"\n",
|
||||
"$$H_{x2} = H_0\\frac{3\\mu_1}{\\mu_2+2\\mu_1}$$"
|
||||
"### $$\\mathbf{H}_2 = H_0\\frac{3\\mu_1}{\\mu_2+2\\mu_1}\\hat{x}$$\n",
|
||||
"\n",
|
||||
"### $$H_{x2} = H_0\\frac{3\\mu_1}{\\mu_2+2\\mu_1}$$"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"### Step5: Projection to receiver plane"
|
||||
"## Step5: Projection to receiver locations"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"xr = np.linspace(-400, 400, 41)\n",
|
||||
"yr = np.linspace(-400, 400, 41)\n",
|
||||
"xr = np.linspace(-300, 300, 41)\n",
|
||||
"yr = np.linspace(-300, 300, 41)\n",
|
||||
"X, Y = np.meshgrid(xr, yr)\n",
|
||||
"Z = np.ones((size(xr), size(yr)))*150"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 62
|
||||
"prompt_number": 20
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
@@ -517,7 +476,7 @@
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 63
|
||||
"prompt_number": 21
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
@@ -538,7 +497,7 @@
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 64
|
||||
"prompt_number": 22
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
@@ -558,21 +517,21 @@
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "pyout",
|
||||
"prompt_number": 65,
|
||||
"prompt_number": 23,
|
||||
"text": [
|
||||
"[<matplotlib.lines.Line2D at 0x2b71c908>]"
|
||||
"[<matplotlib.lines.Line2D at 0x9f5e4a8>]"
|
||||
]
|
||||
},
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x1eed9438>"
|
||||
"<matplotlib.figure.Figure at 0xa5c0908>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 65
|
||||
"prompt_number": 23
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
@@ -592,34 +551,34 @@
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "pyout",
|
||||
"prompt_number": 66,
|
||||
"prompt_number": 24,
|
||||
"text": [
|
||||
"<matplotlib.colorbar.Colorbar instance at 0x00000000236DAD88>"
|
||||
"<matplotlib.colorbar.Colorbar instance at 0x0000000012B67688>"
|
||||
]
|
||||
},
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x1f133518>"
|
||||
"<matplotlib.figure.Figure at 0xa5c0dd8>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 66
|
||||
"prompt_number": 24
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"fig, axes = subplots(1,3, figsize=(14,5))\n",
|
||||
"fig, axes = subplots(1,3, figsize=(16,5))\n",
|
||||
"epsx = np.linalg.norm(Utils.mkvc(Bxr))*1e-6\n",
|
||||
"epsy = np.linalg.norm(Utils.mkvc(Byr))*1e-6\n",
|
||||
"epsz = np.linalg.norm(Utils.mkvc(Bzr))*1e-6\n",
|
||||
"id = 21\n",
|
||||
"axes[0].plot(Y[:,id], Bxra[:,id], 'b', Y[:,id], Bxr[:,id], 'r.')\n",
|
||||
"axes[1].plot(Y[:,id], Byra[:,id], 'b', Y[:,id], Byr[:,id], 'r.')\n",
|
||||
"axes[2].plot(Y[:,id], Bzra[:,id], 'b', Y[:,id], Bzr[:,id], 'r.')\n",
|
||||
"axes[0].plot(Y[:,id], Bxra[:,id], 'b', Y[:,id], Bxr[:,id], 'r.'); axes[0].set_title('$B^s_x$', fontsize = 16)\n",
|
||||
"axes[1].plot(Y[:,id], Byra[:,id], 'b', Y[:,id], Byr[:,id], 'r.'); axes[1].set_title('$B^s_y$', fontsize = 16)\n",
|
||||
"axes[2].plot(Y[:,id], Bzra[:,id], 'b', Y[:,id], Bzr[:,id], 'r.'); axes[2].set_title('$B^s_z$', fontsize = 16)\n",
|
||||
"print X[1,id]"
|
||||
],
|
||||
"language": "python",
|
||||
@@ -629,19 +588,19 @@
|
||||
"output_type": "stream",
|
||||
"stream": "stdout",
|
||||
"text": [
|
||||
"20.0\n"
|
||||
"15.0\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x22f6a828>"
|
||||
"<matplotlib.figure.Figure at 0x12b87908>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 67
|
||||
"prompt_number": 25
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
@@ -651,9 +610,9 @@
|
||||
"epsx = np.linalg.norm(Utils.mkvc(Bxr))*1e-6\n",
|
||||
"epsy = np.linalg.norm(Utils.mkvc(Byr))*1e-6\n",
|
||||
"epsz = np.linalg.norm(Utils.mkvc(Bzr))*1e-6\n",
|
||||
"axes[0].plot(Y[:,id], abs((Bxr[:,id]-Bxra[:,id])/(Bxra[:,id]+epsx)), 'r.')\n",
|
||||
"axes[1].plot(Y[:,id], abs((Byr[:,id]-Byra[:,id])/(Byra[:,id]+epsy)), 'r.')\n",
|
||||
"axes[2].plot(Y[:,id], abs((Bzr[:,id]-Bzra[:,id])/(Bzra[:,id]+epsz)), 'r.')"
|
||||
"axes[0].plot(Y[:,1], abs((Bxtter[:,1]-Bxra[:,1])/(Bxra[:,1]+epsx)), 'r.')\n",
|
||||
"axes[1].plot(Y[:,1], abs((Byr[:,1]-Byra[:,1])/(Byra[:,1]+epsy)), 'r.')\n",
|
||||
"axes[2].plot(Y[:,1], abs((Bzr[:,1]-Bzra[:,1])/(Bzra[:,1]+epsz)), 'r.')"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
@@ -661,41 +620,33 @@
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "pyout",
|
||||
"prompt_number": 68,
|
||||
"prompt_number": 34,
|
||||
"text": [
|
||||
"[<matplotlib.lines.Line2D at 0x1eeea898>]"
|
||||
"[<matplotlib.lines.Line2D at 0x1971ad68>]"
|
||||
]
|
||||
},
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x111e0390>"
|
||||
"<matplotlib.figure.Figure at 0x198a90b8>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 68
|
||||
"prompt_number": 34
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"### Thoughts\n",
|
||||
"## Thoughts\n",
|
||||
"\n",
|
||||
"- It works well with non-uniform mesh!!\n",
|
||||
"- Actual accuray is ~10% relative error in secondary fields. As we pad more we can get better accuracy, since we did not consider secondary field at the boudnary ($\\partial\\Omega$). \n",
|
||||
"- Here, we can try primary secondary field approach to get better accuracy. \n",
|
||||
"- In addition, we can use the congruous sphere method to handle this secondary fields at boundaries"
|
||||
"### - Congruous sphere method works well, which means we need right boundary condition. \n",
|
||||
"### - I am not sure for real situation when we have multiple bodies in our domain ... ?\n",
|
||||
"### - Secondary field shows better accuracy than total field approach as expected\n",
|
||||
"### - Anyway every piece works well for forward modeling!!"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": []
|
||||
}
|
||||
],
|
||||
"metadata": {}
|
||||
|
||||
@@ -12,7 +12,7 @@
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"from SimPEG import *\n",
|
||||
"from test_boundary import spheremodel, MagSphereAnalFun\n",
|
||||
"from MagAnalytics import spheremodel, MagSphereAnalFun, CongruousMagBC, MagSphereAnalFunA\n",
|
||||
"%pylab inline"
|
||||
],
|
||||
"language": "python",
|
||||
@@ -22,19 +22,30 @@
|
||||
"output_type": "stream",
|
||||
"stream": "stdout",
|
||||
"text": [
|
||||
"Populating the interactive namespace from numpy and matplotlib\n"
|
||||
"Warning: Python backend is being used for solver. Run setup.py from the command line.\n",
|
||||
"Warning: mumps solver not available.\n",
|
||||
"Warning: upgrade your scipy to 0.13.0"
|
||||
]
|
||||
},
|
||||
{
|
||||
"output_type": "stream",
|
||||
"stream": "stderr",
|
||||
"stream": "stdout",
|
||||
"text": [
|
||||
"WARNING: pylab import has clobbered these variables: ['axes', 'info', 'flag']\n",
|
||||
"`%pylab --no-import-all` prevents importing * from pylab and numpy\n"
|
||||
"\n",
|
||||
"Populating the interactive namespace from numpy and matplotlib\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 29
|
||||
"prompt_number": 1
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"# Writing magnetostatic problem with total field formulation\n",
|
||||
"\n",
|
||||
"## - Here we focus on cell-centered system with FVM-Weak form"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
@@ -47,16 +58,16 @@
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"hxind = ((10,25,1.3),(41, 25),(10,25,1.3))\n",
|
||||
"hyind = ((10,25,1.3),(41, 25),(10,25,1.3))\n",
|
||||
"hzind = ((10,25,1.3),(40, 25),(10,25,1.3))\n",
|
||||
"hxind = ((5,25,1.3),(41, 12.5),(5,25,1.3))\n",
|
||||
"hyind = ((5,25,1.3),(41, 12.5),(5,25,1.3))\n",
|
||||
"hzind = ((5,25,1.3),(40, 12.5),(1,25,1.3))\n",
|
||||
"hx, hy, hz = Utils.meshTensors(hxind, hyind, hzind)\n",
|
||||
"M3 = Mesh.TensorMesh([hx, hy, hz], [-sum(hx)/2,-sum(hy)/2,-sum(hz)/2])"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 30
|
||||
"prompt_number": 2
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
@@ -76,7 +87,7 @@
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 31
|
||||
"prompt_number": 3
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
@@ -102,7 +113,7 @@
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 32
|
||||
"prompt_number": 4
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
@@ -125,7 +136,7 @@
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 33
|
||||
"prompt_number": 5
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
@@ -138,7 +149,18 @@
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 34
|
||||
"prompt_number": 6
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"Bbc = Bbc[ind] + CongruousMagBC(M3, np.array([Box, Boy, Boz]), chi) "
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 7
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
@@ -150,16 +172,24 @@
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"output_type": "stream",
|
||||
"stream": "stderr",
|
||||
"text": [
|
||||
"C:\\Users\\SEOGI\\AppData\\Local\\Enthought\\Canopy\\App\\appdata\\canopy-1.0.1.1189.win-x86_64\\lib\\site-packages\\matplotlib\\lines.py:483: RuntimeWarning: invalid value encountered in greater_equal\n",
|
||||
" return np.alltrue(x[1:]-x[0:-1]>=0)\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0xa514ed0>"
|
||||
"<matplotlib.figure.Figure at 0x57d1828>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 35
|
||||
"prompt_number": 8
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
@@ -173,21 +203,21 @@
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "pyout",
|
||||
"prompt_number": 36,
|
||||
"prompt_number": 9,
|
||||
"text": [
|
||||
"<matplotlib.collections.QuadMesh at 0xc576050>"
|
||||
"<matplotlib.collections.QuadMesh at 0xaa7f390>"
|
||||
]
|
||||
},
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0xc9469d0>"
|
||||
"<matplotlib.figure.Figure at 0xa0f8ef0>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 36
|
||||
"prompt_number": 9
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
@@ -249,31 +279,31 @@
|
||||
"D = Mc*Dface*Pin.T*Pin\n",
|
||||
"MfmuI = Utils.sdiag(1/M3.getFaceInnerProduct(mu = 1/mu).diagonal())\n",
|
||||
"A = -D*MfmuI*D.T\n",
|
||||
"rhs = -Mc*Dface*Pout.T*Bbc[ind]"
|
||||
"rhs = -Mc*Dface*Pout.T*Bbc"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 37
|
||||
"prompt_number": 10
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"import petsc4py\n",
|
||||
"import sys\n",
|
||||
"from sys import getrefcount\n",
|
||||
"petsc4py.init(sys.argv)\n",
|
||||
"from petsc4py import PETSc\n",
|
||||
"import PETScIO as IO\n",
|
||||
"Apetsc = PETSc.Mat().createAIJ(size=A.shape,csr=(A.indptr, A.indices, A.data))\n",
|
||||
"bpetsc = IO.arrayToVec(rhs)\n",
|
||||
"xpetsc = IO.arrayToVec(0*rhs)"
|
||||
"# import petsc4py\n",
|
||||
"# import sys\n",
|
||||
"# from sys import getrefcount\n",
|
||||
"# petsc4py.init(sys.argv)\n",
|
||||
"# from petsc4py import PETSc\n",
|
||||
"# import PETScIO as IO\n",
|
||||
"# Apetsc = PETSc.Mat().createAIJ(size=A.shape,csr=(A.indptr, A.indices, A.data))\n",
|
||||
"# bpetsc = IO.arrayToVec(rhs)\n",
|
||||
"# xpetsc = IO.arrayToVec(0*rhs)"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 38
|
||||
"prompt_number": 11
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
@@ -288,44 +318,33 @@
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 39
|
||||
"prompt_number": 12
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"%%time\n",
|
||||
"ksp = PETSc.KSP().create()\n",
|
||||
"pc = PETSc.PC().create()\n",
|
||||
"ksp.setOperators(Apetsc)\n",
|
||||
"ksp.setType(ksp.Type.BCGS)\n",
|
||||
"pc = ksp.getPC()\n",
|
||||
"pc.setType(pc.Type.SOR)\n",
|
||||
"OptDB = PETSc.Options()\n",
|
||||
"OptDB[\"ksp_rtol\"] = 1e-8\n",
|
||||
"OptDB[\"pc_factor_levels\"] = 1\n",
|
||||
"ksp.setFromOptions()\n",
|
||||
"ksp.view()\n",
|
||||
"ksp.solve(bpetsc, xpetsc)\n",
|
||||
"print ksp.its# print ksp.its\n",
|
||||
"phi = IO.vecToArray(xpetsc)\n",
|
||||
"print np.linalg.norm(A*phi-rhs)/norm(rhs)"
|
||||
"# %%time\n",
|
||||
"# ksp = PETSc.KSP().create()\n",
|
||||
"# pc = PETSc.PC().create()\n",
|
||||
"# ksp.setOperators(Apetsc)\n",
|
||||
"# ksp.setType(ksp.Type.BCGS)\n",
|
||||
"# pc = ksp.getPC()\n",
|
||||
"# pc.setType(pc.Type.SOR)\n",
|
||||
"# OptDB = PETSc.Options()\n",
|
||||
"# OptDB[\"ksp_rtol\"] = 1e-8\n",
|
||||
"# OptDB[\"pc_factor_levels\"] = 1\n",
|
||||
"# ksp.setFromOptions()\n",
|
||||
"# ksp.view()\n",
|
||||
"# ksp.solve(bpetsc, xpetsc)\n",
|
||||
"# print ksp.its# print ksp.its\n",
|
||||
"# phi = IO.vecToArray(xpetsc)\n",
|
||||
"# print np.linalg.norm(A*phi-rhs)/norm(rhs)"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"output_type": "stream",
|
||||
"stream": "stdout",
|
||||
"text": [
|
||||
"116\n",
|
||||
"4.24430002044e-09\n",
|
||||
"CPU times: user 1.65 s, sys: 0 ns, total: 1.65 s\n",
|
||||
"Wall time: 1.66 s\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 40
|
||||
"outputs": [],
|
||||
"prompt_number": 13
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
@@ -345,12 +364,11 @@
|
||||
"output_type": "stream",
|
||||
"stream": "stdout",
|
||||
"text": [
|
||||
"CPU times: user 2.13 s, sys: 0 ns, total: 2.13 s\n",
|
||||
"Wall time: 2.13 s\n"
|
||||
"Wall time: 1.58 s\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 41
|
||||
"prompt_number": 14
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
@@ -367,17 +385,17 @@
|
||||
"stream": "stdout",
|
||||
"text": [
|
||||
"0\n",
|
||||
"223260\n"
|
||||
"119646\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 42
|
||||
"prompt_number": 15
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"B = MfmuI*(-D.T*phi)\n",
|
||||
"B = -MfmuI*D.T*phi\n",
|
||||
"rhsa = A*phi\n",
|
||||
"print info\n",
|
||||
"print np.linalg.norm(rhs-rhsa)/np.linalg.norm(rhs)"
|
||||
@@ -390,11 +408,11 @@
|
||||
"stream": "stdout",
|
||||
"text": [
|
||||
"0\n",
|
||||
"9.47100435444e-07\n"
|
||||
"7.65372604673e-07\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 43
|
||||
"prompt_number": 16
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
@@ -416,13 +434,13 @@
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": 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|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0xc4624d0>"
|
||||
"<matplotlib.figure.Figure at 0xaa72208>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 44
|
||||
"prompt_number": 17
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
@@ -457,15 +475,15 @@
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"xr = np.linspace(-400, 400, 41)\n",
|
||||
"yr = np.linspace(-400, 400, 41)\n",
|
||||
"xr = np.linspace(-300, 300, 41)\n",
|
||||
"yr = np.linspace(-300, 300, 41)\n",
|
||||
"X, Y = np.meshgrid(xr, yr)\n",
|
||||
"Z = np.ones((size(xr), size(yr)))*50"
|
||||
"Z = np.ones((size(xr), size(yr)))*0."
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 45
|
||||
"prompt_number": 18
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
@@ -479,7 +497,7 @@
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 46
|
||||
"prompt_number": 19
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
@@ -493,7 +511,8 @@
|
||||
"if flag=='secondary':\n",
|
||||
" Bxr = Bxr-Box\n",
|
||||
"\n",
|
||||
"Bxra, Byra, Bzra = MagSphereAnalFun(X, Y, Z, 100, 0., 0., 0., mu0, mu0*(1+chiblk), H0, flag)\n",
|
||||
"# Bxra, Byra, Bzra = MagSphereAnalFun(X, Y, Z, 100, 0., 0., 0., mu0, mu0*(1+chiblk), H0, flag)\n",
|
||||
"Bxra, Byra, Bzra = MagSphereAnalFunA(X, Y, Z, 100., 0., 0., 0., chiblk, np.array([1., 0., 0.]), flag)\n",
|
||||
"\n",
|
||||
"Bxra = np.reshape(Bxra, (size(xr), size(yr)), order='F')\n",
|
||||
"Byra = np.reshape(Byra, (size(xr), size(yr)), order='F')\n",
|
||||
@@ -501,8 +520,16 @@
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 47
|
||||
"outputs": [
|
||||
{
|
||||
"output_type": "stream",
|
||||
"stream": "stdout",
|
||||
"text": [
|
||||
"100.0 kang\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 20
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
@@ -522,21 +549,21 @@
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "pyout",
|
||||
"prompt_number": 48,
|
||||
"prompt_number": 22,
|
||||
"text": [
|
||||
"[<matplotlib.lines.Line2D at 0xc44e810>]"
|
||||
"[<matplotlib.lines.Line2D at 0xa11f550>]"
|
||||
]
|
||||
},
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0xa52a7d0>"
|
||||
"<matplotlib.figure.Figure at 0x1826c630>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 48
|
||||
"prompt_number": 22
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
@@ -556,33 +583,34 @@
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "pyout",
|
||||
"prompt_number": 49,
|
||||
"prompt_number": 24,
|
||||
"text": [
|
||||
"<matplotlib.colorbar.Colorbar instance at 0x47e1518>"
|
||||
"<matplotlib.colorbar.Colorbar instance at 0x000000001244C608>"
|
||||
]
|
||||
},
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": 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|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0xa52a950>"
|
||||
"<matplotlib.figure.Figure at 0x12fb62e8>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 49
|
||||
"prompt_number": 24
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"id = 21\n",
|
||||
"fig, axes = subplots(1,3, figsize=(14,5))\n",
|
||||
"epsx = np.linalg.norm(Utils.mkvc(Bxr))*1e-6\n",
|
||||
"epsy = np.linalg.norm(Utils.mkvc(Byr))*1e-6\n",
|
||||
"epsz = np.linalg.norm(Utils.mkvc(Bzr))*1e-6\n",
|
||||
"axes[0].plot(Y[:,1], Bxra[:,1], 'b', Y[:,1], Bxr[:,1], 'r.')\n",
|
||||
"axes[1].plot(Y[:,1], Byra[:,1], 'b', Y[:,1], Byr[:,1], 'r.')\n",
|
||||
"axes[2].plot(Y[:,1], Bzra[:,1], 'b', Y[:,1], Bzr[:,1], 'r.')\n",
|
||||
"axes[0].plot(Y[:,id], Bxra[:,id], 'b', Y[:,id], Bxr[:,id], 'r.')\n",
|
||||
"axes[1].plot(Y[:,id], Byra[:,id], 'b', Y[:,id], Byr[:,id], 'r.')\n",
|
||||
"axes[2].plot(Y[:,id], Bzra[:,id], 'b', Y[:,id], Bzr[:,id], 'r.')\n",
|
||||
"print X[:,1]"
|
||||
],
|
||||
"language": "python",
|
||||
@@ -592,22 +620,22 @@
|
||||
"output_type": "stream",
|
||||
"stream": "stdout",
|
||||
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||||
" -380. -380. -380. -380. -380.]\n"
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||||
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||||
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|
||||
" -285. -285. -285. -285. -285.]\n"
|
||||
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|
||||
},
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
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truncated
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||||
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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x152faf50>"
|
||||
"<matplotlib.figure.Figure at 0xaa70e80>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 50
|
||||
"prompt_number": 25
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
@@ -627,21 +655,21 @@
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "pyout",
|
||||
"prompt_number": 51,
|
||||
"prompt_number": 26,
|
||||
"text": [
|
||||
"[<matplotlib.lines.Line2D at 0xf0bfc50>]"
|
||||
"[<matplotlib.lines.Line2D at 0x139014e0>]"
|
||||
]
|
||||
},
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": 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|
||||
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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x15309ad0>"
|
||||
"<matplotlib.figure.Figure at 0x12897198>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 51
|
||||
"prompt_number": 26
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
|
||||
@@ -0,0 +1,175 @@
|
||||
{
|
||||
"metadata": {
|
||||
"name": ""
|
||||
},
|
||||
"nbformat": 3,
|
||||
"nbformat_minor": 0,
|
||||
"worksheets": [
|
||||
{
|
||||
"cells": [
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"from SimPEG import *\n",
|
||||
"%pylab inline"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"output_type": "stream",
|
||||
"stream": "stdout",
|
||||
"text": [
|
||||
"Warning: Python backend is being used for solver. Run setup.py from the command line.\n",
|
||||
"Warning: mumps solver not available.\n",
|
||||
"Warning: upgrade your scipy to 0.13.0"
|
||||
]
|
||||
},
|
||||
{
|
||||
"output_type": "stream",
|
||||
"stream": "stdout",
|
||||
"text": [
|
||||
"\n",
|
||||
"Populating the interactive namespace from numpy and matplotlib\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 1
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"hxind = ((10,25,1.3),(41, 12.5),(10,25,1.3))\n",
|
||||
"hyind = ((10,25,1.3),(41, 12.5),(10,25,1.3))\n",
|
||||
"hzind = ((10,25,1.3),(40, 12.5),(10,25,1.3))\n",
|
||||
"hx, hy, hz = Utils.meshTensors(hxind, hyind, hzind)\n",
|
||||
"M3 = Mesh.TensorMesh([hx, hy, hz], [-sum(hx)/2,-sum(hy)/2,-sum(hz)/2])"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 2
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"from MagAnalytics import MagSphereAnalFunA, MagSphereAnalFun"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 3
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"bx,by,bz = MagSphereAnalFunA(M3.gridFx[:,0],M3.gridFx[:,1],M3.gridFx[:,2],100.,0.,0.,0.,0.01,np.array([0.,1.,0.]),'secondary') \n",
|
||||
"Box = 1.\n",
|
||||
"mu0 = 4*pi*1e-7\n",
|
||||
"H0 = Box/mu0\n",
|
||||
"flag = 'secondary'\n",
|
||||
"Bxra, Byra, Bzra = MagSphereAnalFun(M3.gridFx[:,0],M3.gridFx[:,1],M3.gridFx[:,2], 100, 0., 0., 0., mu0, mu0*(1+0.01), H0, flag)\n"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 10
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"colorbar(M3.plotImage(Bxra, imageType='Fx'))"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "pyout",
|
||||
"prompt_number": 11,
|
||||
"text": [
|
||||
"<matplotlib.colorbar.Colorbar instance at 0x000000000AAF71C8>"
|
||||
]
|
||||
},
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0xabe94e0>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 11
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"fig, axes = subplots(1,3, figsize = (15, 5))\n",
|
||||
"bx,by,bz = MagSphereAnalFunA(M3.gridCC[:,0],M3.gridCC[:,1],M3.gridCC[:,2],100.,0.,0.,0.,0.01,np.array([0.,0.,1.]),'secondary') \n",
|
||||
"M3.plotSlice(bx, vType='CC', ind=5, ax = axes[0], grid=True, gridOpts={'color':'b','lw':0.3, 'alpha':0.5}); axes[0].set_title('$b_x$', fontsize = 16); #axes[0].set_xlim(0,500); axes[0].set_ylim(0,500)\n",
|
||||
"M3.plotSlice(by, vType='CC', ind=5, ax = axes[1]); axes[1].set_title('$b_y$', fontsize = 16);# axes[1].set_xlim(0,500); axes[1].set_ylim(0,500)\n",
|
||||
"M3.plotSlice(bz, vType='CC', ind=5, ax = axes[2]); axes[2].set_title('$b_z$', fontsize = 16);# axes[2].set_xlim(0,500); axes[2].set_ylim(0,500)"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "pyout",
|
||||
"prompt_number": 12,
|
||||
"text": [
|
||||
"<matplotlib.text.Text at 0x120c3f60>"
|
||||
]
|
||||
},
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x1073cb70>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 12
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"fig, ax = subplots(1,1, figsize = (5, 5))\n",
|
||||
"M3.plotSlice(np.c_[bx, by, bz], vType='CCv', view='vec', ind=1, ax = ax, grid=False, gridOpts={'color':'b','lw':0.5, 'alpha':0.8}); "
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0xa397518>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 9
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": []
|
||||
}
|
||||
],
|
||||
"metadata": {}
|
||||
}
|
||||
]
|
||||
}
|
||||
Reference in new issue
Block a user