From cc46a893a4dccdec5b2081e7936337896bb21a23 Mon Sep 17 00:00:00 2001 From: philippun Date: Thu, 10 Aug 2023 11:26:41 +0200 Subject: [PATCH] finished BTCS prototype --- proto/BTCS.ipynb | 357 ++++++++++++++++++++++++++++++----------------- proto/FTCS.ipynb | 22 ++- 2 files changed, 244 insertions(+), 135 deletions(-) diff --git a/proto/BTCS.ipynb b/proto/BTCS.ipynb index d985f4b..02bf6b8 100644 --- a/proto/BTCS.ipynb +++ b/proto/BTCS.ipynb @@ -98,9 +98,9 @@ "metadata": {}, "outputs": [], "source": [ - "################\n", - "### CONSTANT ###\n", - "################\n", + "##############\n", + "### CLOSED ###\n", + "##############\n", "\n", "# creates the coeffiecient matrix for a given row\n", "def create_coeff_matrix(alpha_x, row_index, s_x):\n", @@ -218,7 +218,7 @@ " return concentrations\n", "\n", "\n", - "def sim(concentrations, alpha_x, alpha_y, iterations, delta_t, delta_x, delta_y, bc_left, bc_right, bc_top, bc_bottom):\n", + "def sim_constant(concentrations, alpha_x, alpha_y, iterations, delta_t, delta_x, delta_y, bc_left, bc_right, bc_top, bc_bottom):\n", " s_x = sub(delta_t, delta_x)\n", " s_y = sub(delta_t, delta_y)\n", " for i in range(iterations):\n", @@ -229,7 +229,127 @@ }, { "cell_type": "code", - "execution_count": 269, + "execution_count": 279, + "metadata": {}, + "outputs": [], + "source": [ + "################\n", + "### CONSTANT ###\n", + "################\n", + "\n", + "# creates the coeffiecient matrix for a given row\n", + "def create_coeff_matrix(alpha_x, row_index, s_x):\n", + " # alias\n", + " r = row_index\n", + "\n", + " # a square matrix of column^2 dimension for the coefficients\n", + " cm = np.zeros((alpha_x.shape[1],alpha_x.shape[1]))\n", + "\n", + " # top left\n", + " cm[0,0] = 1 + s_x * (alpha_interblock(alpha_x[r,0], alpha_x[r,1])) # alpha_x[0,0]\n", + " cm[0,1] = -s_x * alpha_interblock(alpha_x[r, 0], alpha_x[r, 1])\n", + "\n", + " # inner cells\n", + " for i_cm in range(1, cm.shape[0]-1):\n", + " j_alpha = i_cm #- 1 # ???????\n", + " cm[i_cm,i_cm-1] = -s_x * alpha_interblock(alpha_x[r, j_alpha-1], alpha_x[r, j_alpha])\n", + " cm[i_cm,i_cm] = 1 + s_x * (alpha_interblock(alpha_x[r,j_alpha], alpha_x[r, j_alpha+1]) \\\n", + " + alpha_interblock(alpha_x[r, j_alpha], alpha_x[r, j_alpha-1]))\n", + " cm[i_cm,i_cm+1] = -s_x * alpha_interblock(alpha_x[r, j_alpha], alpha_x[r, j_alpha+1])\n", + "\n", + "\n", + " # bottom right\n", + " n = cm.shape[0]-1\n", + " cm[n,n-1] = -s_x * alpha_interblock(alpha_x[r, n-1], alpha_x[r, n])\n", + " cm[n,n] = 1 + s_x * (alpha_interblock(alpha_x[r, n], alpha_x[r, n-1])) # alpha_x[n,n]? \n", + "\n", + " # print(cm)\n", + " return cm\n", + "\n", + "# creates the solution vector for a given row\n", + "# s_x, alpha_x, row_index?\n", + "def create_solution_vector(concentrations, alpha_x, alpha_y, row_index, s_x, s_y, bc_left, bc_right, bc_top, bc_bottom):\n", + "\n", + " sv = np.zeros(concentrations.shape[1])\n", + " # print(concentrations.shape[1])\n", + " # print(sv.shape[0])\n", + " # print(row_index)\n", + "\n", + " # inner rows\n", + " if row_index > 0 and row_index < concentrations.shape[0]-1:\n", + " for i in range(0, sv.shape[0]):\n", + " sv[i] = s_y * alpha_interblock(alpha_y[row_index+1,i],alpha_y[row_index,i]) * concentrations[row_index+1,i] \\\n", + " + (\n", + " 1 - s_y * (\n", + " alpha_interblock(alpha_y[row_index+1,i], alpha_y[row_index,i]) \\\n", + " + alpha_interblock(alpha_y[row_index,i], alpha_y[row_index-1,i])\n", + " )\n", + " ) * concentrations[row_index,i] \\\n", + " + s_y * alpha_interblock(alpha_y[row_index,i], alpha_y[row_index-1,i]) * concentrations[row_index-1,i]\n", + "\n", + " # first row\n", + " # TODO check formula for alpha boundary cases\n", + " # added factor of 2 in front of alpha_y!!!\n", + " if row_index == 0:\n", + " for i in range(0, sv.shape[0]):\n", + " sv[i] = s_y * alpha_interblock(alpha_y[row_index+1,i],alpha_y[row_index,i]) * concentrations[row_index+1,i] \\\n", + " + (\n", + " 1 - s_y * (\n", + " alpha_interblock(alpha_y[row_index+1,i], alpha_y[row_index,i]) \\\n", + " )\n", + " ) * concentrations[row_index,i]\n", + "\n", + "\n", + " # last row\n", + " # TODO check formula for alpha boundary cases\n", + " # added factor of 2 in front of alpha_y!!!\n", + " if row_index == sv.shape[0]-1:\n", + " for i in range(0, sv.shape[0]):\n", + " i = i\n", + " sv[i] = (\n", + " 1 - s_y * (\n", + " alpha_interblock(alpha_y[row_index,i], alpha_y[row_index-1,i])\n", + " )\n", + " ) * concentrations[row_index,i] \\\n", + " + s_y * alpha_interblock(alpha_y[row_index,i], alpha_y[row_index-1,i]) * concentrations[row_index-1,i]\n", + "\n", + " # print(sv)\n", + " return sv\n", + "\n", + "def calc_sweep(concentrations, alpha_x, alpha_y, s_x, s_y, bc_left, bc_right, bc_top, bc_bottom):\n", + "\n", + " concentrations_t1 = np.zeros((concentrations.shape[0], concentrations.shape[1]))\n", + "\n", + " for i in range(concentrations.shape[0]):\n", + " A = create_coeff_matrix(alpha_x, i, s_x)\n", + " # print(i)\n", + " b = create_solution_vector(concentrations, alpha_x, alpha_y, i, s_x, s_y, bc_left, bc_right, bc_top, bc_bottom)\n", + " concentrations_t1[i,:] = np.linalg.solve(A,b)\n", + "\n", + " # print(concentrations_t1)\n", + " return concentrations_t1\n", + "\n", + "def calc_iteration(concentrations, alpha_x, alpha_y, s_x, s_y, bc_left, bc_right, bc_top, bc_bottom):\n", + " concentrations = calc_sweep(concentrations, alpha_x, alpha_y, s_x, s_y, bc_left, bc_right, bc_top, bc_bottom)\n", + " # concentrations = calc_sweep(concentrations, alpha_x, alpha_y, s_x, s_y, bc_left, bc_right, bc_top, bc_bottom, True)\n", + " concentrations = calc_sweep(concentrations.transpose(), alpha_y.transpose(), alpha_x.transpose(), s_y, s_x, bc_top, bc_bottom, bc_left, bc_right).transpose()\n", + " \n", + " # print(concentrations)\n", + " return concentrations\n", + "\n", + "\n", + "def sim_closed(concentrations, alpha_x, alpha_y, iterations, delta_t, delta_x, delta_y, bc_left, bc_right, bc_top, bc_bottom):\n", + " s_x = sub(delta_t, delta_x)\n", + " s_y = sub(delta_t, delta_y)\n", + " for i in range(iterations):\n", + " concentrations = calc_iteration(concentrations, alpha_x, alpha_y, s_x, s_y, bc_left, bc_right, bc_top, bc_bottom)\n", + "\n", + " return concentrations\n" + ] + }, + { + "cell_type": "code", + "execution_count": 280, "metadata": {}, "outputs": [ { @@ -301,106 +421,106 @@ " [1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]]\n", "\n", "Test Concentrations t=t+100:\n", - "[[1.03406102e-02 2.94500761e-02 4.42425339e-02 5.30261971e-02\n", - " 5.54585202e-02 5.24218517e-02 4.55845468e-02 3.68489169e-02\n", - " 2.78821774e-02 1.98459123e-02 1.33384447e-02 8.49104197e-03\n", - " 5.13286742e-03 2.95307410e-03 1.62013743e-03 8.48919901e-04\n", - " 4.24937081e-04 2.01925178e-04 8.71721193e-05 2.40321537e-05]\n", - " [2.94500761e-02 8.38738682e-02 1.26002814e-01 1.51018702e-01\n", - " 1.57945963e-01 1.49297526e-01 1.29824869e-01 1.04945780e-01\n", - " 7.94084902e-02 5.65211929e-02 3.79879138e-02 2.41825024e-02\n", - " 1.46184154e-02 8.41036020e-03 4.61415423e-03 2.41772537e-03\n", - " 1.21022155e-03 5.75083262e-04 2.48266349e-04 6.84436157e-05]\n", - " [4.42425339e-02 1.26002814e-01 1.89292678e-01 2.26873779e-01\n", - " 2.37280529e-01 2.24288074e-01 1.95034511e-01 1.57658921e-01\n", - " 1.19294525e-01 8.49111829e-02 5.70688361e-02 3.63291144e-02\n", - " 2.19610889e-02 1.26347941e-02 6.93179449e-03 3.63212293e-03\n", - " 1.81810288e-03 8.63941426e-04 3.72967877e-04 1.02822111e-04]\n", - " [5.30261971e-02 1.51018702e-01 2.26873779e-01 2.71916020e-01\n", - " 2.84388867e-01 2.68816963e-01 2.33755563e-01 1.88959635e-01\n", - " 1.42978587e-01 1.01768970e-01 6.83989610e-02 4.35416919e-02\n", - " 2.63211197e-02 1.51432348e-02 8.30799388e-03 4.35322413e-03\n", - " 2.17905877e-03 1.03546348e-03 4.47014816e-04 1.23235833e-04]\n", - " [5.54585202e-02 1.57945963e-01 2.37280529e-01 2.84388867e-01\n", - " 2.97433845e-01 2.81147656e-01 2.44477981e-01 1.97627254e-01\n", - " 1.49537045e-01 1.06437135e-01 7.15364362e-02 4.55389587e-02\n", - " 2.75284751e-02 1.58378583e-02 8.68908336e-03 4.55290746e-03\n", - " 2.27901267e-03 1.08296042e-03 4.67519482e-04 1.28888687e-04]\n", - " [5.24218517e-02 1.49297526e-01 2.24288074e-01 2.68816963e-01\n", - " 2.81147656e-01 2.65753227e-01 2.31091425e-01 1.86806041e-01\n", - " 1.41349044e-01 1.00609098e-01 6.76194106e-02 4.30454425e-02\n", - " 2.60211350e-02 1.49706457e-02 8.21330676e-03 4.30360996e-03\n", - " 2.15422380e-03 1.02366219e-03 4.41920139e-04 1.21831301e-04]\n", - " [4.55845468e-02 1.29824869e-01 1.95034511e-01 2.33755563e-01\n", - " 2.44477981e-01 2.31091425e-01 2.00950511e-01 1.62441204e-01\n", - " 1.22913096e-01 8.74868017e-02 5.87999104e-02 3.74310888e-02\n", - " 2.26272367e-02 1.30180465e-02 7.14205726e-03 3.74229645e-03\n", - " 1.87325156e-03 8.90147442e-04 3.84281146e-04 1.05941024e-04]\n", - " [3.68489169e-02 1.04945780e-01 1.57658921e-01 1.88959635e-01\n", - " 1.97627254e-01 1.86806041e-01 1.62441204e-01 1.31311658e-01\n", - " 9.93585501e-02 7.07212008e-02 4.75317441e-02 3.02579531e-02\n", - " 1.82910487e-02 1.05233230e-02 5.77338359e-03 3.02513857e-03\n", - " 1.51426955e-03 7.19563348e-04 3.10639131e-04 8.56389336e-05]\n", - " [2.78821774e-02 7.94084902e-02 1.19294525e-01 1.42978587e-01\n", - " 1.49537045e-01 1.41349044e-01 1.22913096e-01 9.93585501e-02\n", - " 7.51808454e-02 5.35120496e-02 3.59654675e-02 2.28950452e-02\n", - " 1.38401426e-02 7.96259931e-03 4.36850033e-03 2.28900759e-03\n", - " 1.14579032e-03 5.44466287e-04 2.35048846e-04 6.47997321e-05]\n", - " [1.98459123e-02 5.65211929e-02 8.49111829e-02 1.01768970e-01\n", - " 1.06437135e-01 1.00609098e-01 8.74868017e-02 7.07212008e-02\n", - " 5.35120496e-02 3.80886839e-02 2.55994179e-02 1.62961827e-02\n", - " 9.85110493e-03 5.66760067e-03 3.10940114e-03 1.62926457e-03\n", - " 8.15548004e-04 3.87538964e-04 1.67302528e-04 4.61230046e-05]\n", - " [1.33384447e-02 3.79879138e-02 5.70688361e-02 6.83989610e-02\n", - " 7.15364362e-02 6.76194106e-02 5.87999104e-02 4.75317441e-02\n", - " 3.59654675e-02 2.55994179e-02 1.72053779e-02 1.09526702e-02\n", - " 6.62093111e-03 3.80919642e-03 2.08982961e-03 1.09502929e-03\n", - " 5.48130103e-04 2.60465075e-04 1.12444088e-04 3.09992877e-05]\n", - " [8.49104197e-03 2.41825024e-02 3.63291144e-02 4.35416919e-02\n", - " 4.55389587e-02 4.30454425e-02 3.74310888e-02 3.02579531e-02\n", - " 2.28950452e-02 1.62961827e-02 1.09526702e-02 6.97229584e-03\n", - " 4.21477956e-03 2.42487392e-03 1.33035233e-03 6.97078252e-04\n", - " 3.48930915e-04 1.65807929e-04 7.15801202e-05 1.97336541e-05]\n", - " [5.13286742e-03 1.46184154e-02 2.19610889e-02 2.63211197e-02\n", - " 2.75284751e-02 2.60211350e-02 2.26272367e-02 1.82910487e-02\n", - " 1.38401426e-02 9.85110493e-03 6.62093111e-03 4.21477956e-03\n", - " 2.54785040e-03 1.46584558e-03 8.04203081e-04 4.21386475e-04\n", - " 2.10930076e-04 1.00231528e-04 4.32704570e-05 1.19290695e-05]\n", - " [2.95307410e-03 8.41036020e-03 1.26347941e-02 1.51432348e-02\n", - " 1.58378583e-02 1.49706457e-02 1.30180465e-02 1.05233230e-02\n", - " 7.96259931e-03 5.66760067e-03 3.80919642e-03 2.42487392e-03\n", - " 1.46584558e-03 8.43339650e-04 4.62679258e-04 2.42434761e-04\n", - " 1.21353640e-04 5.76658437e-05 2.48946360e-05 6.86310854e-06]\n", - " [1.62013743e-03 4.61415423e-03 6.93179449e-03 8.30799388e-03\n", - " 8.68908336e-03 8.21330676e-03 7.14205726e-03 5.77338359e-03\n", - " 4.36850033e-03 3.10940114e-03 2.08982961e-03 1.33035233e-03\n", - " 8.04203081e-04 4.62679258e-04 2.53838528e-04 1.33006358e-04\n", - " 6.65779344e-05 3.16370632e-05 1.36578799e-05 3.76528954e-06]\n", - " [8.48919901e-04 2.41772537e-03 3.63212293e-03 4.35322413e-03\n", - " 4.55290746e-03 4.30360996e-03 3.74229645e-03 3.02513857e-03\n", - " 2.28900759e-03 1.62926457e-03 1.09502929e-03 6.97078252e-04\n", - " 4.21386475e-04 2.42434761e-04 1.33006358e-04 6.96926953e-05\n", - " 3.48855181e-05 1.65771940e-05 7.15645839e-06 1.97293709e-06]\n", - " [4.24937081e-04 1.21022155e-03 1.81810288e-03 2.17905877e-03\n", - " 2.27901267e-03 2.15422380e-03 1.87325156e-03 1.51426955e-03\n", - " 1.14579032e-03 8.15548004e-04 5.48130103e-04 3.48930915e-04\n", - " 2.10930076e-04 1.21353640e-04 6.65779344e-05 3.48855181e-05\n", - " 1.74623662e-05 8.29791415e-06 3.58225145e-06 9.87577426e-07]\n", - " [2.01925178e-04 5.75083262e-04 8.63941426e-04 1.03546348e-03\n", - " 1.08296042e-03 1.02366219e-03 8.90147442e-04 7.19563348e-04\n", - " 5.44466287e-04 3.87538964e-04 2.60465075e-04 1.65807929e-04\n", - " 1.00231528e-04 5.76658437e-05 3.16370632e-05 1.65771940e-05\n", - " 8.29791415e-06 3.94307268e-06 1.70224439e-06 4.69285352e-07]\n", - " [8.71721193e-05 2.48266349e-04 3.72967877e-04 4.47014816e-04\n", - " 4.67519482e-04 4.41920139e-04 3.84281146e-04 3.10639131e-04\n", - " 2.35048846e-04 1.67302528e-04 1.12444088e-04 7.15801202e-05\n", - " 4.32704570e-05 2.48946360e-05 1.36578799e-05 7.15645839e-06\n", - " 3.58225145e-06 1.70224439e-06 7.34867500e-07 2.02592857e-07]\n", - " [2.40321537e-05 6.84436157e-05 1.02822111e-04 1.23235833e-04\n", - " 1.28888687e-04 1.21831301e-04 1.05941024e-04 8.56389336e-05\n", - " 6.47997321e-05 4.61230046e-05 3.09992877e-05 1.97336541e-05\n", - " 1.19290695e-05 6.86310854e-06 3.76528954e-06 1.97293709e-06\n", - " 9.87577426e-07 4.69285352e-07 2.02592857e-07 5.58520626e-08]]\n" + "[[6.28591428e+01 5.97567801e+01 5.40111841e+01 4.64274274e+01\n", + " 3.79691932e+01 2.95580781e+01 2.19168076e+01 1.54897130e+01\n", + " 1.04428201e+01 6.72160139e+00 4.13431473e+00 2.43233389e+00\n", + " 1.37011777e+00 7.39680705e-01 3.83120860e-01 1.90615726e-01\n", + " 9.12968457e-02 4.24222400e-02 1.98821745e-02 1.12119045e-02]\n", + " [5.97567801e+01 5.68075320e+01 5.13455053e+01 4.41360389e+01\n", + " 3.60952541e+01 2.80992628e+01 2.08351211e+01 1.47252306e+01\n", + " 9.92742306e+00 6.38986213e+00 3.93026893e+00 2.31228800e+00\n", + " 1.30249670e+00 7.03174355e-01 3.64212236e-01 1.81208039e-01\n", + " 8.67909629e-02 4.03285243e-02 1.89009056e-02 1.06585500e-02]\n", + " [5.40111841e+01 5.13455053e+01 4.64086509e+01 3.98923724e+01\n", + " 3.26247065e+01 2.53975274e+01 1.88318306e+01 1.33094043e+01\n", + " 8.97290440e+00 5.77547886e+00 3.55237479e+00 2.08996222e+00\n", + " 1.17726205e+00 6.35564358e-01 3.29193342e-01 1.63784942e-01\n", + " 7.84460386e-02 3.64509491e-02 1.70835894e-02 9.63373367e-03]\n", + " [4.64274274e+01 4.41360389e+01 3.98923724e+01 3.42910501e+01\n", + " 2.80438435e+01 2.18314387e+01 1.61876371e+01 1.14406194e+01\n", + " 7.71301119e+00 4.96453891e+00 3.05358279e+00 1.79650883e+00\n", + " 1.01196167e+00 5.46324221e-01 2.82971023e-01 1.40787758e-01\n", + " 6.74313630e-02 3.13328401e-02 1.46848680e-02 8.28105286e-03]\n", + " [3.79691932e+01 3.60952541e+01 3.26247065e+01 2.80438435e+01\n", + " 2.29347645e+01 1.78541471e+01 1.32385436e+01 9.35634629e+00\n", + " 6.30784062e+00 4.06009008e+00 2.49727546e+00 1.46921755e+00\n", + " 8.27600633e-01 4.46793869e-01 2.31418841e-01 1.15138785e-01\n", + " 5.51465932e-02 2.56245656e-02 1.20095517e-02 6.77239541e-03]\n", + " [2.95580781e+01 2.80992628e+01 2.53975274e+01 2.18314387e+01\n", + " 1.78541471e+01 1.38990120e+01 1.03058789e+01 7.28368424e+00\n", + " 4.91049795e+00 3.16067973e+00 1.94406720e+00 1.14374953e+00\n", + " 6.44266629e-01 3.47817980e-01 1.80153846e-01 8.96326973e-02\n", + " 4.29302593e-02 1.99480907e-02 9.34913903e-03 5.27214237e-03]\n", + " [2.19168076e+01 2.08351211e+01 1.88318306e+01 1.61876371e+01\n", + " 1.32385436e+01 1.03058789e+01 7.64163230e+00 5.40072685e+00\n", + " 3.64104995e+00 2.34358978e+00 1.44149246e+00 8.48070648e-01\n", + " 4.77712648e-01 2.57901062e-01 1.33580985e-01 6.64611067e-02\n", + " 3.18320504e-02 1.47911669e-02 6.93222614e-03 3.90920308e-03]\n", + " [1.54897130e+01 1.47252306e+01 1.33094043e+01 1.14406194e+01\n", + " 9.35634629e+00 7.28368424e+00 5.40072685e+00 3.81696598e+00\n", + " 2.57331359e+00 1.65633306e+00 1.01877541e+00 5.99374289e-01\n", + " 3.37623616e-01 1.82271685e-01 9.44084172e-02 4.69714152e-02\n", + " 2.24973151e-02 1.04536635e-02 4.89935375e-03 2.76283093e-03]\n", + " [1.04428201e+01 9.92742306e+00 8.97290440e+00 7.71301119e+00\n", + " 6.30784062e+00 4.91049795e+00 3.64104995e+00 2.57331359e+00\n", + " 1.73487080e+00 1.11666292e+00 6.86835725e-01 4.04084817e-01\n", + " 2.27618334e-01 1.22883517e-01 6.36480556e-02 3.16670837e-02\n", + " 1.51671896e-02 7.04762745e-03 3.30303535e-03 1.86263918e-03]\n", + " [6.72160139e+00 6.38986213e+00 5.77547886e+00 4.96453891e+00\n", + " 4.06009008e+00 3.16067973e+00 2.34358978e+00 1.65633306e+00\n", + " 1.11666292e+00 7.18748669e-01 4.42087091e-01 2.60092297e-01\n", + " 1.46508290e-01 7.90949197e-02 4.09675600e-02 2.03827617e-02\n", + " 9.76247810e-03 4.53625956e-03 2.12602408e-03 1.19890202e-03]\n", + " [4.13431473e+00 3.93026893e+00 3.55237479e+00 3.05358279e+00\n", + " 2.49727546e+00 1.94406720e+00 1.44149246e+00 1.01877541e+00\n", + " 6.86835725e-01 4.42087091e-01 2.71918412e-01 1.59977266e-01\n", + " 9.01141476e-02 4.86496108e-02 2.51982789e-02 1.25370053e-02\n", + " 6.00469362e-03 2.79015723e-03 1.30767241e-03 7.37419252e-04]\n", + " [2.43233389e+00 2.31228800e+00 2.08996222e+00 1.79650883e+00\n", + " 1.46921755e+00 1.14374953e+00 8.48070648e-01 5.99374289e-01\n", + " 4.04084817e-01 2.60092297e-01 1.59977266e-01 9.41191353e-02\n", + " 5.30166932e-02 2.86219374e-02 1.48248578e-02 7.37587358e-03\n", + " 3.53273052e-03 1.64152815e-03 7.69340539e-04 4.33844533e-04]\n", + " [1.37011777e+00 1.30249670e+00 1.17726205e+00 1.01196167e+00\n", + " 8.27600633e-01 6.44266629e-01 4.77712648e-01 3.37623616e-01\n", + " 2.27618334e-01 1.46508290e-01 9.01141476e-02 5.30166932e-02\n", + " 2.98639564e-02 1.61225501e-02 8.35074541e-03 4.15478134e-03\n", + " 1.98996399e-03 9.24662067e-04 4.33364493e-04 2.44381787e-04]\n", + " [7.39680705e-01 7.03174355e-01 6.35564358e-01 5.46324221e-01\n", + " 4.46793869e-01 3.47817980e-01 2.57901062e-01 1.82271685e-01\n", + " 1.22883517e-01 7.90949197e-02 4.86496108e-02 2.86219374e-02\n", + " 1.61225501e-02 8.70402492e-03 4.50828782e-03 2.24302732e-03\n", + " 1.07431492e-03 4.99194087e-04 2.33958978e-04 1.31933544e-04]\n", + " [3.83120860e-01 3.64212236e-01 3.29193342e-01 2.82971023e-01\n", + " 2.31418841e-01 1.80153846e-01 1.33580985e-01 9.44084172e-02\n", + " 6.36480556e-02 4.09675600e-02 2.51982789e-02 1.48248578e-02\n", + " 8.35074541e-03 4.50828782e-03 2.33508742e-03 1.16178582e-03\n", + " 5.56446119e-04 2.58559763e-04 1.21180077e-04 6.83355566e-05]\n", + " [1.90615726e-01 1.81208039e-01 1.63784942e-01 1.40787758e-01\n", + " 1.15138785e-01 8.96326973e-02 6.64611067e-02 4.69714152e-02\n", + " 3.16670837e-02 2.03827617e-02 1.25370053e-02 7.37587358e-03\n", + " 4.15478134e-03 2.24302732e-03 1.16178582e-03 5.78028166e-04\n", + " 2.76850968e-04 1.28642322e-04 6.02912313e-05 3.39992757e-05]\n", + " [9.12968457e-02 8.67909629e-02 7.84460386e-02 6.74313630e-02\n", + " 5.51465932e-02 4.29302593e-02 3.18320504e-02 2.24973151e-02\n", + " 1.51671896e-02 9.76247810e-03 6.00469362e-03 3.53273052e-03\n", + " 1.98996399e-03 1.07431492e-03 5.56446119e-04 2.76850968e-04\n", + " 1.32599868e-04 6.16142144e-05 2.88769419e-05 1.62842106e-05]\n", + " [4.24222400e-02 4.03285243e-02 3.64509491e-02 3.13328401e-02\n", + " 2.56245656e-02 1.99480907e-02 1.47911669e-02 1.04536635e-02\n", + " 7.04762745e-03 4.53625956e-03 2.79015723e-03 1.64152815e-03\n", + " 9.24662067e-04 4.99194087e-04 2.58559763e-04 1.28642322e-04\n", + " 6.16142144e-05 2.86298280e-05 1.34180382e-05 7.56666548e-06]\n", + " [1.98821745e-02 1.89009056e-02 1.70835894e-02 1.46848680e-02\n", + " 1.20095517e-02 9.34913903e-03 6.93222614e-03 4.89935375e-03\n", + " 3.30303535e-03 2.12602408e-03 1.30767241e-03 7.69340539e-04\n", + " 4.33364493e-04 2.33958978e-04 1.21180077e-04 6.02912313e-05\n", + " 2.88769419e-05 1.34180382e-05 6.28867725e-06 3.54629466e-06]\n", + " [1.12119045e-02 1.06585500e-02 9.63373367e-03 8.28105286e-03\n", + " 6.77239541e-03 5.27214237e-03 3.90920308e-03 2.76283093e-03\n", + " 1.86263918e-03 1.19890202e-03 7.37419252e-04 4.33844533e-04\n", + " 2.44381787e-04 1.31933544e-04 6.83355566e-05 3.39992757e-05\n", + " 1.62842106e-05 7.56666548e-06 3.54629466e-06 1.99981734e-06]]\n" ] } ], @@ -430,38 +550,19 @@ "print(\"\\nTest Alpha:\")\n", "print(testAlpha)\n", "\n", - "testConcentrations = sim(testConcentrations, testAlpha, testAlpha, iterations, delta_t, delta_x, delta_y, bc_left, bc_right, bc_top, bc_bottom)\n", + "testConcentrations = sim_closed(testConcentrations, testAlpha, testAlpha, iterations, delta_t, delta_x, delta_y, bc_left, bc_right, bc_top, bc_bottom)\n", "print(\"\\nTest Concentrations t=t+\" + str(iterations) + \":\")\n", - "print(testConcentrations)\n", - "\n", - "\n", - "# testA = create_coeff_matrix(testAlpha, 1, 3)\n", - "# print(\"\\nTest A:\")\n", - "# print(testA)\n", - "\n", - "# testb = create_solution_vector(testConcentrations,testAlpha,testAlpha,1,1,3,3,1,1)\n", - "# print(\"\\nTest b:\")\n", - "# print(testb)\n", - "\n", - "# needed to solve: TODO calc boundary in functions\n", - "# testA[0,0] = 1\n", - "# testA[4,4] = 1\n", - "# testb[0] = 1\n", - "# test[4] = 1\n", - "\n", - "# result = solve_row(testA, testb)\n", - "# print(\"\\nResult x:\")\n", - "# print(result)" + "print(testConcentrations)" ] }, { "cell_type": "code", - "execution_count": 270, + "execution_count": 281, "metadata": {}, "outputs": [ { "data": { - "image/png": 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", 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MDU9pMzzQBQCAi69RlhrDfCBLuO0jJTp/agAAgJAxUgcAuIrfhH7v9pb6iEYkdQCAq/htOKcebvtIic6oAABAyBipAwBcxS9L/jAXuoXbPlJI6gAAV+noO8p1JKbfAQBwCOeN1Mu7SXFxYXURW2dTLJI6n7Hn11xslX1LLT0n/Lb0E3e80ZZ+JKlLtT0HPeZUrS39SJJqbfoi1NXb048k09BgT0c2Lt010boMGGiFkxfKOS+pAwDQBr9suE1slJ5Tj86fGgAAIGSM1AEArmJsWP1uonSkTlIHALhKRz+lrSOR1AEAruLkhXK2R5WbmyvLsoKK1+tts01xcbGGDx+uuLg4XXnllXrhhRfsDgsAAMeLyEh90KBB2rJlS+B1p06dWq1bVlamG2+8Uffcc49eeeUV/fGPf9ScOXPUs2dP3XLLLZEIDwDgYky/h9pp587nHZ03eeGFF9SnTx8VFBRIkq6++mrt2bNHTz31FEkdAGA7J98mNiInBQ4dOqSUlBSlpaXptttu08cff9xq3Z07dyorKyto26RJk7Rnzx7V17d+047a2lpVV1cHFQAA3Mz2pD5q1CitWrVKb731ll566SX5fD5lZmbq2LFjLdb3+XxKSkoK2paUlKSGhgYdPXq01ffJz89XYmJioKSmptr6OQAAztQ0/R5uiUa2J/Xs7GzdcsstGjJkiL797W9r06ZNkqSVK1e22saygg+OMabF7V+Uk5OjqqqqQCkvL7chegCA0zk5qUf8krbu3btryJAhOnToUIv7vV6vfD5f0LbKykp17txZl112Wav9ejweeTweW2MFAOCrLOIX2tXW1urAgQNKTk5ucf/o0aNVWFgYtG3z5s0aMWKEunTpEunwAAAu4+SRuu1J/eGHH1ZxcbHKysr07rvv6tZbb1V1dbVmzZol6dy0+cyZMwP177vvPh0+fFjz58/XgQMH9PLLL2vZsmV6+OGH7Q4NAABHJ3Xbp9///ve/6/bbb9fRo0fVs2dPZWRkaNeuXerbt68kqaKiQkeOHAnUT0tL0xtvvKGHHnpIzz33nFJSUvTMM89wORsAACGyPamvWbOmzf0rVqxotm3s2LHau3ev3aEAANCMUfjXmRt7QrEd934HALgKd5QDAMAhSOpfId3+bqlTbHgHu1O9fRMrnWrs6Sv2tN+WfiSpS3WDTf3U2dKPJHU6VWtLP9aZGlv6kSRTa09MpsGe4y1JprHRpo7s+z7Z2heAsDguqQMA0BZG6gAAOISTk3p0PuUdAACEjJE6AMBVjLFkwhxph9s+UkjqAABX4XnqAAAg6jFSBwC4ipMXypHUAQCu4uRz6ky/AwDgEIzUAQCuwvQ7AAAO4eTpd5I6AMBVjA0j9WhN6pxTBwDAIRipAwBcxUgyYT5A075nedqLpA4AcBW/LFncUQ4AAEQzRuoAAFdh9ftXyCUVDercpSGsPmLq7TtbYldfnc6E95mC+jpbb0s/MadqbelHkqwzNbb0Y2rsi0l19hwn1dvUjyT57fk+GZv6sVW4JzmBC+Q3liyHXqfO9DsAAA5BUgcAuIox9pT2ys/Pl2VZmjdv3hdiMsrNzVVKSoq6du2qcePGaf/+/SH3TVIHALhK0zn1cEt77N69Wy+++KK+8Y1vBG1ftGiRFi9erCVLlmj37t3yer2aOHGiTp48GVL/JHUAADrAqVOndMcdd+ill17S1772tcB2Y4wKCgq0cOFCTZkyRYMHD9bKlSt15swZrV69OqT3IKkDAFzFzpF6dXV1UKmtbX2x7ty5c/Xd735X3/72t4O2l5WVyefzKSsrK7DN4/Fo7Nix2rFjR0ifjaQOAHCVpqe0hVskKTU1VYmJiYGSn5/f4nuuWbNGe/fubXG/z+eTJCUlJQVtT0pKCuy7UI67pA0AgLaEu9CtqQ9JKi8vV0JCQmC7x+NpVre8vFwPPvigNm/erLi4uFb7tKzg8/TGmGbbzoekDgBAOyUkJAQl9Za89957qqys1PDhwwPbGhsbtW3bNi1ZskQHDx6UdG7EnpycHKhTWVnZbPR+Pky/AwBc5dxIPdxz6hf+fhMmTNC+fftUWloaKCNGjNAdd9yh0tJSXXnllfJ6vSosLAy0qaurU3FxsTIzM0P6bIzUAQCu0tG3iY2Pj9fgwYODtnXv3l2XXXZZYPu8efOUl5en9PR0paenKy8vT926ddP06dNDioukDgDARbZgwQKdPXtWc+bM0fHjxzVq1Cht3rxZ8fHxIfVDUgcAuIpR+M9DD7d9UVFR0GvLspSbm6vc3Nyw+iWpAwBcxclPaWOhHAAADmF7Ur/iiitkWVazMnfu3BbrFxUVtVj/r3/9q92hAQDw+fx7uCUK2T79vnv3bjU2NgZe/+Uvf9HEiRP1gx/8oM12Bw8eDLrWr2fPnnaHBgCAZMP0u6J0+t32pP7lZPzEE0+oX79+Gjt2bJvtevXqpUsvvdTucAAACGLnHeWiTUTPqdfV1emVV17RnXfeed5b3Q0bNkzJycmaMGGCtm7dGsmwAABwpIiuft+wYYNOnDih2bNnt1onOTlZL774ooYPH67a2lr913/9lyZMmKCioiKNGTOm1Xa1tbVBT8Oprq6WJHX9rEadw/xUVqN9P8Gs+sbzV7qQfuoabOlHkqyaOns6qrWpH0mmjScbhaSu3p5+JJkGe465afTb0s+5vuz5PsnYF1PUDlmAVjh59XtEk/qyZcuUnZ2tlJSUVuv0799f/fv3D7wePXq0ysvL9dRTT7WZ1PPz8/X444/bGi8AwAWMFf458ShN6hGbfj98+LC2bNmiu+++O+S2GRkZOnToUJt1cnJyVFVVFSjl5eXtDRUAAEeI2Eh9+fLl6tWrl7773e+G3LakpCToSTUt8Xg8LT7iDgCAtjh5oVxEkrrf79fy5cs1a9Ysdf7SCe6cnBx98sknWrVqlSSpoKBAV1xxhQYNGhRYWLd27VqtXbs2EqEBANwuGu4TGyERSepbtmzRkSNHdOeddzbbV1FRoSNHjgRe19XV6eGHH9Ynn3yirl27atCgQdq0aZNuvPHGSIQGAIBjRSSpZ2VlybQyN7FixYqg1wsWLNCCBQsiEQYAAM2w+h0AACeJ0unzcPFAFwAAHIKROgDAVZh+BwDAKVj9DgCAU1j/KOH2EX04pw4AgEMwUgcAuAvT7wAAOISDkzrT7wAAOAQjdQCAuzj40askdQCAq/CUtq+QTv93Wp06NYTXiY1/Lauh0Z6O7OpHkqmvt6ejOpv6kWQawvybNbHrs0kyjX6b+rHvbydjT0wAnMlxSR0AgDY5eKEcSR0A4C4OPqfO6ncAAByCkToAwFUsc66E20c0IqkDANyFc+oAADgE59QBAEC0Y6QOAHAXpt8BAHAIByd1pt8BAHAIRuoAAHdx8EidpA4AcBdWvwMAgGjHSB0A4CrcUQ4AAKdw8Dl1pt8BAHAIkjoAAA7B9DsAwFUs2XBO3ZZI7Oe8pH7ytBRTf7GjCDCNjfZ01Oi3px9Jsikm09BgSz+SjcfJb9+JLttiMjb+7exiovSEINARuKQNAABEO+eN1AEAaIuDV7+T1AEA7uLgpM70OwAADkFSBwC4StMd5cItF2rp0qX6xje+oYSEBCUkJGj06NH6wx/+ENhvjFFubq5SUlLUtWtXjRs3Tvv372/XZws5qW/btk2TJ09WSkqKLMvShg0bgva3N7i1a9dq4MCB8ng8GjhwoNavXx9qaAAAnJ+xqVyg3r1764knntCePXu0Z88e3XDDDbr55psDuXHRokVavHixlixZot27d8vr9WrixIk6efJkyB8t5KR++vRpDR06VEuWLGlxf3uC27lzp6ZNm6YZM2bo/fff14wZMzR16lS9++67oYYHAEBUmTx5sm688UZdddVVuuqqq/Rv//ZvuuSSS7Rr1y4ZY1RQUKCFCxdqypQpGjx4sFauXKkzZ85o9erVIb9XyEk9Oztbv/rVrzRlypRm+9obXEFBgSZOnKicnBwNGDBAOTk5mjBhggoKCkINDwCAttk4Uq+urg4qtbW1bb51Y2Oj1qxZo9OnT2v06NEqKyuTz+dTVlZWoI7H49HYsWO1Y8eOkD+arefU2xvczp07g9pI0qRJk9psU1tb2+xgAgBwPnaeU09NTVViYmKg5Ofnt/ie+/bt0yWXXCKPx6P77rtP69ev18CBA+Xz+SRJSUlJQfWTkpIC+0Jh6yVtbQV3+PDhNtuF+oHy8/P1+OOPhxEtAADhKS8vV0JCQuC1x+NpsV7//v1VWlqqEydOaO3atZo1a5aKi4sD+y0r+A51xphm2y5ERFa/tye4UNvk5OSoqqoqUMrLy9sfMADAPZpuExtukQIr2ptKa0k9NjZW//RP/6QRI0YoPz9fQ4cO1b//+7/L6/VKUrNBbGVlZbPB7oWwNam3Nziv1xtyG4/H0+xgAgBwXh28+r3FEIxRbW2t0tLS5PV6VVhYGNhXV1en4uJiZWZmhtyvrUm9vcGNHj06qI0kbd68uV0fCACAtnT0deqPPvqo3nnnHf3tb3/Tvn37tHDhQhUVFemOO+6QZVmaN2+e8vLytH79ev3lL3/R7Nmz1a1bN02fPj3kzxbyOfVTp07po48+CrwuKytTaWmpevTooT59+gSCS09PV3p6uvLy8poFN3PmTF1++eWBBQUPPvigxowZoyeffFI333yzXn/9dW3ZskXbt28P+QMBABBNPvvsM82YMUMVFRVKTEzUN77xDb355puaOHGiJGnBggU6e/as5syZo+PHj2vUqFHavHmz4uPjQ36vkJP6nj17NH78+MDr+fPnS5JmzZqlFStWXFBwR44cUUzM55MEmZmZWrNmjX7+85/rscceU79+/fTaa69p1KhRIX8gAADa1MH3fl+2bFmb+y3LUm5urnJzc8OLSZJljDMerFxdXa3ExERN6HW3OsfEXuxwPsfz1C+sL56n3rGc8a89HKTB1KtIr6uqqipia6Sa8sSVj+WpU1xcWH011tTo4399NKLxtgf3fgcAwCEc9+hVc/asjGXTCMsOfptGaTaOrKJxVGzXaNZEYUy2YoQNhM/Bj151XFIHAKBNDk7qTL8DAOAQjNQBAK4S6nXmrfURjRipAwDgECR1AAAcgul3AIC7OHihHEkdAOAqTj6nTlIHALhPlCblcHFOHQAAh2CkDgBwF86pAwDgDE4+p870OwAADsFIHQDgLky/AwDgDEy/AwCAqMdIHQDgLky/AwDgEA5O6ky/AwDgEI4bqZu6ehnrYkfxBf4o/Dln/DZ1Y+NnsykmW5ko/NsBCJuTF8o5LqkDANAmB0+/k9QBAO7i4KTOOXUAAByCkToAwFU4pw4AgFMw/Q4AAKIdI3UAgKsw/Q4AgFMw/Q4AAKIdI3UAgLs4eKROUgcAuIr1jxJuH9GI6XcAAByCkToAwF2YfgcAwBmcfElbyNPv27Zt0+TJk5WSkiLLsrRhw4bAvvr6ev3sZz/TkCFD1L17d6WkpGjmzJn69NNP2+xzxYoVsiyrWampqQn5AwEA0CZjU4lCISf106dPa+jQoVqyZEmzfWfOnNHevXv12GOPae/evVq3bp0+/PBDfe973ztvvwkJCaqoqAgqcXFxoYYHAIBrhTz9np2drezs7Bb3JSYmqrCwMGjbs88+q2uuuUZHjhxRnz59Wu3Xsix5vd5QwwEAIHRROtIOV8TPqVdVVcmyLF166aVt1jt16pT69u2rxsZGffOb39S//uu/atiwYa3Wr62tVW1tbeB1dXX1uX9obJSs8Bb1G79D/9pNjP9iRxA5xuF/OwBh45x6O9XU1OiRRx7R9OnTlZCQ0Gq9AQMGaMWKFdq4caNeffVVxcXF6dprr9WhQ4dabZOfn6/ExMRASU1NjcRHAADgKyNiSb2+vl633Xab/H6/nn/++TbrZmRk6Ic//KGGDh2q66+/Xr/73e901VVX6dlnn221TU5OjqqqqgKlvLzc7o8AAHAiBy+Ui8j0e319vaZOnaqysjK9/fbbbY7SWxITE6ORI0e2OVL3eDzyeDzhhgoAcBmm30PQlNAPHTqkLVu26LLLLgu5D2OMSktLlZycbHd4AAA4Vsgj9VOnTumjjz4KvC4rK1Npaal69OihlJQU3Xrrrdq7d6/+53/+R42NjfL5fJKkHj16KDY2VpI0c+ZMXX755crPz5ckPf7448rIyFB6erqqq6v1zDPPqLS0VM8995wdnxEAgM9xR7nP7dmzR+PHjw+8nj9/viRp1qxZys3N1caNGyVJ3/zmN4Pabd26VePGjZMkHTlyRDExn08SnDhxQj/+8Y/l8/mUmJioYcOGadu2bbrmmmtCDQ8AgDY5efo95KQ+btw4mTYuG2prX5OioqKg17/5zW/0m9/8JtRQAADAF3DvdwCAuzh4+p1HrwIA3KWDL2nLz8/XyJEjFR8fr169eun73/++Dh48GBySMcrNzVVKSoq6du2qcePGaf/+/SF/NJI6AMBVms6ph1suVHFxsebOnatdu3apsLBQDQ0NysrK0unTpwN1Fi1apMWLF2vJkiXavXu3vF6vJk6cqJMnT4b02Zh+BwAggt58882g18uXL1evXr303nvvacyYMTLGqKCgQAsXLtSUKVMkSStXrlRSUpJWr16te++994Lfi5E6AMBdbJx+r66uDipffCZJa6qqqiSdu9RbOndpuM/nU1ZWVqCOx+PR2LFjtWPHjpA+GkkdAOAqljG2FElKTU0Neg5J0/1XWmOM0fz583Xddddp8ODBkhS4n0tSUlJQ3aSkpMC+C8X0OwAA7VReXh50K/Tz3b78/vvv15///Gdt37692T7LsoJeG2OabTsfkjoAwF1svKQtISHhgp9v8sADD2jjxo3atm2bevfuHdju9XolnRuxf/H26JWVlc1G7+fD9DsAwFU6evW7MUb333+/1q1bp7fffltpaWlB+9PS0uT1elVYWBjYVldXp+LiYmVmZob02RipAwAQQXPnztXq1av1+uuvKz4+PnCePDExUV27dpVlWZo3b57y8vKUnp6u9PR05eXlqVu3bpo+fXpI70VSBwC4SwffUW7p0qWSFHj+SZPly5dr9uzZkqQFCxbo7NmzmjNnjo4fP65Ro0Zp8+bNio+PDyksxyV109goY3FWoU0XcH9+AHCqjn6gy4U8E8WyLOXm5io3N7f9QYlz6gAAOIbjRuoAALTJwQ90IakDAFyF56kDAOAUDh6pc04dAACHYKQOAHCdaJ0+DxdJHQDgLsaEf2lvlF4azPQ7AAAOwUgdAOAqrH4HAMApWP0OAACiHSN1AICrWP5zJdw+ohFJHQDgLky/AwCAaMdIHQDgKqx+BwDAKRx88xmSOgDAVRipf5UYO1ZAAADw1eO8pA4AQFscvPqdpA4AcBUnT79zSRsAAA7BSB0A4C6sfgcAwBmYfv+Cbdu2afLkyUpJSZFlWdqwYUPQ/tmzZ8uyrKCSkZFx3n7Xrl2rgQMHyuPxaODAgVq/fn2ooQEA4GohJ/XTp09r6NChWrJkSat1vvOd76iioiJQ3njjjTb73Llzp6ZNm6YZM2bo/fff14wZMzR16lS9++67oYYHAEDbjE0lCoU8/Z6dna3s7Ow263g8Hnm93gvus6CgQBMnTlROTo4kKScnR8XFxSooKNCrr74aaogAALSK6fcQFRUVqVevXrrqqqt0zz33qLKyss36O3fuVFZWVtC2SZMmaceOHa22qa2tVXV1dVABAMDNbE/q2dnZ+u1vf6u3335bTz/9tHbv3q0bbrhBtbW1rbbx+XxKSkoK2paUlCSfz9dqm/z8fCUmJgZKamqqbZ8BAOBgfmNPiUK2r36fNm1a4J8HDx6sESNGqG/fvtq0aZOmTJnSajvLsoJeG2OabfuinJwczZ8/P/C6urqaxA4AOD/uKNd+ycnJ6tu3rw4dOtRqHa/X22xUXllZ2Wz0/kUej0cej8e2OAEA7mDJhnPqtkRiv4jfUe7YsWMqLy9XcnJyq3VGjx6twsLCoG2bN29WZmZmpMMDAMAxQh6pnzp1Sh999FHgdVlZmUpLS9WjRw/16NFDubm5uuWWW5ScnKy//e1vevTRR/X1r39d//zP/xxoM3PmTF1++eXKz8+XJD344IMaM2aMnnzySd188816/fXXtWXLFm3fvt2GjwgAwBdwR7nP7dmzR+PHjw+8bjqvPWvWLC1dulT79u3TqlWrdOLECSUnJ2v8+PF67bXXFB8fH2hz5MgRxcR8PkmQmZmpNWvW6Oc//7kee+wx9evXT6+99ppGjRoVzmcDAKAZJ1/SFnJSHzdunEwbv1Deeuut8/ZRVFTUbNutt96qW2+9NdRwAADAP3DvdwCAu7D6HQAAZ7CMkRXmOfFw20cKz1MHAMAhGKkDANzF/48Sbh9RiKQOAHAVpt8BAEDUY6QOAHAXVr8DAOAQ3FEOAABncPId5TinDgCAQzBSBwC4C9PvAAA4g+U/V8LtIxox/Q4AgEOQ1AEA7tI0/R5uCcG2bds0efJkpaSkyLIsbdiw4UshGeXm5iolJUVdu3bVuHHjtH///pA/GkkdAOAuxqYSgtOnT2vo0KFasmRJi/sXLVqkxYsXa8mSJdq9e7e8Xq8mTpyokydPhvQ+nFMHACDCsrOzlZ2d3eI+Y4wKCgq0cOFCTZkyRZK0cuVKJSUlafXq1br33nsv+H0YqQMAXKXp3u/hFkmqrq4OKrW1tSHHU1ZWJp/Pp6ysrMA2j8ejsWPHaseOHSH1RVIHALiLjefUU1NTlZiYGCj5+fkhh+Pz+SRJSUlJQduTkpIC+y4U0+8AALRTeXm5EhISAq89Hk+7+7IsK+i1MabZtvMhqQMA3MUo/Oeh/2OhXEJCQlBSbw+v1yvp3Ig9OTk5sL2ysrLZ6P18mH4HALiKnefU7ZCWliav16vCwsLAtrq6OhUXFyszMzOkvhipAwDcxciG28SGVv3UqVP66KOPAq/LyspUWlqqHj16qE+fPpo3b57y8vKUnp6u9PR05eXlqVu3bpo+fXpI70NSBwAgwvbs2aPx48cHXs+fP1+SNGvWLK1YsUILFizQ2bNnNWfOHB0/flyjRo3S5s2bFR8fH9L7kNQBAO5yER7oMm7cOJk22liWpdzcXOXm5oYVFkkdAOAufkmhLSpvuY8oxEI5AAAcgpE6AMBV7Fi9bufqdzuR1AEA7nIRzql3FKbfAQBwCEbqAAB3cfBInaQOAHAXByd1pt8BAHAIRuoAAHdx8HXqJHUAgKtwSRsAAE7BOfXPbdu2TZMnT1ZKSoosy9KGDRuC9luW1WL59a9/3WqfK1asaLFNTU1NyB8IAAC3Cnmkfvr0aQ0dOlQ/+tGPdMsttzTbX1FREfT6D3/4g+66664W635RQkKCDh48GLQtLi4u1PAAAGib30hWmCNtf3SO1ENO6tnZ2crOzm51v9frDXr9+uuva/z48bryyivb7NeyrGZtAQCwHdPv7fPZZ59p06ZNuuuuu85b99SpU+rbt6969+6tm266SSUlJW3Wr62tVXV1dVABAMDNIprUV65cqfj4eE2ZMqXNegMGDNCKFSu0ceNGvfrqq4qLi9O1116rQ4cOtdomPz9fiYmJgZKammp3+AAARzKfj9bbW+TCkfrLL7+sO+6447znxjMyMvTDH/5QQ4cO1fXXX6/f/e53uuqqq/Tss8+22iYnJ0dVVVWBUl5ebnf4AAAnCjeh2zF9HyERu6TtnXfe0cGDB/Xaa6+F3DYmJkYjR45sc6Tu8Xjk8XjCCREAAEeJ2Eh92bJlGj58uIYOHRpyW2OMSktLlZycHIHIAACu5jf2lCgU8kj91KlT+uijjwKvy8rKVFpaqh49eqhPnz6SpOrqav3+97/X008/3WIfM2fO1OWXX678/HxJ0uOPP66MjAylp6erurpazzzzjEpLS/Xcc8+15zMBANA64z9Xwu0jCoWc1Pfs2aPx48cHXs+fP1+SNGvWLK1YsUKStGbNGhljdPvtt7fYx5EjRxQT8/kkwYkTJ/TjH/9YPp9PiYmJGjZsmLZt26Zrrrkm1PAAAHAty5goPdsfourqaiUmJmqcblZnq8vFDgcAEIIGU68iva6qqiolJCRE5D2a8sS3U/9FnWPCW5PV4K/VlvKlEY23Pbj3OwDAXfw2XJLmlHPqAAB8pXFHOQAAEO0YqQMA3MXIhpG6LZHYjqQOAHAXpt8BAEC0Y6QOAHAXv19SmDeP8Tvk5jMAAHylMf0OAACiHSN1AIC7OHikTlIHALiLg+8ox/Q7AAAOwUgdAOAqxvhlwnx0arjtI4WkDgBwF2PCnz7nnDoAAFHA2HBOPUqTOufUAQBwCEbqAAB38fslK8xz4pxTBwAgCjD9DgAAoh0jdQCAqxi/XybM6XcuaQMAIBow/Q4AAKIdI3UAgLv4jWQ5c6ROUgcAuIsxksK9pC06kzrT7wAAOAQjdQCAqxi/kQlz+t1E6UidpA4AcBfjV/jT71zSBgDARefkkTrn1AEAcAjHjNSbfjU1qD7sewoAADpWg+oldcwIuMHUhj193hRvtHFMUj958qQkabveuMiRAADa6+TJk0pMTIxI37GxsfJ6vdrusydPeL1excbG2tKXXSwTrScGQuT3+/Xpp58qPj5elmW1WKe6ulqpqakqLy9XQkJCB0fYfsTd8b6qsRN3xyJu+xhjdPLkSaWkpCgmJnJnhmtqalRXV2dLX7GxsYqLi7OlL7s4ZqQeExOj3r17X1DdhISEqPkih4K4O95XNXbi7ljEbY9IjdC/KC4uLuoSsZ1YKAcAgEOQ1AEAcAhXJXWPx6Nf/OIX8ng8FzuUkBB3x/uqxk7cHYu4EW0cs1AOAAC3c9VIHQAAJyOpAwDgECR1AAAcgqQOAIBDOC6pP//880pLS1NcXJyGDx+ud955p836xcXFGj58uOLi4nTllVfqhRde6KBIz8nPz9fIkSMVHx+vXr166fvf/74OHjzYZpuioiJZltWs/PWvf+2gqKXc3Nxm7+/1ettsc7GPdZMrrriixeM3d+7cFutfrOO9bds2TZ48WSkpKbIsSxs2bAjab4xRbm6uUlJS1LVrV40bN0779+8/b79r167VwIED5fF4NHDgQK1fv77D4q6vr9fPfvYzDRkyRN27d1dKSopmzpypTz/9tM0+V6xY0eLfoKampkPilqTZs2c3e/+MjIzz9nsxj7ekFo+bZVn69a9/3WqfHXG8ERmOSuqvvfaa5s2bp4ULF6qkpETXX3+9srOzdeTIkRbrl5WV6cYbb9T111+vkpISPfroo/rJT36itWvXdljMxcXFmjt3rnbt2qXCwkI1NDQoKytLp0+fPm/bgwcPqqKiIlDS09M7IOLPDRo0KOj99+3b12rdaDjWTXbv3h0Ud2FhoSTpBz/4QZvtOvp4nz59WkOHDtWSJUta3L9o0SItXrxYS5Ys0e7du+X1ejVx4sTAcxBasnPnTk2bNk0zZszQ+++/rxkzZmjq1Kl69913OyTuM2fOaO/evXrssce0d+9erVu3Th9++KG+973vnbffhISEoONfUVFh653Bzne8Jek73/lO0Pu/8Ubb9xC/2MdbUrNj9vLLL8uyLN1yyy1t9hvp440IMQ5yzTXXmPvuuy9o24ABA8wjjzzSYv0FCxaYAQMGBG279957TUZGRsRiPJ/KykojyRQXF7daZ+vWrUaSOX78eMcF9iW/+MUvzNChQy+4fjQe6yYPPvig6devn/H7/S3uj4bjLcmsX78+8Nrv9xuv12ueeOKJwLaamhqTmJhoXnjhhVb7mTp1qvnOd74TtG3SpEnmtttusz1mY5rH3ZI//elPRpI5fPhwq3WWL19uEhMT7Q2uDS3FPWvWLHPzzTeH1E80Hu+bb77Z3HDDDW3W6ejjDfs4ZqReV1en9957T1lZWUHbs7KytGPHjhbb7Ny5s1n9SZMmac+ePaqvvziP1auqqpIk9ejR47x1hw0bpuTkZE2YMEFbt26NdGjNHDp0SCkpKUpLS9Ntt92mjz/+uNW60XispXPfm1deeUV33nlnqw8CanKxj/cXlZWVyefzBR1Tj8ejsWPHtvp9l1r/O7TVJtKqqqpkWZYuvfTSNuudOnVKffv2Ve/evXXTTTeppKSkYwL8gqKiIvXq1UtXXXWV7rnnHlVWVrZZP9qO92effaZNmzbprrvuOm/daDjeCJ1jkvrRo0fV2NiopKSkoO1JSUny+XwttvH5fC3Wb2ho0NGjRyMWa2uMMZo/f76uu+46DR48uNV6ycnJevHFF7V27VqtW7dO/fv314QJE7Rt27YOi3XUqFFatWqV3nrrLb300kvy+XzKzMzUsWPHWqwfbce6yYYNG3TixAnNnj271TrRcLy/rOk7Hcr3valdqG0iqaamRo888oimT5/e5oNFBgwYoBUrVmjjxo169dVXFRcXp2uvvVaHDh3qsFizs7P129/+Vm+//baefvpp7d69WzfccINqa2tbbRNtx3vlypWKj4/XlClT2qwXDccb7eOYp7Q1+fJoyxjT5gispfotbe8I999/v/785z9r+/btbdbr37+/+vfvH3g9evRolZeX66mnntKYMWMiHaakc/+BazJkyBCNHj1a/fr108qVKzV//vwW20TTsW6ybNkyZWdnKyUlpdU60XC8WxPq9729bSKhvr5et912m/x+v55//vk262ZkZAQtSrv22mv1rW99S88++6yeeeaZSIcqSZo2bVrgnwcPHqwRI0aob9++2rRpU5tJMlqOtyS9/PLLuuOOO857bjwajjfaxzEj9a9//evq1KlTs1/AlZWVzX4pN/F6vS3W79y5sy677LKIxdqSBx54QBs3btTWrVsv+BGyX5SRkXFRf0V3795dQ4YMaTWGaDrWTQ4fPqwtW7bo7rvvDrntxT7eTVcahPJ9b2oXaptIqK+v19SpU1VWVqbCwsKQH/8ZExOjkSNHXtS/QXJysvr27dtmDNFyvCXpnXfe0cGDB9v1fY+G440L45ikHhsbq+HDhwdWMjcpLCxUZmZmi21Gjx7drP7mzZs1YsQIdenSJWKxfpExRvfff7/WrVunt99+W2lpae3qp6SkRMnJyTZHd+Fqa2t14MCBVmOIhmP9ZcuXL1evXr303e9+N+S2F/t4p6Wlyev1Bh3Turo6FRcXt/p9l1r/O7TVxm5NCf3QoUPasmVLu37UGWNUWlp6Uf8Gx44dU3l5eZsxRMPxbrJs2TINHz5cQ4cODbltNBxvXKCLtUIvEtasWWO6dOlili1bZj744AMzb9480717d/O3v/3NGGPMI488YmbMmBGo//HHH5tu3bqZhx56yHzwwQdm2bJlpkuXLua///u/Oyzmf/mXfzGJiYmmqKjIVFRUBMqZM2cCdb4c929+8xuzfv168+GHH5q//OUv5pFHHjGSzNq1azss7p/+9KemqKjIfPzxx2bXrl3mpptuMvHx8VF9rL+osbHR9OnTx/zsZz9rti9ajvfJkydNSUmJKSkpMZLM4sWLTUlJSWCV+BNPPGESExPNunXrzL59+8ztt99ukpOTTXV1daCPGTNmBF398cc//tF06tTJPPHEE+bAgQPmiSeeMJ07dza7du3qkLjr6+vN9773PdO7d29TWloa9J2vra1tNe7c3Fzz5ptvmv/93/81JSUl5kc/+pHp3Lmzeffddzsk7pMnT5qf/vSnZseOHaasrMxs3brVjB492lx++eVRfbybVFVVmW7dupmlS5e22MfFON6IDEcldWOMee6550zfvn1NbGys+da3vhV0adisWbPM2LFjg+oXFRWZYcOGmdjYWHPFFVe0+qWPFEktluXLl7ca95NPPmn69etn4uLizNe+9jVz3XXXmU2bNnVo3NOmTTPJycmmS5cuJiUlxUyZMsXs37+/1ZiNufjH+oveeustI8kcPHiw2b5oOd5Nl9J9ucyaNcsYc+6ytl/84hfG6/Uaj8djxowZY/bt2xfUx9ixYwP1m/z+9783/fv3N126dDEDBgyw/cdJW3GXlZW1+p3funVrq3HPmzfP9OnTx8TGxpqePXuarKwss2PHjg6L+8yZMyYrK8v07NnTdOnSxfTp08fMmjXLHDlyJKiPaDveTf7jP/7DdO3a1Zw4caLFPi7G8UZk8OhVAAAcwjHn1AEAcDuSOgAADkFSBwDAIUjqAAA4BEkdAACHIKkDAOAQJHUAAByCpA4AgEOQ1AEAcAiSOgAADkFSBwDAIUjqAAA4xP8D7z4vfwrZU84AAAAASUVORK5CYII=", "text/plain": [ "
" ] diff --git a/proto/FTCS.ipynb b/proto/FTCS.ipynb index d6fecd9..ed81614 100644 --- a/proto/FTCS.ipynb +++ b/proto/FTCS.ipynb @@ -51,7 +51,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 15, "metadata": {}, "outputs": [ { @@ -234,7 +234,7 @@ }, { "cell_type": "code", - "execution_count": 115, + "execution_count": 17, "metadata": {}, "outputs": [], "source": [ @@ -333,12 +333,20 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 18, "metadata": {}, "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/var/folders/8m/wj5j2vnd3c776jn9kyzj818r0000gn/T/ipykernel_58661/2955654588.py:6: RuntimeWarning: divide by zero encountered in scalar divide\n", + " return 2 / ((1/alpha1) + (1/alpha2))\n" + ] + }, { "data": { - "image/png": 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", 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", 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" ] @@ -351,7 +359,7 @@ "records = []\n", "\n", "for i in range(100):\n", - " C_t = simulate_constant_boundary(C_t)\n", + " C_t = simulate_closed_boundary(C_t)\n", " records.append(C_t)\n", "\n", "# with np.printoptions(precision=2,floatmode='fixed',linewidth=200):\n", @@ -364,12 +372,12 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 19, "metadata": {}, "outputs": [ { "data": { - "image/png": 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", + "image/png": 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", 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