run_demo_elasticity_2d.ipynb
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Test number 1: BNN + GenEO "
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Subdomain number 0 contributes 0 coarse vectors as zero energy modes of local solver\n",
"Subdomain number 1 contributes 3 coarse vectors as zero energy modes of local solver\n",
"Subdomain number 3 contributes 3 coarse vectors as zero energy modes of local solver\n",
"Subdomain number 2 contributes 3 coarse vectors as zero energy modes of local solver\n",
"GenEO eigenvalue number 0 for lambdamax in subdomain 2: (1.4945905644205672e-06+0j)\n",
"GenEO eigenvalue number 1 for lambdamax in subdomain 2: (1.3826304534084137e-05+0j)\n",
"GenEO eigenvalue number 2 for lambdamax in subdomain 2: (4.5054862699016505e-05+0j)\n",
"GenEO eigenvalue number 3 for lambdamax in subdomain 2: (0.05405868128473235+0j) <-- not selected (> 0.002)\n",
"GenEO eigenvalue number 4 for lambdamax in subdomain 2: (0.054059009027747504+0j) <-- not selected (> 0.002)\n",
"GenEO eigenvalue number 5 for lambdamax in subdomain 2: (0.056663048124898245+0j) <-- not selected (> 0.002)\n",
"GenEO eigenvalue number 6 for lambdamax in subdomain 2: (0.05707962286789531+0j) <-- not selected (> 0.002)\n",
"GenEO eigenvalue number 7 for lambdamax in subdomain 2: (0.1590121284975672+0j) <-- not selected (> 0.002)\n",
"GenEO eigenvalue number 8 for lambdamax in subdomain 2: (0.15905866059775023+0j) <-- not selected (> 0.002)\n",
"GenEO eigenvalue number 9 for lambdamax in subdomain 2: (0.22127754627425406+0j) <-- not selected (> 0.002)\n",
"Subdomain number 2 contributes 6 coarse vectors after first GenEO\n",
"Subdomain number 2 contributes 6 coarse vectors in total\n",
"GenEO eigenvalue number 0 for lambdamax in subdomain 1: (1.4945905644205672e-06+0j)\n",
"GenEO eigenvalue number 1 for lambdamax in subdomain 1: (1.3826304534084137e-05+0j)\n",
"GenEO eigenvalue number 2 for lambdamax in subdomain 1: (4.5054862699016505e-05+0j)\n",
"GenEO eigenvalue number 3 for lambdamax in subdomain 1: (0.05405868128473235+0j) <-- not selected (> 0.002)\n",
"GenEO eigenvalue number 4 for lambdamax in subdomain 1: (0.054059009027747504+0j) <-- not selected (> 0.002)\n",
"GenEO eigenvalue number 5 for lambdamax in subdomain 1: (0.056663048124898245+0j) <-- not selected (> 0.002)\n",
"GenEO eigenvalue number 6 for lambdamax in subdomain 1: (0.05707962286789531+0j) <-- not selected (> 0.002)\n",
"GenEO eigenvalue number 7 for lambdamax in subdomain 1: (0.1590121284975672+0j) <-- not selected (> 0.002)\n",
"GenEO eigenvalue number 8 for lambdamax in subdomain 1: (0.15905866059775023+0j) <-- not selected (> 0.002)\n",
"GenEO eigenvalue number 9 for lambdamax in subdomain 1: (0.22127754627425406+0j) <-- not selected (> 0.002)\n",
"Subdomain number 1 contributes 6 coarse vectors after first GenEO\n",
"Subdomain number 1 contributes 6 coarse vectors in total\n",
"GenEO eigenvalue number 0 for lambdamax in subdomain 0: (0.00031732419879194125+0j)\n",
"GenEO eigenvalue number 1 for lambdamax in subdomain 0: (0.0003370240261628236+0j)\n",
"GenEO eigenvalue number 2 for lambdamax in subdomain 0: (0.028282401567833855+0j) <-- not selected (> 0.002)\n",
"GenEO eigenvalue number 3 for lambdamax in subdomain 0: (0.028283168511417482+0j) <-- not selected (> 0.002)\n",
"GenEO eigenvalue number 4 for lambdamax in subdomain 0: (0.111982986271491+0j) <-- not selected (> 0.002)\n",
"GenEO eigenvalue number 5 for lambdamax in subdomain 0: (0.11219184197646168+0j) <-- not selected (> 0.002)\n",
"GenEO eigenvalue number 6 for lambdamax in subdomain 0: (0.22129077270330236+0j) <-- not selected (> 0.002)\n",
"GenEO eigenvalue number 7 for lambdamax in subdomain 0: (0.2212907735051293+0j) <-- not selected (> 0.002)\n",
"GenEO eigenvalue number 8 for lambdamax in subdomain 0: (0.5564840670455399+0j) <-- not selected (> 0.002)\n",
"GenEO eigenvalue number 9 for lambdamax in subdomain 0: (0.5839813243185191+0j) <-- not selected (> 0.002)\n",
"Subdomain number 0 contributes 2 coarse vectors after first GenEO\n",
"This is BNN so eigmin = 1, no eigenvalue problem will be solved for eigmin\n",
"Subdomain number 0 contributes 2 coarse vectors in total\n",
"GenEO eigenvalue number 0 for lambdamax in subdomain 3: (2.1208234833446384e-05+0j)\n",
"GenEO eigenvalue number 1 for lambdamax in subdomain 3: (3.18585278025384e-05+0j)\n",
"GenEO eigenvalue number 2 for lambdamax in subdomain 3: (0.008267951049146533+0j) <-- not selected (> 0.002)\n",
"GenEO eigenvalue number 3 for lambdamax in subdomain 3: (0.22129069514149202+0j) <-- not selected (> 0.002)\n",
"GenEO eigenvalue number 4 for lambdamax in subdomain 3: (0.22129069789192596+0j) <-- not selected (> 0.002)\n",
"GenEO eigenvalue number 5 for lambdamax in subdomain 3: (0.5564838682522003+0j) <-- not selected (> 0.002)\n",
"GenEO eigenvalue number 6 for lambdamax in subdomain 3: (0.5839813228857347+0j) <-- not selected (> 0.002)\n",
"GenEO eigenvalue number 7 for lambdamax in subdomain 3: (0.5839813229177968+0j) <-- not selected (> 0.002)\n",
"GenEO eigenvalue number 8 for lambdamax in subdomain 3: (0.6574284065235355+0j) <-- not selected (> 0.002)\n",
"GenEO eigenvalue number 9 for lambdamax in subdomain 3: (0.6574287754614184+0j) <-- not selected (> 0.002)\n",
"GenEO eigenvalue number 10 for lambdamax in subdomain 3: (0.8078884348812645+0j) <-- not selected (> 0.002)\n",
"Subdomain number 3 contributes 5 coarse vectors after first GenEO\n",
"Subdomain number 3 contributes 5 coarse vectors in total\n",
"There are 19 vectors in the coarse space.\n",
" 0 KSP Residual norm 9.515337417150e+00 \n",
" 1 KSP Residual norm 2.241544961913e+00 \n",
" 2 KSP Residual norm 2.096050355878e-01 \n",
" 3 KSP Residual norm 2.583843851009e-02 \n",
" 4 KSP Residual norm 2.926817141436e-03 \n",
" 5 KSP Residual norm 2.212556097743e-03 \n",
" 6 KSP Residual norm 3.194562886397e-04 \n",
" 7 KSP Residual norm 5.660224748481e-05 \n",
" 8 KSP Residual norm 1.603233943223e-05 \n"
]
}
],
"source": [
"!mpiexec -np 4 --oversubscribe python demo_elasticity_2d.py -ksp_monitor -PCBNN_verbose -AMPCG_tau 0 -PCBNN_GenEO true -PCBNN_GenEO_eigmax 1000"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"from plot import plot_solution"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "7c6dd9363c594bafb15d07ef0b19f0d6",
"version_major": 2,
"version_minor": 0
},
"text/plain": [
"HBox(children=(Renderer(camera=PerspectiveCamera(position=(0.0, 0.0, 13.0)), controls=[OrbitControls(controlli…"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot_solution('output_2d', 'solution_2d.vts')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Test number 2: turn GenEO off, use AMPCG instead"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Subdomain number 0 contributes 0 coarse vectors as zero energy modes of local solver\n",
"Subdomain number 0 contributes 0 coarse vectors in total\n",
"Subdomain number 1 contributes 3 coarse vectors as zero energy modes of local solver\n",
"Subdomain number 3 contributes 3 coarse vectors as zero energy modes of local solver\n",
"Subdomain number 1 contributes 3 coarse vectors in total\n",
"Subdomain number 3 contributes 3 coarse vectors in total\n",
"Subdomain number 2 contributes 3 coarse vectors as zero energy modes of local solver\n",
"Subdomain number 2 contributes 3 coarse vectors in total\n",
"There are 9 vectors in the coarse space.\n",
"multipreconditioning initial iteration\n",
" 0 KSP Residual norm 2.004620149430e+02 \n",
"\tnatural_norm -> 2.00462015e+02\n",
"\tti -> 0.00000000e+00\n",
"multipreconditioning this iteration\n",
" 1 KSP Residual norm 4.374828777103e+01 \n",
"\tnatural_norm -> 4.37482878e+01\n",
"\tti -> 7.47461287e-02\n",
"multipreconditioning this iteration\n",
" 2 KSP Residual norm 2.958649246685e+01 \n",
"\tnatural_norm -> 2.95864925e+01\n",
"\tti -> 2.30818061e-04\n",
" 3 KSP Residual norm 1.024755579359e+01 \n",
"\tnatural_norm -> 1.02475558e+01\n",
"\tti -> 5.65467747e-01\n",
" 4 KSP Residual norm 9.372894221106e+00 \n",
"\tnatural_norm -> 9.37289422e+00\n",
"\tti -> 4.89891002e-01\n",
" 5 KSP Residual norm 2.352543555987e+00 \n",
"\tnatural_norm -> 2.35254356e+00\n",
"\tti -> 3.99677455e+00\n",
" 6 KSP Residual norm 7.435092501873e-01 \n",
"\tnatural_norm -> 7.43509250e-01\n",
"\tti -> 5.03558194e+00\n",
" 7 KSP Residual norm 2.836186311046e-01 \n",
"\tnatural_norm -> 2.83618631e-01\n",
"\tti -> 1.11136617e+00\n",
" 8 KSP Residual norm 5.349601693695e-02 \n",
"\tnatural_norm -> 5.34960169e-02\n",
"\tti -> 1.18962182e+01\n",
" 9 KSP Residual norm 2.654138922049e-02 \n",
"\tnatural_norm -> 2.65413892e-02\n",
"\tti -> 2.86043835e+00\n",
" 10 KSP Residual norm 1.551097234944e-02 \n",
"\tnatural_norm -> 1.55109723e-02\n",
"\tti -> 6.35652858e-01\n",
" 11 KSP Residual norm 1.674013551698e-03 \n",
"\tnatural_norm -> 1.67401355e-03\n",
"\tti -> 2.60089314e+01\n",
" 12 KSP Residual norm 3.869200838851e-04 \n",
"\tnatural_norm -> 3.86920084e-04\n",
"\tti -> 9.40812431e+00\n",
" 13 KSP Residual norm 7.112289906963e-05 \n",
"\tnatural_norm -> 7.11228991e-05\n",
"\tti -> 1.70599964e+01\n",
" 14 KSP Residual norm 1.700329004360e-05 \n",
"\tnatural_norm -> 1.70032900e-05\n",
"\tti -> 8.38258375e+00\n"
]
}
],
"source": [
"!mpiexec -np 4 --oversubscribe python demo_elasticity_2d.py -ksp_monitor -PCBNN_verbose -AMPCG_verbose -AMPCG_tau 0.1 -PCBNN_GenEO false "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Test number 3: turn GenEO off, use AMPCG, switch to Additive Schwarz\n",
"\n",
"In this case the $\\tau$-test is useless (because the lower part of the spectrum is problematic) so we turn it off with -AMPCG_fullMP true which means that every iteration is preconditioned"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The user has chosen to switch to Additive Schwarz instead of BNN.\n",
"Subdomain number 0 contributes 0 coarse vectors as zero energy modes of local solver\n",
"Subdomain number 1 contributes 0 coarse vectors as zero energy modes of local solver\n",
"Subdomain number 1 contributes 0 coarse vectors in total\n",
"Subdomain number 2 contributes 0 coarse vectors as zero energy modes of local solver\n",
"Subdomain number 3 contributes 0 coarse vectors as zero energy modes of local solver\n",
"Subdomain number 3 contributes 0 coarse vectors in total\n",
"Subdomain number 2 contributes 0 coarse vectors in total\n",
"Subdomain number 0 contributes 0 coarse vectors in total\n",
"There are 0 vectors in the coarse space.\n",
" 0 KSP Residual norm 1.724079391945e+00 \n",
" 1 KSP Residual norm 3.373302734591e-01 \n",
" 2 KSP Residual norm 2.042876162594e-01 \n",
" 3 KSP Residual norm 2.156223995841e-01 \n",
" 4 KSP Residual norm 1.352561227531e-01 \n",
" 5 KSP Residual norm 1.394282296431e-01 \n",
" 6 KSP Residual norm 1.942448996389e-01 \n",
" 7 KSP Residual norm 3.226564021398e-01 \n",
" 8 KSP Residual norm 4.706847735329e-01 \n",
" 9 KSP Residual norm 2.371689132224e-01 \n",
" 10 KSP Residual norm 2.980361010918e-01 \n",
" 11 KSP Residual norm 1.595884695320e+00 \n",
" 12 KSP Residual norm 1.225731007444e+00 \n",
" 13 KSP Residual norm 1.897029642041e+00 \n",
" 14 KSP Residual norm 2.235755992899e+00 \n",
" 15 KSP Residual norm 9.182951918913e-01 \n",
" 16 KSP Residual norm 1.008821812233e+00 \n",
" 17 KSP Residual norm 7.352608730021e-01 \n",
" 18 KSP Residual norm 1.109783686886e+00 \n",
" 19 KSP Residual norm 1.915717554777e+00 \n",
" 20 KSP Residual norm 2.137625341900e+00 \n",
" 21 KSP Residual norm 3.282705657299e+00 \n",
" 22 KSP Residual norm 1.779953007574e+00 \n",
" 23 KSP Residual norm 4.179889891060e+00 \n",
" 24 KSP Residual norm 2.662846151493e+00 \n",
" 25 KSP Residual norm 4.356862947976e-01 \n",
" 26 KSP Residual norm 6.535717680476e-01 \n",
" 27 KSP Residual norm 1.877307983243e-01 \n",
" 28 KSP Residual norm 2.969194716815e-01 \n",
" 29 KSP Residual norm 3.488046756047e-01 \n",
" 30 KSP Residual norm 2.286702041179e-02 \n",
" 31 KSP Residual norm 5.661239229556e-03 \n",
" 32 KSP Residual norm 1.621064626917e-02 \n",
" 33 KSP Residual norm 2.489920496400e-02 \n",
" 34 KSP Residual norm 2.247672471231e-02 \n",
" 35 KSP Residual norm 5.910146383553e-03 \n",
" 36 KSP Residual norm 5.660960282547e-04 \n",
" 37 KSP Residual norm 2.262037471456e-05 \n"
]
}
],
"source": [
"!mpiexec -np 4 --oversubscribe python demo_elasticity_2d.py -ksp_monitor -PCBNN_verbose -AMPCG_fullMP true -PCBNN_GenEO false -PCBNN_switchtoASM true"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Test number 4: turn GenEO off, don't use AMPCG, switch to Additive Schwarz"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The user has chosen to switch to Additive Schwarz instead of BNN.\n",
"Subdomain number 0 contributes 0 coarse vectors as zero energy modes of local solver\n",
"Subdomain number 1 contributes 0 coarse vectors as zero energy modes of local solver\n",
"Subdomain number 2 contributes 0 coarse vectors as zero energy modes of local solver\n",
"Subdomain number 3 contributes 0 coarse vectors as zero energy modes of local solver\n",
"Subdomain number 0 contributes 0 coarse vectors in total\n",
"Subdomain number 2 contributes 0 coarse vectors in total\n",
"Subdomain number 3 contributes 0 coarse vectors in total\n",
"Subdomain number 1 contributes 0 coarse vectors in total\n",
"There are 0 vectors in the coarse space.\n",
" 0 KSP Residual norm 1.724079391945e+00 \n",
" 1 KSP Residual norm 3.374962873737e-01 \n",
" 2 KSP Residual norm 1.469748887210e-01 \n",
" 3 KSP Residual norm 2.729956941437e-01 \n",
" 4 KSP Residual norm 1.497379150637e-01 \n",
" 5 KSP Residual norm 8.711268434171e-02 \n",
" 6 KSP Residual norm 9.932062571129e-02 \n",
" 7 KSP Residual norm 1.308938077458e-01 \n",
" 8 KSP Residual norm 7.113892815756e-02 \n",
" 9 KSP Residual norm 3.268246252895e-01 \n",
" 10 KSP Residual norm 2.787796870991e-01 \n",
" 11 KSP Residual norm 3.532500573761e-01 \n",
" 12 KSP Residual norm 8.707159935911e-01 \n",
" 13 KSP Residual norm 3.080199843197e-01 \n",
" 14 KSP Residual norm 9.663025317604e-02 \n",
" 15 KSP Residual norm 1.767978874232e-01 \n",
" 16 KSP Residual norm 2.783133360999e-01 \n",
" 17 KSP Residual norm 3.797967838183e-01 \n",
" 18 KSP Residual norm 2.444097106069e+00 \n",
" 19 KSP Residual norm 4.703851916928e+00 \n",
" 20 KSP Residual norm 1.730876887992e+00 \n",
" 21 KSP Residual norm 2.363568671910e+00 \n",
" 22 KSP Residual norm 6.055456447926e+00 \n",
" 23 KSP Residual norm 2.194455974272e+00 \n",
" 24 KSP Residual norm 5.704302750970e-01 \n",
" 25 KSP Residual norm 1.433095612482e+00 \n",
" 26 KSP Residual norm 6.403771961174e-01 \n",
" 27 KSP Residual norm 2.144832889194e-01 \n",
" 28 KSP Residual norm 1.400619575381e-01 \n",
" 29 KSP Residual norm 1.318994656417e-01 \n",
" 30 KSP Residual norm 2.562475790344e-01 \n",
" 31 KSP Residual norm 4.513054641844e-01 \n",
" 32 KSP Residual norm 4.926135067656e-01 \n",
" 33 KSP Residual norm 4.476392862232e-01 \n",
" 34 KSP Residual norm 1.341720071537e-01 \n",
" 35 KSP Residual norm 1.439982024707e-01 \n",
" 36 KSP Residual norm 1.268024095395e-01 \n",
" 37 KSP Residual norm 1.941361920604e-02 \n",
" 38 KSP Residual norm 1.108621764821e-02 \n",
" 39 KSP Residual norm 5.672737676361e-02 \n",
" 40 KSP Residual norm 1.726607226972e-01 \n",
" 41 KSP Residual norm 1.214300901300e-01 \n",
" 42 KSP Residual norm 1.436946553821e-01 \n",
" 43 KSP Residual norm 2.131249012577e-01 \n",
" 44 KSP Residual norm 1.080970611095e-01 \n",
" 45 KSP Residual norm 1.428241474487e-01 \n",
" 46 KSP Residual norm 3.100144584693e-02 \n",
" 47 KSP Residual norm 1.226502474853e-02 \n",
" 48 KSP Residual norm 4.119697660803e-03 \n",
" 49 KSP Residual norm 3.077879923914e-03 \n",
" 50 KSP Residual norm 1.091483838563e-03 \n",
" 51 KSP Residual norm 3.214339363955e-04 \n",
" 52 KSP Residual norm 7.505519085313e-04 \n",
" 53 KSP Residual norm 8.117732046764e-04 \n",
" 54 KSP Residual norm 8.653837675167e-05 \n",
" 55 KSP Residual norm 1.413254191641e-05 \n"
]
}
],
"source": [
"!mpiexec -np 4 --oversubscribe python demo_elasticity_2d.py -ksp_monitor -PCBNN_verbose -AMPCG_tau 0 -PCBNN_GenEO false -PCBNN_switchtoASM true"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
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