{ "format": "fastandaccurate-result", "formatVersion": 1, "problem": "laplace-dirichlet-2d", "problemVersion": 1, "instance": "star-nearfield", "spec": { "a": 0.3, "d": 0.08, "instance": "star-nearfield", "k": 5, "problem": "laplace-dirichlet-2d", "problemVersion": 1, "nearBoundary": true }, "specHash": "8283a59db276842f8024202c0ee279cf8052854b709e0bfa12b687fe00fd5df0", "solver": { "id": "mfs", "version": "1.0.0", "backend": "cpu", "source": "builtin" }, "environment": { "kind": "node", "runtime": "node v24.14.1", "numblVersion": "0.4.18", "os": "linux 6.12.101+deb13-amd64", "cpu": "13th Gen Intel(R) Core(TM) i7-1355U", "machineLabel": "linux laptop (i7-1355U)", "browserReproducible": true }, "protocol": { "warmupRuns": 2, "minTimedRuns": 5, "timeBudgetSeconds": 0.5, "maxTimedRuns": 50, "statistic": "min", "timer": "numbl tic/toc" }, "createdUtc": "2026-08-18T20:33:47.660Z", "points": [ { "n": 8, "solveSeconds": 0.0003730760000000277, "solveSecondsAll": [ 0.003125150000000021, 0.00139725199999996, 0.0010082099999999539, 0.0010181120000000154, 0.0008684319999999746, 0.0007769420000000027, 0.0008356969999999686, 0.0008172220000000063, 0.0009612820000000077, 0.0007868940000000935, 0.0007901590000000125, 0.0006393790000001065, 0.0005808959999999974, 0.0006631730000000724, 0.0005955709999999614, 0.0005710219999999211, 0.0006165599999999882, 0.0005584189999999767, 0.0005934779999999806, 0.0006233669999999858, 0.0007212400000001784, 0.0005891239999999964, 0.0006525259999999866, 0.0005425089999999688, 0.0005261579999999988, 0.0004942000000000002, 0.0005776790000000531, 0.0005340729999999683, 0.000493216000000074, 0.0004758379999999507, 0.0005082830000000538, 0.0005169400000000213, 0.00046757199999991617, 0.0005201979999999162, 0.00048075800000002555, 0.0004912050000001056, 0.0005083940000000231, 0.0004429740000000404, 0.00043472099999997127, 0.00047447099999997633, 0.000413168999999991, 0.0004075699999999127, 0.0004357039999999257, 0.00040846699999996794, 0.0003730760000000277, 0.0003988529999999768, 0.00041913699999995835, 0.00037718700000000105, 0.00039044900000007043, 0.00039998399999996437 ], "coldSeconds": 0.011212071000000101, "relMax": 0.31876908283445937, "relL2": 0.22920408611780665 }, { "n": 12, "solveSeconds": 0.0003616229999999776, "solveSecondsAll": [ 0.0006032200000000154, 0.000494377999999962, 0.0005061459999999851, 0.0004890310000000841, 0.0005192880000000066, 0.0005678070000000313, 0.0005432199999999554, 0.0005610839999999895, 0.0005019580000000801, 0.0006140939999998984, 0.0004883820000000094, 0.00048635399999996665, 0.0004306939999999537, 0.00040866100000003236, 0.00039668999999997734, 0.0003884369999999082, 0.00045595300000000893, 0.000441741000000051, 0.0004301190000000066, 0.00040903999999997165, 0.004104247000000005, 0.0007954270000000152, 0.0005002370000000145, 0.00045177799999995827, 0.0004244550000001013, 0.00043456499999994236, 0.0004819130000000005, 0.00046979700000004954, 0.00043659899999992646, 0.00042705300000001056, 0.000474388999999964, 0.0004555000000000531, 0.0004575649999999376, 0.00046626199999999507, 0.0004836010000001112, 0.0004336890000000704, 0.0003978040000001126, 0.00038466900000011517, 0.0003969440000001212, 0.00044268000000013963, 0.00039837900000005977, 0.0003616229999999776, 0.0003698320000000699, 0.00038889200000002955, 0.00036612999999996454, 0.0004314519999999433, 0.00039004200000003486, 0.00039424300000001633, 0.0004959139999999307, 0.0004937890000000777 ], "coldSeconds": 0.0064490779999999415, "relMax": 0.6479335663256959, "relL2": 0.31490611239376337 }, { "n": 16, "solveSeconds": 0.0003546039999999806, "solveSecondsAll": [ 0.0005790629999999908, 0.0005002870000001547, 0.00042611700000017017, 0.00044559500000007635, 0.00044311600000002116, 0.00041415299999991717, 0.00043852700000002187, 0.0004739489999998625, 0.00042839500000002584, 0.0004151399999998695, 0.00036491699999996463, 0.0004274979999999706, 0.00038565800000001094, 0.00037665299999989355, 0.0004553509999999372, 0.0004199179999999636, 0.00043754900000003705, 0.0003929400000000083, 0.0003771439999998849, 0.0003884480000000412, 0.0003823649999999956, 0.0003546039999999806, 0.0004422280000000445, 0.000502189999999958, 0.00046024099999997237, 0.00045793599999999213, 0.0005501089999999653, 0.0005376710000000173, 0.0005044760000000315, 0.00048647100000009935, 0.0006232560000001275, 0.0005006990000000489, 0.0004982050000000848, 0.0005520609999999371, 0.0004889839999999701, 0.0005241830000000114, 0.0005001929999999266, 0.0004999589999999943, 0.00047232399999996844, 0.0004833039999999622, 0.00045538099999997694, 0.00047127999999996284, 0.0004782469999999872, 0.0005108190000000512, 0.00047816899999997275, 0.0004507430000000312, 0.0004758719999999883, 0.0004543140000000667, 0.0005274840000001335, 0.0005476840000000482 ], "coldSeconds": 0.007300886999999978, "relMax": 0.15566792181802974, "relL2": 0.09010733269316437 }, { "n": 24, "solveSeconds": 0.00042173599999995037, "solveSecondsAll": [ 0.0008196079999999162, 0.0006905130000000037, 0.0006281619999999322, 0.0006567880000000192, 0.0005833280000000496, 0.0006223519999999372, 0.0006551460000000509, 0.0006205440000001117, 0.0011835659999999137, 0.006597966000000066, 0.0008646460000000245, 0.0006496979999999208, 0.0005196040000000623, 0.0004538649999998867, 0.0004754790000001119, 0.0004845360000000909, 0.00042840899999996296, 0.000651318999999928, 0.00047134800000003807, 0.0004950989999999988, 0.00045337700000003256, 0.0004840019999999834, 0.0005110819999999405, 0.0005311340000000442, 0.0005108349999999318, 0.000533379000000056, 0.0004969710000001237, 0.0004444829999999955, 0.0004746079999999875, 0.0004762289999999947, 0.000432969999999977, 0.00044974799999997206, 0.00042886399999997327, 0.000438149999999915, 0.0004732430000000676, 0.0004370209999999819, 0.0004793669999999528, 0.00044144499999998477, 0.00045081700000004776, 0.0004995290000000541, 0.00044637800000002503, 0.0004323929999999754, 0.00042173599999995037, 0.0004260069999999505, 0.0004278160000000808, 0.0004305620000000232, 0.0004303050000000752, 0.0004435309999999415, 0.00048746599999993645, 0.0004880149999999528 ], "coldSeconds": 0.00802431299999995, "relMax": 0.11505858289222723, "relL2": 0.06007397726136398 }, { "n": 32, "solveSeconds": 0.00048658099999998594, "solveSecondsAll": [ 0.0006665390000000215, 0.0006087200000001181, 0.0005621559999999803, 0.0005607089999999371, 0.0005421199999999793, 0.000565331999999974, 0.0005129839999999941, 0.0004920489999999944, 0.00048658099999998594, 0.0005631589999999242, 0.0005331249999999121, 0.000561151000000093, 0.0005691129999999545, 0.0011905739999999998, 0.001102348999999947, 0.0011384169999999472, 0.0011957760000000928, 0.0009474550000000415, 0.0008990829999999672, 0.0009245239999999821, 0.000995495999999929, 0.0010442360000001427, 0.0008992990000000756, 0.0008919290000000135, 0.0009757290000000918, 0.0009150249999999582, 0.0009626459999999559, 0.00112646499999991, 0.0011139860000000112, 0.0009698339999999472, 0.0009266130000001871, 0.0011687659999999322, 0.0013337069999999063, 0.001703488999999947, 0.0075999549999998806, 0.0012915340000000386, 0.00116814799999998, 0.0012075230000000436, 0.0009841600000000117, 0.000948217000000029, 0.0011615970000000697, 0.0009858379999999611, 0.0009377710000000317, 0.0009671700000000172, 0.0009596000000000604, 0.0009353429999999774, 0.0008870530000001375, 0.0008866480000000454, 0.0009375029999999507, 0.0008888709999999023 ], "coldSeconds": 0.008028843000000063, "relMax": 3.4231353851200677, "relL2": 0.8095640158692636 }, { "n": 48, "solveSeconds": 0.0005720020000000714, "solveSecondsAll": [ 0.0013164669999999878, 0.0013122679999998388, 0.0009750520000000318, 0.0007393150000000182, 0.000624778000000048, 0.0005765830000000749, 0.0005720020000000714, 0.0006578599999998991, 0.0006351949999999773, 0.0006768200000000224, 0.0005869410000000075, 0.0007849079999999731, 0.0010304559999999574, 0.0010798240000000625, 0.000828556999999952, 0.0008389480000000615, 0.0008575500000000957, 0.000759913000000001, 0.0007320299999998836, 0.0007206490000001287, 0.0007001960000000418, 0.0007277530000000532, 0.0007784170000000312, 0.000722728999999922, 0.0006887500000000157, 0.0006613489999999222, 0.0006873640000000236, 0.0006473449999999659, 0.000646185999999993, 0.0013437080000000545, 0.006114457000000018, 0.0013992449999998824, 0.0008341410000000105, 0.0006408130000000734, 0.0006955560000000416, 0.0006584139999999961, 0.0006797339999999874, 0.0006317590000000095, 0.0006176870000000889, 0.0007245619999999287, 0.0006913070000000854, 0.000710407000000024, 0.0006968210000000141, 0.0006987659999999618, 0.0006828380000000189, 0.0007012060000000098, 0.0009801489999999857, 0.0008618599999999921, 0.0006934649999998932, 0.0006577289999999403 ], "coldSeconds": 0.013754386000000007, "relMax": 0.13224837934128633, "relL2": 0.05823182181528383 }, { "n": 64, "solveSeconds": 0.0007699029999999052, "solveSecondsAll": [ 0.0009835209999999872, 0.0009356970000000686, 0.0008368739999999875, 0.0008415320000000337, 0.0008256149999998907, 0.0008584030000000631, 0.0008286940000000742, 0.0008564979999999833, 0.0008679620000000554, 0.0008680130000000563, 0.0016208470000000919, 0.0018920259999999356, 0.0016260070000000404, 0.002005150999999983, 0.008601794000000051, 0.0019034629999999941, 0.0016478709999999674, 0.0016049089999999877, 0.0008394270000000592, 0.0008459550000000648, 0.0007699029999999052, 0.0007832379999999084, 0.0014410659999999353, 0.001403539999999981, 0.0015341920000000453, 0.0012056510000000298, 0.0010962569999999339, 0.0011171880000000467, 0.0011137720000000684, 0.0010357690000000197, 0.0010831649999998305, 0.0009840219999999178, 0.0009633579999999142, 0.000931652000000005, 0.0009044529999999718, 0.0008932029999999536, 0.000930968000000032, 0.0008949299999998495, 0.0008691499999999852, 0.0008449580000000623, 0.0008781260000001456, 0.0008739550000000929, 0.0008915739999999506, 0.0008820090000001279, 0.0016195629999999905, 0.006487531000000102, 0.0016058939999998856, 0.0008839720000002327, 0.0007706490000001232, 0.0008042729999999665 ], "coldSeconds": 0.011021999999999976, "relMax": 0.29779805277278637, "relL2": 0.09689817562048464 }, { "n": 96, "solveSeconds": 0.0015216520000000955, "solveSecondsAll": [ 0.0019049970000000194, 0.0017682279999999828, 0.0017609450000000137, 0.001655557999999946, 0.0016335030000000916, 0.001644704999999913, 0.001540918999999974, 0.0015216520000000955, 0.0015556580000000153, 0.0016051630000000205, 0.0016416120000000145, 0.0015641809999997758, 0.0015543009999998691, 0.003551288999999791, 0.004375151999999716, 0.0015948390000000146, 0.0015725549999998645, 0.0015952040000000167, 0.0017058719999998306, 0.0017711510000000263, 0.0016385650000001473, 0.0016222660000000388, 0.00163408399999998, 0.0015520349999997851, 0.001562378000000031, 0.0016570250000000897, 0.0016440230000001055, 0.0016136950000000816, 0.0016662789999999372, 0.0016312779999998472, 0.0017239660000001322, 0.001643032999999905, 0.0025600990000000934, 0.0050439550000001, 0.0016291750000001493, 0.0015540380000000908, 0.0015833280000001615, 0.0015560049999998604, 0.0015553919999999888, 0.0016540599999996797, 0.0015858900000000897, 0.0016254209999999603, 0.0016757299999998754, 0.001674583999999868, 0.001592955000000229, 0.0016256370000000686, 0.0015769510000001041, 0.001579897999999913, 0.0015323559999997904, 0.0016138289999998445 ], "coldSeconds": 0.01246248800000016, "relMax": 0.20533227296706327, "relL2": 0.06144931735410734 }, { "n": 128, "solveSeconds": 0.002266533000000015, "solveSecondsAll": [ 0.002702333000000001, 0.0026404780000002237, 0.0032337380000000415, 0.003000654000000047, 0.002775087000000065, 0.0027193750000000794, 0.002700878999999823, 0.0026291810000000915, 0.0026125190000001464, 0.002580638999999829, 0.002682202999999772, 0.0030645170000001, 0.006535508000000023, 0.003095075000000058, 0.0025361959999998795, 0.002622651999999892, 0.002871376000000092, 0.0027755980000001568, 0.0027946609999998095, 0.002717335000000043, 0.002766669999999971, 0.0026639100000001026, 0.002712277999999957, 0.002835021000000104, 0.0031035339999998524, 0.007718618000000177, 0.00396505700000005, 0.002266533000000015, 0.0031791469999999933, 0.0024731039999998927, 0.002405572999999883, 0.0034752250000000817, 0.002569132000000085, 0.0035217240000002814, 0.0024124239999998576, 0.002535822000000021, 0.0036020130000000705, 0.003166262000000142, 0.008441194999999846, 0.0025453250000000427, 0.0025930549999999553, 0.0037451699999999644, 0.002678984999999967, 0.0037932780000000665, 0.0024917330000000515, 0.003483517000000047, 0.0026778690000002214, 0.002644528000000035, 0.003303052999999778, 0.002563057999999785 ], "coldSeconds": 0.020638788999999935, "relMax": 0.4713234244281906, "relL2": 0.1617527727044675 }, { "n": 192, "solveSeconds": 0.0055746779999998886, "solveSecondsAll": [ 0.007509042999999993, 0.007333938000000151, 0.007259516999999827, 0.007092363000000157, 0.007700969999999918, 0.008307365000000289, 0.011374999000000052, 0.008533112000000065, 0.007161982000000178, 0.006984745000000014, 0.007229753999999922, 0.0070803319999999115, 0.007353799999999744, 0.007537260999999962, 0.011777249999999961, 0.007385141999999956, 0.006972546000000079, 0.006923805000000005, 0.0073399880000000195, 0.006914336999999771, 0.0068751340000001715, 0.009976637999999927, 0.007133661999999985, 0.006834331000000082, 0.0072160169999999635, 0.006941606999999905, 0.006756065999999894, 0.007049708000000043, 0.0071161619999999814, 0.011448497000000168, 0.007015219999999989, 0.007187508999999981, 0.007039876999999972, 0.007156032000000145, 0.007145144999999964, 0.007013491000000149, 0.0073267140000001785, 0.011349509000000202, 0.007121487000000037, 0.007019453000000286, 0.007203497999999975, 0.007019761999999874, 0.007066190999999833, 0.006111321999999975, 0.00706436800000021, 0.008914945000000118, 0.0055746779999998886, 0.005929548999999978, 0.006017936999999973, 0.005992917000000153 ], "coldSeconds": 0.03088530399999989, "relMax": 0.009254776177763296, "relL2": 0.0023102909112462855 }, { "n": 256, "solveSeconds": 0.011594202000000386, "solveSecondsAll": [ 0.013552035999999879, 0.01266874699999998, 0.012991230999999992, 0.016487714000000153, 0.014902577999999833, 0.017898860000000072, 0.012332044000000097, 0.012551594000000055, 0.013170399999999916, 0.013113612999999802, 0.016137999000000125, 0.01269804100000016, 0.012724765000000193, 0.01254966500000032, 0.012869307999999524, 0.013254293000000139, 0.016331702999999642, 0.012797780000000092, 0.013139792000000039, 0.012761458000000392, 0.013013007000000076, 0.01678213900000003, 0.01282340599999987, 0.012735125000000291, 0.01279719200000029, 0.012958683999999554, 0.015838100999999938, 0.012125751999999768, 0.011594202000000386, 0.011963198999999758, 0.01210469500000011, 0.0144870410000002, 0.012507391000000201, 0.012359249999999822, 0.012304525999999871, 0.012371409000000444, 0.012778954000000287, 0.015895709999999674 ], "coldSeconds": 0.03166890499999986, "relMax": 0.05171407811485954, "relL2": 0.014473176284697962 }, { "n": 384, "solveSeconds": 0.03560884999999958, "solveSecondsAll": [ 0.0408802399999999, 0.03596451899999975, 0.03635384300000011, 0.04092481200000009, 0.035769103000000246, 0.03601784999999991, 0.03924298300000029, 0.03560884999999958, 0.03570307599999989, 0.03893645999999995, 0.03669168899999997, 0.03659634899999986, 0.03869493299999993, 0.03653295599999984 ], "coldSeconds": 0.06277334700000026, "relMax": 0.0005436078187947673, "relL2": 0.00014177752459500198 }, { "n": 512, "solveSeconds": 0.08099865300000042, "solveSecondsAll": [ 0.08176507599999949, 0.08726250000000046, 0.08202920999999996, 0.08744488600000011, 0.08099865300000042, 0.08444771500000003 ], "coldSeconds": 0.12032347499999974, "relMax": 0.0000077702463788788, "relL2": 0.0000064113086286031665 }, { "n": 768, "solveSeconds": 0.2602630340000003, "solveSecondsAll": [ 0.26539002199999917, 0.2602630340000003, 0.26236037299999904, 0.2641303129999999, 0.26314328300000067 ], "coldSeconds": 0.34356460300000036, "relMax": 0.000003872613062061364, "relL2": 0.000003876177968242255 } ] }