1{
2 "format": "fastandaccurate-result",
3 "formatVersion": 1,
4 "problem": "laplace-dirichlet-2d",
5 "problemVersion": 1,
6 "instance": "square-corners",
7 "spec": {
8 "a": 0,
9 "d": 0.25,
10 "instance": "square-corners",
11 "k": 0,
12 "problem": "laplace-dirichlet-2d",
13 "problemVersion": 1,
14 "p": 100,
15 "shape": "rounded-square"
16 },
17 "specHash": "4d945fc4e496e584d24975e6709a5bfeb73aa149f71a7ef875acd50e49b3f42a",
18 "solver": {
19 "id": "nystrom-dlp-mat",
20 "version": "1.0.0",
21 "backend": "cpu",
22 "source": "builtin"
23 },
24 "environment": {
25 "kind": "matlab",
26 "runtime": "MATLAB 26.2.0.3320248 (R2026b) Prerelease Update 2",
27 "os": "linux 6.12.101+deb13-amd64",
28 "cpu": "13th Gen Intel(R) Core(TM) i7-1355U",
29 "machineLabel": "linux laptop (i7-1355U)",
30 "browserReproducible": false
31 },
32 "protocol": {
33 "warmupRuns": 2,
34 "minTimedRuns": 5,
35 "timeBudgetSeconds": 0.5,
36 "maxTimedRuns": 50,
37 "statistic": "min",
38 "timer": "matlab tic/toc"
39 },
40 "createdUtc": "2026-08-18T11:15:18.351Z",
41 "points": [
42 {
43 "n": 64,
44 "solveSeconds": 0.000459,
45 "solveSecondsAll": [
46 0.011525,
47 0.000636,
48 0.000636,
49 0.00093,
50 0.00158,
51 0.00133,
52 0.000746,
53 0.000738,
54 0.001679,
55 0.001792,
56 0.000866,
57 0.001346,
58 0.001879,
59 0.00188,
60 0.001695,
61 0.00189,
62 0.00192,
63 0.001795,
64 0.001658,
65 0.001636,
66 0.001253,
67 0.001701,
68 0.000859,
69 0.000526,
70 0.000552,
71 0.000705,
72 0.00071,
73 0.000682,
74 0.000821,
75 0.000697,
76 0.000733,
77 0.00067,
78 0.000643,
79 0.000594,
80 0.000634,
81 0.000625,
82 0.000626,
83 0.00068,
84 0.000638,
85 0.00052,
86 0.000589,
87 0.000622,
88 0.000573,
89 0.000502,
90 0.00057,
91 0.00054,
92 0.000552,
93 0.000471,
94 0.00055,
95 0.000459
96 ],
97 "coldSeconds": 0.003409,
98 "relMax": 2.863145739656076,
99 "relL2": 0.6411353536694087
100 },
101 {
102 "n": 96,
103 "solveSeconds": 0.000559,
104 "solveSecondsAll": [
105 0.002536,
106 0.001188,
107 0.002569,
108 0.000853,
109 0.001173,
110 0.001749,
111 0.001691,
112 0.001779,
113 0.001745,
114 0.001603,
115 0.00162,
116 0.001692,
117 0.001498,
118 0.001372,
119 0.001441,
120 0.001409,
121 0.001343,
122 0.001188,
123 0.00114,
124 0.001022,
125 0.001024,
126 0.000988,
127 0.000963,
128 0.00092,
129 0.000914,
130 0.00088,
131 0.000879,
132 0.000858,
133 0.000842,
134 0.000831,
135 0.000836,
136 0.000773,
137 0.000795,
138 0.000736,
139 0.000778,
140 0.00072,
141 0.000699,
142 0.000701,
143 0.000681,
144 0.000662,
145 0.000654,
146 0.000683,
147 0.000642,
148 0.000648,
149 0.000678,
150 0.000559,
151 0.000611,
152 0.000654,
153 0.000612,
154 0.000703
155 ],
156 "coldSeconds": 0.000966,
157 "relMax": 2.18883584142697,
158 "relL2": 0.4863389173131757
159 },
160 {
161 "n": 128,
162 "solveSeconds": 0.000734,
163 "solveSecondsAll": [
164 0.000876,
165 0.000795,
166 0.000865,
167 0.000847,
168 0.0008,
169 0.000898,
170 0.000874,
171 0.000842,
172 0.000734,
173 0.000865,
174 0.000784,
175 0.000866,
176 0.000836,
177 0.000787,
178 0.000783,
179 0.000869,
180 0.000869,
181 0.00091,
182 0.000888,
183 0.000932,
184 0.001081,
185 0.000802,
186 0.000873,
187 0.001418,
188 0.001312,
189 0.002456,
190 0.000989,
191 0.000857,
192 0.00092,
193 0.000872,
194 0.000882,
195 0.000811,
196 0.000874,
197 0.000933,
198 0.000888,
199 0.000978,
200 0.001083,
201 0.001041,
202 0.001562,
203 0.001115,
204 0.00093,
205 0.000912,
206 0.000856,
207 0.000879,
208 0.000891,
209 0.000933,
210 0.000897,
211 0.000907,
212 0.000904,
213 0.000899
214 ],
215 "coldSeconds": 0.000928,
216 "relMax": 1.709665533106157,
217 "relL2": 0.3761618266378366
218 },
219 {
220 "n": 192,
221 "solveSeconds": 0.001407,
222 "solveSecondsAll": [
223 0.00148,
224 0.001407,
225 0.001452,
226 0.001441,
227 0.001466,
228 0.001423,
229 0.001545,
230 0.00201,
231 0.001781,
232 0.001924,
233 0.001848,
234 0.001816,
235 0.001901,
236 0.001715,
237 0.001736,
238 0.001743,
239 0.001819,
240 0.001761,
241 0.001767,
242 0.00178,
243 0.00186,
244 0.001803,
245 0.002724,
246 0.002001,
247 0.001954,
248 0.001903,
249 0.001449,
250 0.001476,
251 0.001436,
252 0.001584,
253 0.001467,
254 0.00189,
255 0.001689,
256 0.001887,
257 0.001841,
258 0.001943,
259 0.00189,
260 0.001904,
261 0.002462,
262 0.001807,
263 0.002076,
264 0.001943,
265 0.001754,
266 0.00179,
267 0.001753,
268 0.001755,
269 0.001915,
270 0.001893,
271 0.001762,
272 0.002171
273 ],
274 "coldSeconds": 0.001745,
275 "relMax": 1.0872325900106483,
276 "relL2": 0.2361869184687327
277 },
278 {
279 "n": 256,
280 "solveSeconds": 0.002041,
281 "solveSecondsAll": [
282 0.002454,
283 0.002881,
284 0.002111,
285 0.002148,
286 0.002248,
287 0.002109,
288 0.002121,
289 0.002065,
290 0.002041,
291 0.002158,
292 0.002139,
293 0.002134,
294 0.002063,
295 0.002185,
296 0.002162,
297 0.002272,
298 0.00217,
299 0.002632,
300 0.002876,
301 0.003483,
302 0.00271,
303 0.002837,
304 0.002882,
305 0.002482,
306 0.002109,
307 0.002083,
308 0.002137,
309 0.002202,
310 0.002185,
311 0.002127,
312 0.002418,
313 0.002794,
314 0.002519,
315 0.002392,
316 0.002361,
317 0.002338,
318 0.002763,
319 0.003067,
320 0.002681,
321 0.002233,
322 0.00232,
323 0.002244,
324 0.002298,
325 0.002271,
326 0.002695,
327 0.002831,
328 0.003261,
329 0.003183,
330 0.003027,
331 0.00265
332 ],
333 "coldSeconds": 0.002883,
334 "relMax": 0.7164525480412305,
335 "relL2": 0.15506601852436075
336 },
337 {
338 "n": 384,
339 "solveSeconds": 0.003527,
340 "solveSecondsAll": [
341 0.003627,
342 0.003575,
343 0.004066,
344 0.004118,
345 0.003828,
346 0.003745,
347 0.003625,
348 0.003561,
349 0.003624,
350 0.003731,
351 0.003527,
352 0.003933,
353 0.004534,
354 0.004618,
355 0.004006,
356 0.004723,
357 0.005129,
358 0.00481,
359 0.00461,
360 0.004336,
361 0.003991,
362 0.003931,
363 0.003678,
364 0.003719,
365 0.003758,
366 0.003607,
367 0.003717,
368 0.004294,
369 0.004216,
370 0.003924,
371 0.004001,
372 0.003824,
373 0.003662,
374 0.005437,
375 0.005335,
376 0.006975,
377 0.005317,
378 0.004409,
379 0.004089,
380 0.004714,
381 0.004337,
382 0.00449,
383 0.004827,
384 0.004485,
385 0.004269,
386 0.004203,
387 0.004066,
388 0.003871,
389 0.005982,
390 0.005385
391 ],
392 "coldSeconds": 0.003629,
393 "relMax": 0.33328135092225547,
394 "relL2": 0.07144368708504326
395 },
396 {
397 "n": 512,
398 "solveSeconds": 0.006507,
399 "solveSecondsAll": [
400 0.006676,
401 0.006881,
402 0.00711,
403 0.006895,
404 0.006759,
405 0.006507,
406 0.006884,
407 0.007303,
408 0.007437,
409 0.006691,
410 0.006697,
411 0.006806,
412 0.007473,
413 0.007495,
414 0.007131,
415 0.007429,
416 0.007229,
417 0.007576,
418 0.007799,
419 0.007383,
420 0.008549,
421 0.007588,
422 0.007532,
423 0.006973,
424 0.00718,
425 0.007669,
426 0.0073,
427 0.007155,
428 0.007834,
429 0.016861,
430 0.007607,
431 0.007027,
432 0.007917,
433 0.007523,
434 0.007352,
435 0.006724,
436 0.007563,
437 0.016242,
438 0.007435,
439 0.006844,
440 0.036186,
441 0.008627,
442 0.007433,
443 0.008565,
444 0.008605,
445 0.008729,
446 0.00694,
447 0.006905,
448 0.006516,
449 0.006793
450 ],
451 "coldSeconds": 0.008728,
452 "relMax": 0.16539760757817354,
453 "relL2": 0.03552444030506169
454 },
455 {
456 "n": 768,
457 "solveSeconds": 0.018662,
458 "solveSecondsAll": [
459 0.020029,
460 0.022786,
461 0.027101,
462 0.021155,
463 0.036658,
464 0.021796,
465 0.027324,
466 0.027138,
467 0.036973,
468 0.021599,
469 0.02509,
470 0.020699,
471 0.018662,
472 0.036637,
473 0.0248,
474 0.024516,
475 0.023236,
476 0.020119,
477 0.022669,
478 0.021712
479 ],
480 "coldSeconds": 0.023034,
481 "relMax": 0.04554029343700318,
482 "relL2": 0.009620120323947703
483 },
484 {
485 "n": 1024,
486 "solveSeconds": 0.028336,
487 "solveSecondsAll": [
488 0.034087,
489 0.033941,
490 0.063779,
491 0.034348,
492 0.040838,
493 0.046626,
494 0.048154,
495 0.029984,
496 0.028338,
497 0.028336,
498 0.033086,
499 0.031906,
500 0.034068,
501 0.036307
502 ],
503 "coldSeconds": 0.040028,
504 "relMax": 0.013366296792625262,
505 "relL2": 0.0028206037009742115
506 },
507 {
508 "n": 1536,
509 "solveSeconds": 0.10389,
510 "solveSecondsAll": [
511 0.124124,
512 0.104102,
513 0.104132,
514 0.10389,
515 0.111191
516 ],
517 "coldSeconds": 0.106693,
518 "relMax": 0.001202860109490264,
519 "relL2": 0.00025379689758792725
520 },
521 {
522 "n": 2048,
523 "solveSeconds": 0.244718,
524 "solveSecondsAll": [
525 0.302583,
526 0.273966,
527 0.244718,
528 0.276534,
529 0.281116
530 ],
531 "coldSeconds": 0.244574,
532 "relMax": 0.00010921638746077781,
533 "relL2": 0.00002304405546853593
534 },
535 {
536 "n": 3072,
537 "solveSeconds": 0.472443,
538 "solveSecondsAll": [
539 0.500343,
540 0.556459,
541 0.472443,
542 0.515149,
543 0.491804
544 ],
545 "coldSeconds": 0.48274,
546 "relMax": 9.01755589884286e-7,
547 "relL2": 1.9026545616975062e-7
548 },
549 {
550 "n": 4096,
551 "solveSeconds": 1.048958,
552 "solveSecondsAll": [
553 1.10629,
554 1.182119,
555 1.105386,
556 1.048958,
557 1.087501
558 ],
559 "coldSeconds": 1.115023,
560 "relMax": 7.4459688365643635e-9,
561 "relL2": 1.5710583623527977e-9
562 }
563 ]
564}