These are timing and accuracy results to solve the system $$ \gathered -\nabla\cdot(a\nabla u)+b\cdot\nabla u+cu=f\quad\text{on }\Omega, \\ a\frac{\partial u}{\partial n}+\gamma u=g\quad\text{on }\partial Omega. \endgathered $$ with $b=0$ with $\Omega=[0,1]^2$ and a regular grid of size $257 \times 257$ with one set of diagonals and linear finite elements. Multigrid was used, with m1 presmoothing steps, m2 postsmoothing steps, and p coarse-correction steps in each MG-step, and r iterations of MG-step at each refinement level. The four columns of numbers are L2 error, H1 error, User ms, and GC ms. The L2 and H1 errors were estimated by injecting the approximate solution into a $513 \times 513$ grid and comparing it with the interpolant of the true solution on the fine grid. The problems are roughly in increasing order of difficulty; in the last problem, for example, the stiffness coefficient $a$ varies from 1.0 to 21.0 over the domain. User ms is the amount of user+system time to solve the linear system only; every once in a while there was a garbage collection during the solution process, whose time is measured separately. The tests were run on a dual processor, 500 MHz, Alpha 21264 DS20 clone with 4 Mbytes of cache on each processor and 2 Gbytes of main memory. The program was coded in Scheme with the Meroon object system and compiled from Scheme->C by a hacked version of Gambit-C 3.0; the C code was compiled with gcc-2.95.1 with options "-mcpu=ev6 -fno-math-errno -mieee -O2". Based on these results, I would recommend 4 presmoothing and 4 postsmoothing tests, two coarse-grid corrections, and two repetitions of MG-step at each level of the multigrid solver. To put the GC results in perspective, in the middle of solving a problem, there is about .65 Gbytes of live data in a 1.3 Gbyte heap. popov-157% gsi++ -:m100000 [ Meroon V3 Noel+3 $Revision: 1.1 $ ] Gambit Version 3.0 > (load "all") "/.amd_mnt/peano/export/home3/lucier/programs/615project/all.o7" > (time (load "final-tests") ) (time (load "final-tests")) 130606 ms real time 129939 ms cpu time (127800 user, 2140 system) 12 collections accounting for 25562 ms cpu time (25171 user, 392 system) 3307347592 bytes allocated 995480 minor faults 80 major faults "/.amd_mnt/peano/export/home3/lucier/programs/615project/final-tests.o2" > (run-multigrid-tests) a=1, c=1, u=x^2-y^2, Neumann MG: r = 1, m1 = 1, m2 = 1, p = 1. .0000040408 .0027767859 218 0 MG: r = 2, m1 = 1, m2 = 1, p = 1. .0000015614 .0027623124 427 0 MG: r = 3, m1 = 1, m2 = 1, p = 1. .0000015574 .0027621442 566 0 MG: r = 4, m1 = 1, m2 = 1, p = 1. .0000015573 .0027621367 755 0 MG: r = 5, m1 = 1, m2 = 1, p = 1. .0000015573 .0027621363 926 0 MG: r = 6, m1 = 1, m2 = 1, p = 1. .0000015573 .0027621363 1141 0 MG: r = 1, m1 = 2, m2 = 2, p = 1. .0000015697 .0027623167 306 0 MG: r = 2, m1 = 2, m2 = 2, p = 1. .0000015573 .0027621367 660 0 MG: r = 3, m1 = 2, m2 = 2, p = 1. .0000015573 .0027621363 838 0 MG: r = 4, m1 = 2, m2 = 2, p = 1. .0000015573 .0027621363 1116 0 MG: r = 5, m1 = 2, m2 = 2, p = 1. .0000015573 .0027621363 1516 0 MG: r = 6, m1 = 2, m2 = 2, p = 1. .0000015573 .0027621363 1721 0 MG: r = 1, m1 = 3, m2 = 3, p = 1. .0000015584 .0027621446 403 0 MG: r = 2, m1 = 3, m2 = 3, p = 1. .0000015573 .0027621363 788 0 MG: r = 3, m1 = 3, m2 = 3, p = 1. .0000015573 .0027621363 1140 0 MG: r = 4, m1 = 3, m2 = 3, p = 1. .0000015573 .0027621363 1513 0 MG: r = 5, m1 = 3, m2 = 3, p = 1. .0000015573 .0027621363 1759 3429 MG: r = 6, m1 = 3, m2 = 3, p = 1. .0000015573 .0027621363 2026 0 MG: r = 1, m1 = 4, m2 = 4, p = 1. .0000015575 .0027621367 494 0 MG: r = 2, m1 = 4, m2 = 4, p = 1. .0000015573 .0027621363 854 0 MG: r = 3, m1 = 4, m2 = 4, p = 1. .0000015573 .0027621363 1278 0 MG: r = 4, m1 = 4, m2 = 4, p = 1. .0000015573 .0027621363 1751 3433 MG: r = 5, m1 = 4, m2 = 4, p = 1. .0000015573 .0027621363 2383 0 MG: r = 6, m1 = 4, m2 = 4, p = 1. .0000015573 .0027621363 2823 3439 MG: r = 1, m1 = 1, m2 = 1, p = 2. .0000015944 .0027746554 350 0 MG: r = 2, m1 = 1, m2 = 1, p = 2. .0000015580 .0027623068 690 0 MG: r = 3, m1 = 1, m2 = 1, p = 2. .0000015573 .0027621442 1023 0 MG: r = 4, m1 = 1, m2 = 1, p = 2. .0000015573 .0027621367 1356 0 MG: r = 5, m1 = 1, m2 = 1, p = 2. .0000015573 .0027621363 1687 0 MG: r = 6, m1 = 1, m2 = 1, p = 2. .0000015573 .0027621363 1937 0 MG: r = 1, m1 = 2, m2 = 2, p = 2. .0000015588 .0027623106 499 0 MG: r = 2, m1 = 2, m2 = 2, p = 2. .0000015573 .0027621367 961 3418 MG: r = 3, m1 = 2, m2 = 2, p = 2. .0000015573 .0027621363 1436 0 MG: r = 4, m1 = 2, m2 = 2, p = 2. .0000015573 .0027621363 2085 0 MG: r = 5, m1 = 2, m2 = 2, p = 2. .0000015573 .0027621363 2429 0 MG: r = 6, m1 = 2, m2 = 2, p = 2. .0000015573 .0027621363 3133 3399 MG: r = 1, m1 = 3, m2 = 3, p = 2. .0000015576 .0027621445 688 0 MG: r = 2, m1 = 3, m2 = 3, p = 2. .0000015573 .0027621363 1367 0 MG: r = 3, m1 = 3, m2 = 3, p = 2. .0000015573 .0027621363 1930 0 MG: r = 4, m1 = 3, m2 = 3, p = 2. .0000015573 .0027621363 2740 0 MG: r = 5, m1 = 3, m2 = 3, p = 2. .0000015573 .0027621363 3179 0 MG: r = 6, m1 = 3, m2 = 3, p = 2. .0000015573 .0027621363 4151 3467 MG: r = 1, m1 = 4, m2 = 4, p = 2. .0000015574 .0027621368 809 0 MG: r = 2, m1 = 4, m2 = 4, p = 2. .0000015573 .0027621363 1616 0 MG: r = 3, m1 = 4, m2 = 4, p = 2. .0000015573 .0027621363 2380 0 MG: r = 4, m1 = 4, m2 = 4, p = 2. .0000015573 .0027621363 3357 3512 MG: r = 5, m1 = 4, m2 = 4, p = 2. .0000015573 .0027621363 4197 0 MG: r = 6, m1 = 4, m2 = 4, p = 2. .0000015573 .0027621363 4981 0 a=1, c=1, u=\cos(\pi x), Neumann MG: r = 1, m1 = 1, m2 = 1, p = 1. .0004080450 .0076568118 196 0 MG: r = 2, m1 = 1, m2 = 1, p = 1. .0000176764 .0068170917 376 0 MG: r = 3, m1 = 1, m2 = 1, p = 1. .0000091037 .0068153116 496 0 MG: r = 4, m1 = 1, m2 = 1, p = 1. .0000081061 .0068152132 657 0 MG: r = 5, m1 = 1, m2 = 1, p = 1. .0000078287 .0068151968 813 0 MG: r = 6, m1 = 1, m2 = 1, p = 1. .0000077237 .0068151920 990 0 MG: r = 1, m1 = 2, m2 = 2, p = 1. .0000343717 .0068205459 261 0 MG: r = 2, m1 = 2, m2 = 2, p = 1. .0000087836 .0068152377 563 0 MG: r = 3, m1 = 2, m2 = 2, p = 1. .0000078582 .0068151956 781 3493 MG: r = 4, m1 = 2, m2 = 2, p = 1. .0000076978 .0068151904 1023 0 MG: r = 5, m1 = 2, m2 = 2, p = 1. .0000076593 .0068151892 1367 0 MG: r = 6, m1 = 2, m2 = 2, p = 1. .0000076492 .0068151889 1488 0 MG: r = 1, m1 = 3, m2 = 3, p = 1. .0000160305 .0068158364 348 0 MG: r = 2, m1 = 3, m2 = 3, p = 1. .0000081208 .0068152020 689 0 MG: r = 3, m1 = 3, m2 = 3, p = 1. .0000077179 .0068151906 993 0 MG: r = 4, m1 = 3, m2 = 3, p = 1. .0000076587 .0068151891 1320 0 MG: r = 5, m1 = 3, m2 = 3, p = 1. .0000076480 .0068151889 1690 3422 MG: r = 6, m1 = 3, m2 = 3, p = 1. .0000076459 .0068151888 2207 0 MG: r = 1, m1 = 4, m2 = 4, p = 1. .0000121727 .0068153981 435 0 MG: r = 2, m1 = 4, m2 = 4, p = 1. .0000079150 .0068151949 859 0 MG: r = 3, m1 = 4, m2 = 4, p = 1. .0000076789 .0068151895 1283 0 MG: r = 4, m1 = 4, m2 = 4, p = 1. .0000076502 .0068151889 1729 3438 MG: r = 5, m1 = 4, m2 = 4, p = 1. .0000076461 .0068151888 2119 0 MG: r = 6, m1 = 4, m2 = 4, p = 1. .0000076455 .0068151888 2711 3457 MG: r = 1, m1 = 1, m2 = 1, p = 2. .0000125837 .0068489866 371 0 MG: r = 2, m1 = 1, m2 = 1, p = 2. .0000078563 .0068157098 723 0 MG: r = 3, m1 = 1, m2 = 1, p = 2. .0000076585 .0068152188 1036 3447 MG: r = 4, m1 = 1, m2 = 1, p = 2. .0000076469 .0068151919 1356 0 MG: r = 5, m1 = 1, m2 = 1, p = 2. .0000076457 .0068151895 1708 0 MG: r = 6, m1 = 1, m2 = 1, p = 2. .0000076455 .0068151890 2014 0 MG: r = 1, m1 = 2, m2 = 2, p = 2. .0000086214 .0068157638 516 0 MG: r = 2, m1 = 2, m2 = 2, p = 2. .0000076497 .0068151938 1010 3421 MG: r = 3, m1 = 2, m2 = 2, p = 2. .0000076455 .0068151893 1468 0 MG: r = 4, m1 = 2, m2 = 2, p = 2. .0000076454 .0068151889 1966 0 MG: r = 5, m1 = 2, m2 = 2, p = 2. .0000076454 .0068151888 2479 0 MG: r = 6, m1 = 2, m2 = 2, p = 2. .0000076454 .0068151888 3008 3455 MG: r = 1, m1 = 3, m2 = 3, p = 2. .0000078626 .0068152400 686 0 MG: r = 2, m1 = 3, m2 = 3, p = 2. .0000076457 .0068151899 1339 0 MG: r = 3, m1 = 3, m2 = 3, p = 2. .0000076454 .0068151889 1980 3556 MG: r = 4, m1 = 3, m2 = 3, p = 2. .0000076454 .0068151888 2662 0 MG: r = 5, m1 = 3, m2 = 3, p = 2. .0000076454 .0068151888 3199 0 MG: r = 6, m1 = 3, m2 = 3, p = 2. .0000076454 .0068151888 3984 3453 MG: r = 1, m1 = 4, m2 = 4, p = 2. .0000077048 .0068152045 850 0 MG: r = 2, m1 = 4, m2 = 4, p = 2. .0000076455 .0068151894 1667 0 MG: r = 3, m1 = 4, m2 = 4, p = 2. .0000076454 .0068151888 2453 0 MG: r = 4, m1 = 4, m2 = 4, p = 2. .0000076454 .0068151888 3307 3483 MG: r = 5, m1 = 4, m2 = 4, p = 2. .0000076454 .0068151888 4087 0 MG: r = 6, m1 = 4, m2 = 4, p = 2. .0000076454 .0068151888 4873 0 a=1, c=1, u=\sin(\pi x)+\sin(\pi y), Neumann MG: r = 1, m1 = 1, m2 = 1, p = 1. .0013524584 .0120023220 203 0 MG: r = 2, m1 = 1, m2 = 1, p = 1. .0000378929 .0096398764 380 0 MG: r = 3, m1 = 1, m2 = 1, p = 1. .0000154271 .0096382942 514 0 MG: r = 4, m1 = 1, m2 = 1, p = 1. .0000124481 .0096382321 679 0 MG: r = 5, m1 = 1, m2 = 1, p = 1. .0000115628 .0096382237 848 0 MG: r = 6, m1 = 1, m2 = 1, p = 1. .0000112275 .0096382216 1087 0 MG: r = 1, m1 = 2, m2 = 2, p = 1. .0001010815 .0096485314 288 0 MG: r = 2, m1 = 2, m2 = 2, p = 1. .0000142652 .0096382533 504 0 MG: r = 3, m1 = 2, m2 = 2, p = 1. .0000116459 .0096382244 787 3437 MG: r = 4, m1 = 2, m2 = 2, p = 1. .0000111546 .0096382212 1053 0 MG: r = 5, m1 = 2, m2 = 2, p = 1. .0000110292 .0096382205 1382 0 MG: r = 6, m1 = 2, m2 = 2, p = 1. .0000109946 .0096382203 1524 0 MG: r = 1, m1 = 3, m2 = 3, p = 1. .0000331786 .0096389584 355 0 MG: r = 2, m1 = 3, m2 = 3, p = 1. .0000121872 .0096382286 683 0 MG: r = 3, m1 = 3, m2 = 3, p = 1. .0000111858 .0096382214 1024 0 MG: r = 4, m1 = 3, m2 = 3, p = 1. .0000110210 .0096382204 1372 0 MG: r = 5, m1 = 3, m2 = 3, p = 1. .0000109890 .0096382202 1708 3454 MG: r = 6, m1 = 3, m2 = 3, p = 1. .0000109824 .0096382202 2005 0 MG: r = 1, m1 = 4, m2 = 4, p = 1. .0000208468 .0096383988 433 0 MG: r = 2, m1 = 4, m2 = 4, p = 1. .0000115982 .0096382240 865 0 MG: r = 3, m1 = 4, m2 = 4, p = 1. .0000110664 .0096382207 1287 0 MG: r = 4, m1 = 4, m2 = 4, p = 1. .0000109939 .0096382203 1698 3452 MG: r = 5, m1 = 4, m2 = 4, p = 1. .0000109828 .0096382202 2104 0 MG: r = 6, m1 = 4, m2 = 4, p = 1. .0000109811 .0096382202 2538 3520 MG: r = 1, m1 = 1, m2 = 1, p = 2. .0000158551 .0096789939 377 0 MG: r = 2, m1 = 1, m2 = 1, p = 2. .0000111649 .0096387274 723 0 MG: r = 3, m1 = 1, m2 = 1, p = 2. .0000109893 .0096382421 1052 3469 MG: r = 4, m1 = 1, m2 = 1, p = 2. .0000109814 .0096382213 1379 0 MG: r = 5, m1 = 1, m2 = 1, p = 2. .0000109808 .0096382203 1814 0 MG: r = 6, m1 = 1, m2 = 1, p = 2. .0000109808 .0096382202 2024 0 MG: r = 1, m1 = 2, m2 = 2, p = 2. .0000118956 .0096387388 538 0 MG: r = 2, m1 = 2, m2 = 2, p = 2. .0000109830 .0096382213 1041 3457 MG: r = 3, m1 = 2, m2 = 2, p = 2. .0000109808 .0096382202 1496 0 MG: r = 4, m1 = 2, m2 = 2, p = 2. .0000109807 .0096382202 2010 0 MG: r = 5, m1 = 2, m2 = 2, p = 2. .0000109807 .0096382202 2461 0 MG: r = 6, m1 = 2, m2 = 2, p = 2. .0000109807 .0096382202 2943 3467 MG: r = 1, m1 = 3, m2 = 3, p = 2. .0000111661 .0096382433 680 0 MG: r = 2, m1 = 3, m2 = 3, p = 2. .0000109808 .0096382202 1327 0 MG: r = 3, m1 = 3, m2 = 3, p = 2. .0000109807 .0096382202 2035 3431 MG: r = 4, m1 = 3, m2 = 3, p = 2. .0000109807 .0096382202 2614 0 MG: r = 5, m1 = 3, m2 = 3, p = 2. .0000109807 .0096382202 3228 0 MG: r = 6, m1 = 3, m2 = 3, p = 2. .0000109807 .0096382202 3984 3451 MG: r = 1, m1 = 4, m2 = 4, p = 2. .0000110217 .0096382216 847 0 MG: r = 2, m1 = 4, m2 = 4, p = 2. .0000109807 .0096382202 1666 0 MG: r = 3, m1 = 4, m2 = 4, p = 2. .0000109807 .0096382202 2562 0 MG: r = 4, m1 = 4, m2 = 4, p = 2. .0000109807 .0096382202 3469 3452 MG: r = 5, m1 = 4, m2 = 4, p = 2. .0000109807 .0096382202 4122 0 MG: r = 6, m1 = 4, m2 = 4, p = 2. .0000109807 .0096382202 4817 0 a=11.0+10.0*\cos\pi x, c=1, u=xy, Neumann MG: r = 1, m1 = 1, m2 = 1, p = 1. .0098043142 .0694362722 199 0 MG: r = 2, m1 = 1, m2 = 1, p = 1. .0035301521 .0321544668 411 0 MG: r = 3, m1 = 1, m2 = 1, p = 1. .0016418992 .0177539666 508 0 MG: r = 4, m1 = 1, m2 = 1, p = 1. .0008767024 .0109447084 663 0 MG: r = 5, m1 = 1, m2 = 1, p = 1. .0005165777 .0073602507 842 0 MG: r = 6, m1 = 1, m2 = 1, p = 1. .0003287080 .0053283421 1000 0 MG: r = 1, m1 = 2, m2 = 2, p = 1. .0053360460 .0422628424 265 0 MG: r = 2, m1 = 2, m2 = 2, p = 1. .0012801872 .0137884854 513 0 MG: r = 3, m1 = 2, m2 = 2, p = 1. .0004486911 .0062853342 801 3460 MG: r = 4, m1 = 2, m2 = 2, p = 1. .0002005865 .0037127897 1041 0 MG: r = 5, m1 = 2, m2 = 2, p = 1. .0001052502 .0027051347 1327 0 MG: r = 6, m1 = 2, m2 = 2, p = 1. .0000610435 .0022889465 1510 0 MG: r = 1, m1 = 3, m2 = 3, p = 1. .0031460412 .0268933916 363 0 MG: r = 2, m1 = 3, m2 = 3, p = 1. .0005631190 .0070982736 779 0 MG: r = 3, m1 = 3, m2 = 3, p = 1. .0001697754 .0032898289 1005 0 MG: r = 4, m1 = 3, m2 = 3, p = 1. .0000694140 .0023357577 1444 0 MG: r = 5, m1 = 3, m2 = 3, p = 1. .0000336461 .0020763878 1819 3465 MG: r = 6, m1 = 3, m2 = 3, p = 1. .0000182879 .0019988026 2049 0 MG: r = 1, m1 = 4, m2 = 4, p = 1. .0020032743 .0182086022 469 0 MG: r = 2, m1 = 4, m2 = 4, p = 1. .0002879355 .0043364796 840 0 MG: r = 3, m1 = 4, m2 = 4, p = 1. .0000785205 .0023845206 1266 0 MG: r = 4, m1 = 4, m2 = 4, p = 1. .0000298466 .0020484191 1751 3451 MG: r = 5, m1 = 4, m2 = 4, p = 1. .0000139533 .0019801456 2143 0 MG: r = 6, m1 = 4, m2 = 4, p = 1. .0000079148 .0019626215 2693 3456 MG: r = 1, m1 = 1, m2 = 1, p = 2. .0001116703 .0050150093 429 0 MG: r = 2, m1 = 1, m2 = 1, p = 2. .0000287634 .0029899390 850 0 MG: r = 3, m1 = 1, m2 = 1, p = 2. .0000128746 .0024795507 1259 0 MG: r = 4, m1 = 1, m2 = 1, p = 2. .0000077751 .0022722443 1682 0 MG: r = 5, m1 = 1, m2 = 1, p = 2. .0000057218 .0021659093 2088 0 MG: r = 6, m1 = 1, m2 = 1, p = 2. .0000047788 .0021034627 2501 0 MG: r = 1, m1 = 2, m2 = 2, p = 2. .0000307944 .0030034487 627 0 MG: r = 2, m1 = 2, m2 = 2, p = 2. .0000081144 .0022730951 1145 0 MG: r = 3, m1 = 2, m2 = 2, p = 2. .0000048999 .0021036039 1743 0 MG: r = 4, m1 = 2, m2 = 2, p = 2. .0000040883 .0020365393 2399 3485 MG: r = 5, m1 = 2, m2 = 2, p = 2. .0000038007 .0020034963 2920 0 MG: r = 6, m1 = 2, m2 = 2, p = 2. .0000036722 .0019851429 3497 3467 MG: r = 1, m1 = 3, m2 = 3, p = 2. .0000143787 .0024860271 748 0 MG: r = 2, m1 = 3, m2 = 3, p = 2. .0000050446 .0021038026 1474 0 MG: r = 3, m1 = 3, m2 = 3, p = 2. .0000039596 .0020174634 2267 0 MG: r = 4, m1 = 3, m2 = 3, p = 2. .0000036915 .0019851542 3229 0 MG: r = 5, m1 = 3, m2 = 3, p = 2. .0000035935 .0019703304 3665 0 MG: r = 6, m1 = 3, m2 = 3, p = 2. .0000035499 .0019627738 4410 3447 MG: r = 1, m1 = 4, m2 = 4, p = 2. .0000090751 .0022757049 1050 0 MG: r = 2, m1 = 4, m2 = 4, p = 2. .0000042326 .0020366761 1862 4067 MG: r = 3, m1 = 4, m2 = 4, p = 2. .0000037135 .0019851695 2746 0 MG: r = 4, m1 = 4, m2 = 4, p = 2. .0000035835 .0019672651 3554 3747 MG: r = 5, m1 = 4, m2 = 4, p = 2. .0000035376 .0019597920 4851 3864 MG: r = 6, m1 = 4, m2 = 4, p = 2. .0000035189 .0019563877 5295 0 a=1, c=1+xy, u=x^2-y^2, Neumann MG: r = 1, m1 = 1, m2 = 1, p = 1. .0000040875 .0027767908 194 0 MG: r = 2, m1 = 1, m2 = 1, p = 1. .0000015614 .0027623124 339 0 MG: r = 3, m1 = 1, m2 = 1, p = 1. .0000015574 .0027621442 502 0 MG: r = 4, m1 = 1, m2 = 1, p = 1. .0000015573 .0027621367 665 0 MG: r = 5, m1 = 1, m2 = 1, p = 1. .0000015573 .0027621363 828 0 MG: r = 6, m1 = 1, m2 = 1, p = 1. .0000015573 .0027621363 985 0 MG: r = 1, m1 = 2, m2 = 2, p = 1. .0000015695 .0027623167 290 0 MG: r = 2, m1 = 2, m2 = 2, p = 1. .0000015573 .0027621367 511 0 MG: r = 3, m1 = 2, m2 = 2, p = 1. .0000015573 .0027621363 754 0 MG: r = 4, m1 = 2, m2 = 2, p = 1. .0000015573 .0027621363 1063 0 MG: r = 5, m1 = 2, m2 = 2, p = 1. .0000015573 .0027621363 1225 0 MG: r = 6, m1 = 2, m2 = 2, p = 1. .0000015573 .0027621363 1650 0 MG: r = 1, m1 = 3, m2 = 3, p = 1. .0000015584 .0027621446 405 0 MG: r = 2, m1 = 3, m2 = 3, p = 1. .0000015573 .0027621363 699 0 MG: r = 3, m1 = 3, m2 = 3, p = 1. .0000015573 .0027621363 1041 0 MG: r = 4, m1 = 3, m2 = 3, p = 1. .0000015573 .0027621363 1389 3452 MG: r = 5, m1 = 3, m2 = 3, p = 1. .0000015573 .0027621363 1611 0 MG: r = 6, m1 = 3, m2 = 3, p = 1. .0000015573 .0027621363 2361 0 MG: r = 1, m1 = 4, m2 = 4, p = 1. .0000015575 .0027621367 439 0 MG: r = 2, m1 = 4, m2 = 4, p = 1. .0000015573 .0027621363 843 0 MG: r = 3, m1 = 4, m2 = 4, p = 1. .0000015573 .0027621363 1270 3409 MG: r = 4, m1 = 4, m2 = 4, p = 1. .0000015573 .0027621363 1698 0 MG: r = 5, m1 = 4, m2 = 4, p = 1. .0000015573 .0027621363 2341 0 MG: r = 6, m1 = 4, m2 = 4, p = 1. .0000015573 .0027621363 2508 0 MG: r = 1, m1 = 1, m2 = 1, p = 2. .0000015944 .0027746555 346 0 MG: r = 2, m1 = 1, m2 = 1, p = 2. .0000015580 .0027623068 668 0 MG: r = 3, m1 = 1, m2 = 1, p = 2. .0000015573 .0027621442 980 0 MG: r = 4, m1 = 1, m2 = 1, p = 2. .0000015573 .0027621367 1353 0 MG: r = 5, m1 = 1, m2 = 1, p = 2. .0000015573 .0027621363 1625 0 MG: r = 6, m1 = 1, m2 = 1, p = 2. .0000015573 .0027621363 2005 0 MG: r = 1, m1 = 2, m2 = 2, p = 2. .0000015588 .0027623106 505 0 MG: r = 2, m1 = 2, m2 = 2, p = 2. .0000015573 .0027621367 997 0 MG: r = 3, m1 = 2, m2 = 2, p = 2. .0000015573 .0027621363 1478 0 MG: r = 4, m1 = 2, m2 = 2, p = 2. .0000015573 .0027621363 1920 0 MG: r = 5, m1 = 2, m2 = 2, p = 2. .0000015573 .0027621363 2641 0 MG: r = 6, m1 = 2, m2 = 2, p = 2. .0000015573 .0027621363 2886 0 MG: r = 1, m1 = 3, m2 = 3, p = 2. .0000015576 .0027621445 740 0 MG: r = 2, m1 = 3, m2 = 3, p = 2. .0000015573 .0027621363 1327 3463 MG: r = 3, m1 = 3, m2 = 3, p = 2. .0000015573 .0027621363 1912 0 MG: r = 4, m1 = 3, m2 = 3, p = 2. .0000015573 .0027621363 2605 3711 MG: r = 5, m1 = 3, m2 = 3, p = 2. .0000015573 .0027621363 3186 0 MG: r = 6, m1 = 3, m2 = 3, p = 2. .0000015573 .0027621363 3819 0 MG: r = 1, m1 = 4, m2 = 4, p = 2. .0000015574 .0027621368 866 0 MG: r = 2, m1 = 4, m2 = 4, p = 2. .0000015573 .0027621363 1609 0 MG: r = 3, m1 = 4, m2 = 4, p = 2. .0000015573 .0027621363 2397 0 MG: r = 4, m1 = 4, m2 = 4, p = 2. .0000015573 .0027621363 3174 0 MG: r = 5, m1 = 4, m2 = 4, p = 2. .0000015573 .0027621363 4110 3434 MG: r = 6, m1 = 4, m2 = 4, p = 2. .0000015573 .0027621363 4674 0 a=1, c=2+\cos(\pi y), u=\cos(\pi x), Neumann MG: r = 1, m1 = 1, m2 = 1, p = 1. .0003736578 .0075782609 199 0 MG: r = 2, m1 = 1, m2 = 1, p = 1. .0000163119 .0068170120 352 0 MG: r = 3, m1 = 1, m2 = 1, p = 1. .0000084672 .0068153083 518 0 MG: r = 4, m1 = 1, m2 = 1, p = 1. .0000075544 .0068152127 688 0 MG: r = 5, m1 = 1, m2 = 1, p = 1. .0000073010 .0068151968 851 0 MG: r = 6, m1 = 1, m2 = 1, p = 1. .0000072053 .0068151922 1007 0 MG: r = 1, m1 = 2, m2 = 2, p = 1. .0000313878 .0068201205 310 0 MG: r = 2, m1 = 2, m2 = 2, p = 1. .0000081454 .0068152356 519 0 MG: r = 3, m1 = 2, m2 = 2, p = 1. .0000073234 .0068151956 756 0 MG: r = 4, m1 = 2, m2 = 2, p = 1. .0000071811 .0068151906 1107 0 MG: r = 5, m1 = 2, m2 = 2, p = 1. .0000071469 .0068151895 1252 0 MG: r = 6, m1 = 2, m2 = 2, p = 1. .0000071379 .0068151892 1659 0 MG: r = 1, m1 = 3, m2 = 3, p = 1. .0000145258 .0068157861 407 0 MG: r = 2, m1 = 3, m2 = 3, p = 1. .0000075451 .0068152015 688 0 MG: r = 3, m1 = 3, m2 = 3, p = 1. .0000071973 .0068151908 1008 0 MG: r = 4, m1 = 3, m2 = 3, p = 1. .0000071460 .0068151894 1546 3432 MG: r = 5, m1 = 3, m2 = 3, p = 1. .0000071367 .0068151892 1690 0 MG: r = 6, m1 = 3, m2 = 3, p = 1. .0000071349 .0068151891 2156 0 MG: r = 1, m1 = 4, m2 = 4, p = 1. .0000110300 .0068153811 442 0 MG: r = 2, m1 = 4, m2 = 4, p = 1. .0000073625 .0068151948 856 0 MG: r = 3, m1 = 4, m2 = 4, p = 1. .0000071628 .0068151898 1291 3418 MG: r = 4, m1 = 4, m2 = 4, p = 1. .0000071386 .0068151892 1706 0 MG: r = 5, m1 = 4, m2 = 4, p = 1. .0000071351 .0068151891 2307 0 MG: r = 6, m1 = 4, m2 = 4, p = 1. .0000071346 .0068151891 2553 0 MG: r = 1, m1 = 1, m2 = 1, p = 2. .0000116379 .0068489766 408 0 MG: r = 2, m1 = 1, m2 = 1, p = 2. .0000073240 .0068157098 801 0 MG: r = 3, m1 = 1, m2 = 1, p = 2. .0000071461 .0068152191 1150 0 MG: r = 4, m1 = 1, m2 = 1, p = 2. .0000071358 .0068151923 1556 0 MG: r = 5, m1 = 1, m2 = 1, p = 2. .0000071347 .0068151898 1896 0 MG: r = 6, m1 = 1, m2 = 1, p = 2. .0000071345 .0068151893 2347 0 MG: r = 1, m1 = 2, m2 = 2, p = 2. .0000080154 .0068157628 581 0 MG: r = 2, m1 = 2, m2 = 2, p = 2. .0000071383 .0068151942 1202 0 MG: r = 3, m1 = 2, m2 = 2, p = 2. .0000071346 .0068151896 1771 0 MG: r = 4, m1 = 2, m2 = 2, p = 2. .0000071345 .0068151892 2174 0 MG: r = 5, m1 = 2, m2 = 2, p = 2. .0000071345 .0068151891 2796 0 MG: r = 6, m1 = 2, m2 = 2, p = 2. .0000071345 .0068151891 3254 0 MG: r = 1, m1 = 3, m2 = 3, p = 2. .0000073297 .0068152400 770 0 MG: r = 2, m1 = 3, m2 = 3, p = 2. .0000071347 .0068151902 1441 0 MG: r = 3, m1 = 3, m2 = 3, p = 2. .0000071345 .0068151892 2216 0 MG: r = 4, m1 = 3, m2 = 3, p = 2. .0000071345 .0068151891 2741 3438 MG: r = 5, m1 = 3, m2 = 3, p = 2. .0000071345 .0068151891 3352 0 MG: r = 6, m1 = 3, m2 = 3, p = 2. .0000071345 .0068151891 4261 0 MG: r = 1, m1 = 4, m2 = 4, p = 2. .0000071877 .0068152047 923 0 MG: r = 2, m1 = 4, m2 = 4, p = 2. .0000071345 .0068151897 1818 0 MG: r = 3, m1 = 4, m2 = 4, p = 2. .0000071345 .0068151892 2837 0 MG: r = 4, m1 = 4, m2 = 4, p = 2. .0000071345 .0068151891 3506 0 MG: r = 5, m1 = 4, m2 = 4, p = 2. .0000071345 .0068151891 4341 3472 MG: r = 6, m1 = 4, m2 = 4, p = 2. .0000071345 .0068151891 6429 4216 a=1, c=1, gamma=2+\cos(\pi x), u=\sin(\pi x)+\sin(\pi y), Robin MG: r = 1, m1 = 1, m2 = 1, p = 1. .0002186942 .0097647153 204 0 MG: r = 2, m1 = 1, m2 = 1, p = 1. .0000135575 .0096387622 380 0 MG: r = 3, m1 = 1, m2 = 1, p = 1. .0000091427 .0096382419 559 0 MG: r = 4, m1 = 1, m2 = 1, p = 1. .0000084065 .0096382214 710 0 MG: r = 5, m1 = 1, m2 = 1, p = 1. .0000082101 .0096382208 870 0 MG: r = 6, m1 = 1, m2 = 1, p = 1. .0000081493 .0096382208 1050 0 MG: r = 1, m1 = 2, m2 = 2, p = 1. .0000219813 .0096389614 268 0 MG: r = 2, m1 = 2, m2 = 2, p = 1. .0000088446 .0096382213 507 0 MG: r = 3, m1 = 2, m2 = 2, p = 1. .0000082312 .0096382207 753 0 MG: r = 4, m1 = 2, m2 = 2, p = 1. .0000081396 .0096382209 1017 0 MG: r = 5, m1 = 2, m2 = 2, p = 1. .0000081229 .0096382209 1250 0 MG: r = 6, m1 = 2, m2 = 2, p = 1. .0000081195 .0096382209 1488 0 MG: r = 1, m1 = 3, m2 = 3, p = 1. .0000128633 .0096382693 344 0 MG: r = 2, m1 = 3, m2 = 3, p = 1. .0000083874 .0096382205 694 0 MG: r = 3, m1 = 3, m2 = 3, p = 1. .0000081507 .0096382209 1031 0 MG: r = 4, m1 = 3, m2 = 3, p = 1. .0000081230 .0096382209 1379 3393 MG: r = 5, m1 = 3, m2 = 3, p = 1. .0000081193 .0096382209 1690 0 MG: r = 6, m1 = 3, m2 = 3, p = 1. .0000081187 .0096382209 2131 3432 MG: r = 1, m1 = 4, m2 = 4, p = 1. .0000108004 .0096382289 438 0 MG: r = 2, m1 = 4, m2 = 4, p = 1. .0000082630 .0096382207 863 0 MG: r = 3, m1 = 4, m2 = 4, p = 1. .0000081325 .0096382209 1309 3710 MG: r = 4, m1 = 4, m2 = 4, p = 1. .0000081201 .0096382209 1673 0 MG: r = 5, m1 = 4, m2 = 4, p = 1. .0000081188 .0096382209 2298 3554 MG: r = 6, m1 = 4, m2 = 4, p = 1. .0000081187 .0096382209 2605 0 MG: r = 1, m1 = 1, m2 = 1, p = 2. .0000125782 .0096788613 414 0 MG: r = 2, m1 = 1, m2 = 1, p = 2. .0000082766 .0096387231 765 0 MG: r = 3, m1 = 1, m2 = 1, p = 2. .0000081262 .0096382425 1120 0 MG: r = 4, m1 = 1, m2 = 1, p = 2. .0000081193 .0096382219 1547 0 MG: r = 5, m1 = 1, m2 = 1, p = 2. .0000081187 .0096382210 1811 0 MG: r = 6, m1 = 1, m2 = 1, p = 2. .0000081187 .0096382209 2156 0 MG: r = 1, m1 = 2, m2 = 2, p = 2. .0000089087 .0096387271 533 0 MG: r = 2, m1 = 2, m2 = 2, p = 2. .0000081203 .0096382219 1039 0 MG: r = 3, m1 = 2, m2 = 2, p = 2. .0000081187 .0096382209 1530 0 MG: r = 4, m1 = 2, m2 = 2, p = 2. .0000081186 .0096382209 2071 0 MG: r = 5, m1 = 2, m2 = 2, p = 2. .0000081186 .0096382209 2743 0 MG: r = 6, m1 = 2, m2 = 2, p = 2. .0000081186 .0096382209 3103 0 MG: r = 1, m1 = 3, m2 = 3, p = 2. .0000082774 .0096382420 722 0 MG: r = 2, m1 = 3, m2 = 3, p = 2. .0000081188 .0096382209 1333 0 MG: r = 3, m1 = 3, m2 = 3, p = 2. .0000081186 .0096382209 2001 0 MG: r = 4, m1 = 3, m2 = 3, p = 2. .0000081186 .0096382209 2607 3449 MG: r = 5, m1 = 3, m2 = 3, p = 2. .0000081186 .0096382209 3304 0 MG: r = 6, m1 = 3, m2 = 3, p = 2. .0000081186 .0096382209 3940 0 MG: r = 1, m1 = 4, m2 = 4, p = 2. .0000081527 .0096382217 861 0 MG: r = 2, m1 = 4, m2 = 4, p = 2. .0000081186 .0096382209 1730 0 MG: r = 3, m1 = 4, m2 = 4, p = 2. .0000081186 .0096382209 2596 0 MG: r = 4, m1 = 4, m2 = 4, p = 2. .0000081186 .0096382209 3388 0 MG: r = 5, m1 = 4, m2 = 4, p = 2. .0000081186 .0096382209 4269 3463 MG: r = 6, m1 = 4, m2 = 4, p = 2. .0000081186 .0096382209 5043 3442 a=11.0+10.0*\cos\pi x, c=1+xy, gamma=2+\cos(\pi x), u=xy, Robin MG: r = 1, m1 = 1, m2 = 1, p = 1. .0077858740 .0577600625 187 0 MG: r = 2, m1 = 1, m2 = 1, p = 1. .0025536096 .0250662476 345 0 MG: r = 3, m1 = 1, m2 = 1, p = 1. .0011238963 .0133935480 509 0 MG: r = 4, m1 = 1, m2 = 1, p = 1. .0005822482 .0081693441 688 3425 MG: r = 5, m1 = 1, m2 = 1, p = 1. .0003386236 .0055346223 858 0 MG: r = 6, m1 = 1, m2 = 1, p = 1. .0002148046 .0040984904 1001 0 MG: r = 1, m1 = 2, m2 = 2, p = 1. .0038005395 .0320874439 268 0 MG: r = 2, m1 = 2, m2 = 2, p = 1. .0007982681 .0097622891 509 0 MG: r = 3, m1 = 2, m2 = 2, p = 1. .0002686912 .0045532981 762 0 MG: r = 4, m1 = 2, m2 = 2, p = 1. .0001205417 .0029282507 1014 3445 MG: r = 5, m1 = 2, m2 = 2, p = 1. .0000637519 .0023501835 1237 0 MG: r = 6, m1 = 2, m2 = 2, p = 1. .0000369916 .0021290480 1489 0 MG: r = 1, m1 = 3, m2 = 3, p = 1. .0020564913 .0191253888 344 0 MG: r = 2, m1 = 3, m2 = 3, p = 1. .0003221868 .0049445928 674 0 MG: r = 3, m1 = 3, m2 = 3, p = 1. .0000969053 .0026408442 1015 0 MG: r = 4, m1 = 3, m2 = 3, p = 1. .0000401406 .0021436195 1340 0 MG: r = 5, m1 = 3, m2 = 3, p = 1. .0000195028 .0020174987 1703 0 MG: r = 6, m1 = 3, m2 = 3, p = 1. .0000106621 .0019790837 2107 3454 MG: r = 1, m1 = 4, m2 = 4, p = 1. .0012217048 .0123588871 425 0 MG: r = 2, m1 = 4, m2 = 4, p = 1. .0001569797 .0031817222 843 0 MG: r = 3, m1 = 4, m2 = 4, p = 1. .0000435445 .0021584154 1259 0 MG: r = 4, m1 = 4, m2 = 4, p = 1. .0000167489 .0020020473 1678 0 MG: r = 5, m1 = 4, m2 = 4, p = 1. .0000080293 .0019688766 2130 3477 MG: r = 6, m1 = 4, m2 = 4, p = 1. .0000048968 .0019593357 2470 0 MG: r = 1, m1 = 1, m2 = 1, p = 2. .0001019723 .0048347891 448 3472 MG: r = 2, m1 = 1, m2 = 1, p = 2. .0000268175 .0029610010 820 0 MG: r = 3, m1 = 1, m2 = 1, p = 2. .0000121284 .0024718285 1226 0 MG: r = 4, m1 = 1, m2 = 1, p = 2. .0000072772 .0022694739 1646 3835 MG: r = 5, m1 = 1, m2 = 1, p = 2. .0000052689 .0021646954 2069 0 MG: r = 6, m1 = 1, m2 = 1, p = 2. .0000043265 .0021028470 2480 3454 MG: r = 1, m1 = 2, m2 = 2, p = 2. .0000282861 .0029697258 587 0 MG: r = 2, m1 = 2, m2 = 2, p = 2. .0000075617 .0022700647 1156 0 MG: r = 3, m1 = 2, m2 = 2, p = 2. .0000044348 .0021029514 1712 3473 MG: r = 4, m1 = 2, m2 = 2, p = 2. .0000036234 .0020363131 2283 0 MG: r = 5, m1 = 2, m2 = 2, p = 2. .0000033396 .0020033897 2966 3443 MG: r = 6, m1 = 2, m2 = 2, p = 2. .0000032169 .0019850809 3481 0 MG: r = 1, m1 = 3, m2 = 3, p = 2. .0000133191 .0024763740 739 0 MG: r = 2, m1 = 3, m2 = 3, p = 2. .0000045618 .0021031095 1489 0 MG: r = 3, m1 = 3, m2 = 3, p = 2. .0000034906 .0020173068 2409 0 MG: r = 4, m1 = 3, m2 = 3, p = 2. .0000032334 .0019850904 3107 0 MG: r = 5, m1 = 3, m2 = 3, p = 2. .0000031442 .0019702938 3872 3406 MG: r = 6, m1 = 3, m2 = 3, p = 2. .0000031065 .0019627482 4686 0 MG: r = 1, m1 = 4, m2 = 4, p = 2. .0000083556 .0022720622 917 0 MG: r = 2, m1 = 4, m2 = 4, p = 2. .0000037502 .0020364261 1850 0 MG: r = 3, m1 = 4, m2 = 4, p = 2. .0000032521 .0019851033 2742 3451 MG: r = 4, m1 = 4, m2 = 4, p = 2. .0000031349 .0019672324 3922 0 MG: r = 5, m1 = 4, m2 = 4, p = 2. .0000030960 .0019597700 4627 0 MG: r = 6, m1 = 4, m2 = 4, p = 2. .0000030812 .0019563703 5539 3462 >