This page contains the raw performance data of the GESP algorithm. The summary charts appear in the following paper SuperLU_DIST: A Scalable Distributed-memory Sparse Direct Solver for Unsymmetric Linear Systems, Technical report, LBNL-49388.

Unsymmetric Test Matrices
Matrix N nnz(A) nnz(L+U) Discipline
1   add32 4960 23884 33724 circuit simulation
2   af23560 23560 484256 11795256 fluid flow
3   bayer01 57735 277774 1509401 chemical process
4   bayer02 13925 63679 266944 chemical process
5   bayer04 20545 159082 655252 chemical process
6   bbmat 38744 1771722 36881778 CFD
7   bramley117933 1021849 5524383 nonlinear CFD
8   bramley217933 1021849 5449586 nonlinear CFD
9   cry1000010000 49699 429655 crystal growth simulation
10 dw8192 8192 41746 511544 dielectric waveguide
11 ecl32 51993 380415 41752318 device simulation
12 ex11 16614 1096948 11540142 fluid flow
13 ex19 12005 259879 675117 fluid flow
14 extr1 2837 11407 35729 chemical engineering
15 fidap011 16614 1091362 11993828 fluid flow
16 fidap019 12005 259863 675117 fluid flow
17 fidapm11 22294 623554 26590861 fluid flow
18 fidapm29 13668 186294 1462650 fluid flow
19 fs_541_2 541 4285 18825 stiff ODE
20 garon2 13535 390607 2555223 fluid flow, 2D FEM
21 gemat11 4929 33185 65796 power flow modelling
22 goodwin 7320 324784 1199369 fluid mechanics
23 graham1 9035 335504 1359726 fluid flow
24 gre_1107 1107 5664 99010 circuit simulation
25 gre_115 115 421 2094 circuit simulation
26 hydr1 5308 23752 83176 chemical engineering
27 inaccura 16146 1015156 6154878 fluid flow
28 inv-extrusion-130412 1793881 30301246 fluid flow
29 jpwh_991 991 6027 56572 circuit physics
30 lhr01 1477 18592 83185 chemical engineering
31 lhr71c 70304 1528092 8133895 chemical engineering
32 lns_3937 3937 25407 328874 fluid flow
33 lnsp3937 3937 25407 323398 fluid flow
34 mahindas 1258 7682 29712 economics
35 mcfe 765 24382 79460 astrophysics
36 memplus 17758 126150 152116 circuit simulation
37 mhd500 250000 1242016 17085029 MagnetoHydroDynamics
38 mixing-tank 29957 1995041 43508740 fluid flow
39 olm5000 5000 19996 20080 olmstead flow model
40 onetone1 36057 341088 3210570 circuit simulation
41 onetone2 36057 227628 1580803 circuit simulation
42 orani678 2529 90158 192974 economics
43 orsreg_1 2205 14133 237566 petroleum engineering
44 pores_2 1224 9613 64175 reservoir modelling
45 psmigr_1 3140 543162 5737679 demography
46 psmigr_2 3140 540022 6296789 demography
47 psmigr_3 3140 543162 5737679 demography
48 radfr1 1048 13299 25622 chemical engineering
49 raefsky3 21200 1488768 8132736 CFD
50 raefsky4 19779 1328611 13158991 CFD
51 rdist1 4134 94408 210080 chemical engineering
52 rdist2 3198 56934 117897 chemical engineering
53 rdist3a 2398 61896 140715 chemical engineering
54 rma10 46835 2374001 9489073 fluid flow
55 saylr4 3564 22316 330810 petroleum engineering
56 sherman3 5005 20033 221269 petroleum engineering
57 sherman4 1104 3786 18284 petroleum engineering
58 sherman5 3312 20793 150766 petroleum engineering
59 tols4000 4000 8784 21458 aeroelasticity
60 twotone 120750 1224224 11524112 circuit simulation
61 utm5940 5940 83842 767312 plasma physics
62 av4408 4408 95752 432105 finite element PDE
63 av11924 11924 306842 1707649 finite element PDE
64 venkat01 62424 1717792 11902656 CFD
65 wang3 26064 177168 11188368 device simulation
66 wang4 26068 177196 10716624 device simulation
67 west2021 2021 7353 18451 chemical engineering
68 wu 5292 88368 488668 fluid flow


Numerical Results from GESP

Matrix RPG RCOND Steps BERR True error
1   add32 1.0e+00 8.7e-03 1 1.8e-16 5.8e-15
2   af23560 2.5e-04 8.6e-06 2 3.0e-16 2.1e-14
3   bayer01 4.5e-02 2.1e-05 2 2.2e-16 1.4e-06
4   bayer02 1.5e-01 2.8e-04 2 2.1e-16 1.6e-06
5   bayer04 2.3e-05 4.1e-06 2 2.8e-16 8.6e-05
6   bbmat 1.8e-10 4.2e-08 3 6.1e-16 4.4e-09
7   bramley11.9e-02 4.5e-09 2 5.2e-16 2.1e-09
8   bramley22.1e-02 4.5e-09 2 5.9e-16 4.0e-09
9   cry100004.5e-05 1.1e-21 2 2.6e-16 1.7e-04
10 dw8192 8.6e-04 1.0e-06 2 2.3e-16 5.0e-13
11 ecl32 5.3e-02 7.0e-09 2 4.5e-16 2.0e-11
12 ex11 6.5e-01 4.4e-12 2 4.5e-16 1.9e-06
13 ex19 7.0e-01 8.2e-12 1 3.0e-16 3.6e-07
14 extr1 5.2e-13 2.4e-05 2 1.6e-16 8.4e-11
15 fidap011 6.2e-01 4.4e-12 1 5.6e-16 1.3-06
16 fidap019 7.0e-01 8.2e-12 1 3.0e-16 3.4e-07
17 fidapm11 1.8e-21 2.6e-10 7 3.7e-16 1.4e-12
18 fidapm29 7.3e-07 2.1e-06 2 4.9e-16 5.1e-13
19 fs_541_2 9.7e-01 6.0e-04 2 1.5e-16 8.0e-11
20 garon2 4.2e-02 3.7e-05 2 3.6e-16 2.4e-12
21 gemat11 4.0e-02 1.8e-07 2 2.2e-16 1.8e-11
22 goodwin 1.0e-12 1.8e-08 5 5.2e-16 5.2e-10
23 graham1 7.3e-12 2.2e-07 5 3.0e-16 1.2e-09
24 gre_1107 4.2e-05 1.8e-07 2 1.4e-16 6.0e-10
25 gre_115 5.8e-01 4.2e-03 1 1.0e-16 2.7e-15
26 hydr1 3.0e-03 2.0e-05 2 2.6e-16 9.9e-09
27 inaccura 5.6e-01 9.8e-10 1 5.4e-16 6.7e-09
28 inv-extrusion-12.2e-07 3.3e-10 3 6.8e-16 1.7e-05
29 jpwh_991 4.1e-25 3.8e-14 3 2.0e-16 1.0e-14
30 lhr01 5.5e-03 6.1e-05 2 1.9e-16 2.1e-12
31 lhr71c 2.9e-12 1.3e-13 6 9.8e-14 2.7e-02
32 lns_3937 9.8e-10 2.7e-05 3 2.4e-16 1.7e-11
33 lnsp3937 2.6e-03 2.7e-05 2 2.4e-16 2.2e-11
34 mahindas 1.4e-01 1.3e-05 2 1.2e-16 1.8e-10
35 mcfe 1.2e-01 4.1e-03 2 1.7e-16 1.8e-15
36 memplus 1.0e+00 4.2e-05 2 3.8e-16 2.0e-12
37 mhd500 1.0e+00 6.8e-06 2 2.5e-16 2.1e-13
38 mixing-tank 4.9e-13 6.8e-06 6 5.8e-16 1.9e-11
39 olm5000 4.9e-01 3.9e-07 1 1.1e-16 3.6e-11
40 onetone1 3.7e-05 3.3e-09 2 5.8e-16 1.9e-11
41 onetone2 2.4e-07 1.9e-09 2 3.2e-16 4.7e-12
42 orani678 1.0e-01 1.2e-07 2 1.9e-16 1.1e-14
43 orsreg_1 8.7e-14 1.5e-05 7 3.0e-15 4.2e-11
44 pores_2 4.7e-01 3.0e-06 2 2.0e-16 8.5e-13
45 psmigr_1 7.7e-01 9.6e-05 2 1.3e-16 3.9e-11
46 psmigr_2 6.2e-17 9.0e-08 2 1.9e-15 2.0e-12
47 psmigr_3 7.7e-01 1.2e-03 2 2.2e-16 7.0e-14
48 radfr1 2.2e-07 6.7e-09 2 1.6e-16 2.7e-10
49 raefsky3 1.9e-01 2.5e-05 2 5.3e-16 2.7e-13
50 raefsky4 1.4e-01 1.6e-12 2 6.3e-16 1.1e-06
51 rdist1 3.7e-03 1.5e-05 2 2.7e-16 8.7e-14
52 rdist2 3.6e-02 5.7e-05 2 2.0e-16 2.2e-14
53 rdist3a 2.7e-02 1.5e-05 2 2.6e-16 3.1e-13
54 rma10 1.3e-10 3.5e-06 3 4.9e-16 9.3e-13
55 saylr4 1.0e+00 1.7e-07 2 2.0e-16 2.0e-10
56 sherman3 1.0e+00 1.9e-05 2 2.2e-16 6.7e-13
57 sherman4 1.0e+00 1.2e-04 1 2.1e-16 3.1e-15
58 sherman5 5.3e-01 5.8e-05 2 1.5e-16 5.1e-15
59 tols4000 1.0e+00 9.3e-03 1 8.2e-17 2.4e-15
60 twotone 2.4e-05 8.0e-08 2 6.1e-16 1.5e-11
61 utm5940 8.9e-04 3.6e-10 2 3.5e-16 3.8e-09
62 av4408 2.3e-15 3.8e-04 6 2.1e-16 4.7e-14
63 av11924 1.0e-12 1.7e-04 4 4.2e-16 1.1e-13
64 venkat01 6.0e-01 2.6e-03 2 3.0e-16 5.3e-15
65 wang3 1.0e+00 2.9e-04 2 2.1e-16 4.7e-13
66 wang4 1.0e+00 5.1e-04 2 2.4e-16 1.2e-12
67 west2021 3.9e-08 6.2e-06 2 2.0e-16 1.0e-09
68 wu 1.7e-09 2.2e-18 2 4.1e-16 1.6e-06


Runtime of various steps