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Asymptotic properties of an infinite horizon partial cheap control problem for linear systems with known disturbances
Experiments with sparse Cholesky using a sequential task-flow implementation
Scientific Computing Department, STFC Rutherford Appleton Laboratory, Harwell Campus, Oxfordshire, OX11 0QX, UK |
We describe the development of a prototype code for the solution of large sparse symmetric positive definite systems that is efficient on parallel architectures. We implement a DAG-based Cholesky factorization that offers good performance and scalability on multicore architectures. Our approach uses a runtime system to execute the DAG. The runtime system plays the role of a software layer between the application and the architecture and handles the management of task dependencies as well as the task scheduling. In this model, the application is expressed using a high-level API, independent of the hardware details, thus enabling portability across different architectures. Although widely used in dense linear algebra, this approach is nevertheless challenging for sparse algorithms because of the irregularity and variable granularity of the DAGs arising in these systems. We assess the ability of two different Sequential Task Flow implementations to address this challenge: one implemented with the OpenMP standard, and the other with the modern runtime system StarPU. We compare these implementations to the state-of-the-art solver HSL_MA87 and demonstrate comparable performance on a multicore architecture.
References:
[1] |
E. Agullo, A. Buttari, A. Guermouche and F. Lopez, Implementing multifrontal sparse solvers for multicore architectures with sequential task flow runtime systems, ACM Trans. Math. Softw., 43 (2016), 13: 1-13: 22,
doi: 10.1145/2898348. |
[2] |
E. Agullo, J. Demmel, J. Dongarra, B. Hadri, J. Kurzak, J. Langou, H. Ltaief, P. Luszczek and S. Tomov, Numerical linear algebra on emerging architectures: The PLASMA and MAGMA projects, Journal of Physics: Conference Series, 180 (2009), 012037, http://stacks.iop.org/1742-6596/180/i=1/a=012037.
doi: 10.1088/1742-6596/180/1/012037. |
[3] |
P. R. Amestoy, T. A. Davis and I. S. Duff, An approximate minimum degree ordering algorithm, SIAM J. Matrix Anal. Appl., 17 (1996), 886-905,
doi: 10.1137/S0895479894278952. |
[4] |
P. R. Amestoy, T. A. Davis and I. S. Duff, Algorithm 837: Amd, an approximate minimum degree ordering algorithm, ACM Trans. Math. Softw., 30 (2004), 381-388,
doi: 10.1145/1024074.1024081. |
[5] |
C. Augonnet, S. Thibault, R. Namyst and P. -A. Wacrenier, Starpu: a unified platform for task scheduling on heterogeneous multicore architectures, Concurrency and Computation: Practice and Experience, 23 (2011), 187-198,
doi: 10.1007/978-3-642-03869-3_80. |
[6] |
G. Bosilca, A. Bouteiller, A. Danalis, M. Faverge, A. Haidar, T. Hérault, J. Kurzak, J. Langou, P. Lemarinier, H. Ltaief, P. Luszczek, A. Yarkhan and J. J. Dongarra, Distibuted dense numerical linear algebra algorithms on massively parallel architectures: DPLASMA, in Proceedings of the 25th IEEE International Symposium on Parallel and Distributed Processing Workshops and Phd Forum (IPDPSW'11), PDSEC 2011, Anchorage, United States, (2011), 1432-1441, https://hal.inria.fr/hal-00809680. |
[7] |
G. Bosilca, A. Bouteiller, A. Danalis, M. Faverge, T. Hérault and J. J. Dongarra, Parsec: Exploiting heterogeneity to enhance scalability, Computing in Science and Engineering, 15 (2013), 36-45,
doi: 10.1109/MCSE.2013.98. |
[8] |
A. Buttari, Fine-grained multithreading for the multifrontal QR factorization of sparse matrices, SIAM Journal on Scientific Computing, 35 (2013), C323-C345,
doi: 10.1137/110846427. |
[9] |
M. Cosnard and M. Loi, Automatic task graph generation techniques, in System Sciences, 1995. Proceedings of the Twenty-Eighth Hawaii International Conference on, 2 (1995), 113-122.
doi: 10.1109/HICSS.1995.375471. |
[10] |
T. A. Davis and Y. Hu,
The university of Florida sparse matrix collection, ACM Trans. Math. Softw., 38 (2011), 1:1-1:25.
doi: 10.1145/2049662.2049663. |
[11] |
G. A. Geist and E. Ng,
Task scheduling for parallel sparse cholesky factorization, Int. J. Parallel Program., 18 (1990), 291-314.
doi: 10.1007/BF01407861. |
[12] |
A. George and J. W. H. Liu,
An automatic nested dissection algorithm for irregular finite element problems, SINUM, 15 (1978), 1053-1069.
doi: 10.1137/0715069. |
[13] |
P. Hénon, P. Ramet and J. Roman,
PaStiX: A high-performance parallel direct solver For sparse symmetric definite systems, Parallel Computing, 28 (2002), 301-321.
doi: 10.1016/S0167-8191(01)00141-7. |
[14] |
J. D. Hogg, J. K. Reid and J. A. Scott,
Design of a multicore sparse cholesky factorization using dags, SIAM Journal on Scientific Computing, 32 (2010), 3627-3649.
doi: 10.1137/090757216. |
[15] |
J. D. Hogg and J. A. Scott, A modern analyse phase for sparse tree-based direct methods, Technical Report RAL-TR-2010-031, STFC Rutherford Appleton Lab., 2010, https://epubs.stfc.ac.uk/work/54246. |
[16] |
F. D. Igual, E. Chan, E. S. Quintana-Ortí, G. Quintana-Ortí, R. A. van de Geijn and F. G. V. Zee,
The flame approach: From dense linear algebra algorithms to high-performance multi-accelerator implementations, J. Parallel Distrib. Comput., 72 (2012), 1134-1143.
doi: 10.1016/j.jpdc.2011.10.014. |
[17] |
G. Karypis and V. Kumar, A fast and high quality multilevel scheme for partitioning irregular graphs,
SIAM J. Sci. Comput., 20 (1998), 359-392,
doi: 10.1137/S1064827595287997. |
[18] |
J. W. H. Liu, Modification of the minimum-degree algorithm by multiple elimination, ACM Trans. Math. Softw., 11 (1985), 141-153,
doi: 10.1145/214392.214398. |
[19] |
F. Lopez, Task-based Multifrontal QR Solver for Heterogeneous Architectures, Thèse de doctorat, Université Paul Sabatier, Toulouse, France, 2015. |
[20] |
W. F. Tinney and J. W. Walker,
Direct solutions of sparse network equations by optimally ordered triangular factorization, Proceedings of the IEEE, 55 (1967), 1801-1809.
doi: 10.1109/PROC.1967.6011. |
show all references
References:
[1] |
E. Agullo, A. Buttari, A. Guermouche and F. Lopez, Implementing multifrontal sparse solvers for multicore architectures with sequential task flow runtime systems, ACM Trans. Math. Softw., 43 (2016), 13: 1-13: 22,
doi: 10.1145/2898348. |
[2] |
E. Agullo, J. Demmel, J. Dongarra, B. Hadri, J. Kurzak, J. Langou, H. Ltaief, P. Luszczek and S. Tomov, Numerical linear algebra on emerging architectures: The PLASMA and MAGMA projects, Journal of Physics: Conference Series, 180 (2009), 012037, http://stacks.iop.org/1742-6596/180/i=1/a=012037.
doi: 10.1088/1742-6596/180/1/012037. |
[3] |
P. R. Amestoy, T. A. Davis and I. S. Duff, An approximate minimum degree ordering algorithm, SIAM J. Matrix Anal. Appl., 17 (1996), 886-905,
doi: 10.1137/S0895479894278952. |
[4] |
P. R. Amestoy, T. A. Davis and I. S. Duff, Algorithm 837: Amd, an approximate minimum degree ordering algorithm, ACM Trans. Math. Softw., 30 (2004), 381-388,
doi: 10.1145/1024074.1024081. |
[5] |
C. Augonnet, S. Thibault, R. Namyst and P. -A. Wacrenier, Starpu: a unified platform for task scheduling on heterogeneous multicore architectures, Concurrency and Computation: Practice and Experience, 23 (2011), 187-198,
doi: 10.1007/978-3-642-03869-3_80. |
[6] |
G. Bosilca, A. Bouteiller, A. Danalis, M. Faverge, A. Haidar, T. Hérault, J. Kurzak, J. Langou, P. Lemarinier, H. Ltaief, P. Luszczek, A. Yarkhan and J. J. Dongarra, Distibuted dense numerical linear algebra algorithms on massively parallel architectures: DPLASMA, in Proceedings of the 25th IEEE International Symposium on Parallel and Distributed Processing Workshops and Phd Forum (IPDPSW'11), PDSEC 2011, Anchorage, United States, (2011), 1432-1441, https://hal.inria.fr/hal-00809680. |
[7] |
G. Bosilca, A. Bouteiller, A. Danalis, M. Faverge, T. Hérault and J. J. Dongarra, Parsec: Exploiting heterogeneity to enhance scalability, Computing in Science and Engineering, 15 (2013), 36-45,
doi: 10.1109/MCSE.2013.98. |
[8] |
A. Buttari, Fine-grained multithreading for the multifrontal QR factorization of sparse matrices, SIAM Journal on Scientific Computing, 35 (2013), C323-C345,
doi: 10.1137/110846427. |
[9] |
M. Cosnard and M. Loi, Automatic task graph generation techniques, in System Sciences, 1995. Proceedings of the Twenty-Eighth Hawaii International Conference on, 2 (1995), 113-122.
doi: 10.1109/HICSS.1995.375471. |
[10] |
T. A. Davis and Y. Hu,
The university of Florida sparse matrix collection, ACM Trans. Math. Softw., 38 (2011), 1:1-1:25.
doi: 10.1145/2049662.2049663. |
[11] |
G. A. Geist and E. Ng,
Task scheduling for parallel sparse cholesky factorization, Int. J. Parallel Program., 18 (1990), 291-314.
doi: 10.1007/BF01407861. |
[12] |
A. George and J. W. H. Liu,
An automatic nested dissection algorithm for irregular finite element problems, SINUM, 15 (1978), 1053-1069.
doi: 10.1137/0715069. |
[13] |
P. Hénon, P. Ramet and J. Roman,
PaStiX: A high-performance parallel direct solver For sparse symmetric definite systems, Parallel Computing, 28 (2002), 301-321.
doi: 10.1016/S0167-8191(01)00141-7. |
[14] |
J. D. Hogg, J. K. Reid and J. A. Scott,
Design of a multicore sparse cholesky factorization using dags, SIAM Journal on Scientific Computing, 32 (2010), 3627-3649.
doi: 10.1137/090757216. |
[15] |
J. D. Hogg and J. A. Scott, A modern analyse phase for sparse tree-based direct methods, Technical Report RAL-TR-2010-031, STFC Rutherford Appleton Lab., 2010, https://epubs.stfc.ac.uk/work/54246. |
[16] |
F. D. Igual, E. Chan, E. S. Quintana-Ortí, G. Quintana-Ortí, R. A. van de Geijn and F. G. V. Zee,
The flame approach: From dense linear algebra algorithms to high-performance multi-accelerator implementations, J. Parallel Distrib. Comput., 72 (2012), 1134-1143.
doi: 10.1016/j.jpdc.2011.10.014. |
[17] |
G. Karypis and V. Kumar, A fast and high quality multilevel scheme for partitioning irregular graphs,
SIAM J. Sci. Comput., 20 (1998), 359-392,
doi: 10.1137/S1064827595287997. |
[18] |
J. W. H. Liu, Modification of the minimum-degree algorithm by multiple elimination, ACM Trans. Math. Softw., 11 (1985), 141-153,
doi: 10.1145/214392.214398. |
[19] |
F. Lopez, Task-based Multifrontal QR Solver for Heterogeneous Architectures, Thèse de doctorat, Université Paul Sabatier, Toulouse, France, 2015. |
[20] |
W. F. Tinney and J. W. Walker,
Direct solutions of sparse network equations by optimally ordered triangular factorization, Proceedings of the IEEE, 55 (1967), 1801-1809.
doi: 10.1109/PROC.1967.6011. |




















# | Name | MA87 | spLLT | ||||
MA87 | OpenMP (gnu) | StarPU | |||||
nb | factor. (s) |
nb | factor. (s) |
nb | factor. (s) |
||
1 | Schmid/thermal2 | 1024 | 0.391 | 1024 | 1.742 | 512 | 2.215 |
2 | Rothberg/gearbox | 256 | 0.253 | 384 | 0.236 | 512 | 0.339 |
3 | DNVS/m_t1 | 256 | 0.206 | 256 | 0.208 | 1024 | 0.298 |
4 | Boeing/pwtk | 768 | 0.249 | 768 | 0.262 | 768 | 0.396 |
5 | Chen/pkustk13 | 256 | 0.218 | 256 | 0.242 | 384 | 0.344 |
6 | GHS_psdef/crankseg_1 | 256 | 0.233 | 256 | 0.234 | 384 | 0.281 |
7 | Rothberg/cfd2 | 256 | 0.242 | 256 | 0.256 | 384 | 0.386 |
8 | DNVS/thread | 256 | 0.236 | 256 | 0.223 | 384 | 0.222 |
9 | DNVS/shipsec8 | 256 | 0.253 | 256 | 0.234 | 384 | 0.380 |
10 | DNVS/shipsec1 | 256 | 0.245 | 256 | 0.270 | 384 | 0.398 |
11 | GHS_psdef/crankseg_2 | 256 | 0.267 | 256 | 0.268 | 384 | 0.326 |
12 | DNVS/fcondp2 | 256 | 0.294 | 384 | 0.347 | 384 | 0.479 |
13 | Schenk_AFE/af _shell3 | 256 | 0.437 | 512 | 0.550 | 512 | 0.906 |
14 | DNVS/troll | 256 | 0.381 | 384 | 0.434 | 512 | 0.599 |
15 | AMD/G3_circuit | 256 | 0.607 | 768 | 2.534 | 768 | 3.561 |
16 | GHS_psdef/bmwcra_1 | 256 | 0.339 | 256 | 0.356 | 512 | 0.466 |
17 | DNVS/halfb | 256 | 0.370 | 256 | 0.442 | 384 | 0.631 |
18 | Um/2cubes_sphere | 256 | 0.321 | 384 | 0.451 | 512 | 0.634 |
19 | GHS_psdef/ldoor | 256 | 0.620 | 512 | 1.058 | 768 | 1.726 |
20 | DNVS/ship_003 | 256 | 0.361 | 384 | 0.457 | 512 | 0.554 |
21 | DNVS/fullb | 256 | 0.445 | 256 | 0.469 | 384 | 0.651 |
22 | GHS_psdef/inline_1 | 256 | 0.659 | 384 | 0.711 | 768 | 0.995 |
23 | Chen/pkustk14 | 256 | 0.557 | 256 | 0.576 | 512 | 0.768 |
24 | GHS_psdef/apache2 | 256 | 0.710 | 768 | 1.448 | 512 | 2.053 |
25 | Koutsovasilis/F1 | 384 | 0.776 | 384 | 0.829 | 768 | 0.981 |
26 | Oberwolfach/boneS10 | 256 | 1.102 | 256 | 1.185 | 768 | 1.702 |
27 | ND/nd12k | 384 | 1.452 | 384 | 1.479 | 768 | 1.611 |
28 | JGD_Trefethen/Trefethen_20000 | 768 | 4.233 | 512 | 3.700 | 768 | 3.843 |
29 | ND/nd24k | 384 | 5.350 | 512 | 5.570 | 768 | 5.485 |
30 | Janna/Flan_1565 | 384 | 7.722 | 512 | 7.921 | 768 | 8.419 |
31 | Oberwolfach/bone010 | 384 | 7.117 | 768 | 7.350 | 768 | 7.525 |
32 | Janna/StocF-1465 | 768 | 8.337 | 768 | 9.455 | 768 | 9.869 |
33 | GHS_psdef/audikw_1 | 384 | 10.419 | 768 | 10.630 | 768 | 10.680 |
34 | Janna/Fault_639 | 384 | 14.392 | 768 | 14.350 | 768 | 14.260 |
35 | Janna/Hook_1498 | 512 | 17.019 | 384 | 16.860 | 768 | 16.960 |
36 | Janna/Emilia_923 | 768 | 23.221 | 384 | 22.620 | 768 | 23.060 |
37 | Janna/Geo_1438 | 768 | 29.654 | 768 | 29.250 | 1024 | 29.380 |
38 | Janna/Serena | 768 | 52.830 | 384 | 51.170 | 768 | 51.900 |
# | Name | MA87 | spLLT | ||||
MA87 | OpenMP (gnu) | StarPU | |||||
nb | factor. (s) |
nb | factor. (s) |
nb | factor. (s) |
||
1 | Schmid/thermal2 | 1024 | 0.391 | 1024 | 1.742 | 512 | 2.215 |
2 | Rothberg/gearbox | 256 | 0.253 | 384 | 0.236 | 512 | 0.339 |
3 | DNVS/m_t1 | 256 | 0.206 | 256 | 0.208 | 1024 | 0.298 |
4 | Boeing/pwtk | 768 | 0.249 | 768 | 0.262 | 768 | 0.396 |
5 | Chen/pkustk13 | 256 | 0.218 | 256 | 0.242 | 384 | 0.344 |
6 | GHS_psdef/crankseg_1 | 256 | 0.233 | 256 | 0.234 | 384 | 0.281 |
7 | Rothberg/cfd2 | 256 | 0.242 | 256 | 0.256 | 384 | 0.386 |
8 | DNVS/thread | 256 | 0.236 | 256 | 0.223 | 384 | 0.222 |
9 | DNVS/shipsec8 | 256 | 0.253 | 256 | 0.234 | 384 | 0.380 |
10 | DNVS/shipsec1 | 256 | 0.245 | 256 | 0.270 | 384 | 0.398 |
11 | GHS_psdef/crankseg_2 | 256 | 0.267 | 256 | 0.268 | 384 | 0.326 |
12 | DNVS/fcondp2 | 256 | 0.294 | 384 | 0.347 | 384 | 0.479 |
13 | Schenk_AFE/af _shell3 | 256 | 0.437 | 512 | 0.550 | 512 | 0.906 |
14 | DNVS/troll | 256 | 0.381 | 384 | 0.434 | 512 | 0.599 |
15 | AMD/G3_circuit | 256 | 0.607 | 768 | 2.534 | 768 | 3.561 |
16 | GHS_psdef/bmwcra_1 | 256 | 0.339 | 256 | 0.356 | 512 | 0.466 |
17 | DNVS/halfb | 256 | 0.370 | 256 | 0.442 | 384 | 0.631 |
18 | Um/2cubes_sphere | 256 | 0.321 | 384 | 0.451 | 512 | 0.634 |
19 | GHS_psdef/ldoor | 256 | 0.620 | 512 | 1.058 | 768 | 1.726 |
20 | DNVS/ship_003 | 256 | 0.361 | 384 | 0.457 | 512 | 0.554 |
21 | DNVS/fullb | 256 | 0.445 | 256 | 0.469 | 384 | 0.651 |
22 | GHS_psdef/inline_1 | 256 | 0.659 | 384 | 0.711 | 768 | 0.995 |
23 | Chen/pkustk14 | 256 | 0.557 | 256 | 0.576 | 512 | 0.768 |
24 | GHS_psdef/apache2 | 256 | 0.710 | 768 | 1.448 | 512 | 2.053 |
25 | Koutsovasilis/F1 | 384 | 0.776 | 384 | 0.829 | 768 | 0.981 |
26 | Oberwolfach/boneS10 | 256 | 1.102 | 256 | 1.185 | 768 | 1.702 |
27 | ND/nd12k | 384 | 1.452 | 384 | 1.479 | 768 | 1.611 |
28 | JGD_Trefethen/Trefethen_20000 | 768 | 4.233 | 512 | 3.700 | 768 | 3.843 |
29 | ND/nd24k | 384 | 5.350 | 512 | 5.570 | 768 | 5.485 |
30 | Janna/Flan_1565 | 384 | 7.722 | 512 | 7.921 | 768 | 8.419 |
31 | Oberwolfach/bone010 | 384 | 7.117 | 768 | 7.350 | 768 | 7.525 |
32 | Janna/StocF-1465 | 768 | 8.337 | 768 | 9.455 | 768 | 9.869 |
33 | GHS_psdef/audikw_1 | 384 | 10.419 | 768 | 10.630 | 768 | 10.680 |
34 | Janna/Fault_639 | 384 | 14.392 | 768 | 14.350 | 768 | 14.260 |
35 | Janna/Hook_1498 | 512 | 17.019 | 384 | 16.860 | 768 | 16.960 |
36 | Janna/Emilia_923 | 768 | 23.221 | 384 | 22.620 | 768 | 23.060 |
37 | Janna/Geo_1438 | 768 | 29.654 | 768 | 29.250 | 1024 | 29.380 |
38 | Janna/Serena | 768 | 52.830 | 384 | 51.170 | 768 | 51.900 |
# | Name | DAG stats | SpLLT (StarPU) | ||
# task | time/task avg. (ms) | task insert (s) | factor. time (s) | ||
1 | Schmid/thermal2 | 166695 | 0.071 | 2.213 | 2.215 |
2 | Rothberg/gearbox | 19392 | 0.417 | 0.326 | 0.339 |
8 | DNVS/thread | 7481 | 0.746 | 0.155 | 0.222 |
13 | Schenk_AFE/af _shell3 | 65195 | 0.250 | 0.906 | 0.906 |
15 | AMD/G3_circuit | 290235 | 0.154 | 3.558 | 3.561 |
19 | GHS_psdef/ldoor | 126786 | 0.230 | 1.724 | 1.726 |
24 | GHS_psdef/apache2 | 163804 | 0.264 | 2.052 | 2.053 |
32 | Janna/Flan_1565 | 226486 | 1.007 | 3.452 | 8.419 |
35 | Janna/Hook_1498 | 639060 | 0.867 | 8.441 | 16.960 |
38 | Janna/Serena | 795367 | 1.857 | 10.920 | 51.900 |
# | Name | DAG stats | SpLLT (StarPU) | ||
# task | time/task avg. (ms) | task insert (s) | factor. time (s) | ||
1 | Schmid/thermal2 | 166695 | 0.071 | 2.213 | 2.215 |
2 | Rothberg/gearbox | 19392 | 0.417 | 0.326 | 0.339 |
8 | DNVS/thread | 7481 | 0.746 | 0.155 | 0.222 |
13 | Schenk_AFE/af _shell3 | 65195 | 0.250 | 0.906 | 0.906 |
15 | AMD/G3_circuit | 290235 | 0.154 | 3.558 | 3.561 |
19 | GHS_psdef/ldoor | 126786 | 0.230 | 1.724 | 1.726 |
24 | GHS_psdef/apache2 | 163804 | 0.264 | 2.052 | 2.053 |
32 | Janna/Flan_1565 | 226486 | 1.007 | 3.452 | 8.419 |
35 | Janna/Hook_1498 | 639060 | 0.867 | 8.441 | 16.960 |
38 | Janna/Serena | 795367 | 1.857 | 10.920 | 51.900 |
# | Name | n (103) |
nz(A) (106) |
nz(L) (106) |
Flops (109) |
Application/Description |
1 | Schmid/thermal2 | 1228 | 4.9 | 51.6 | 14.6 | Unstructured thermal FEM |
2 | Rothberg/gearbox | 154 | 4.6 | 37.1 | 20.6 | Aircraft flap actuator |
3 | DNVS/m_t1 | 97.6 | 4.9 | 34.2 | 21.9 | Tubular joint |
4 | Boeing/pwtk | 218 | 5.9 | 48.6 | 22.4 | Pressurised wind tunnel |
5 | Chen/pkustk13 | 94.9 | 3.4 | 30.4 | 25.9 | Machine element |
6 | GHS_psdef/crankseg_1 | 52.8 | 5.3 | 33.4 | 32.3 | Linear static analysis |
7 | Rothberg/cfd2 | 123 | 1.6 | 38.3 | 32.7 | CFD pressure matrix |
8 | DNVS/thread | 29.7 | 2.2 | 24.1 | 34.9 | Threaded connector |
9 | DNVS/shipsec8 | 115 | 3.4 | 35.9 | 38.1 | Ship section |
10 | DNVS/shipsec1 | 141 | 4.0 | 39.4 | 38.1 | Ship section |
11 | GHS_psdef/crankseg_2 | 63.8 | 7.1 | 43.8 | 46.7 | Linear static analysis |
12 | DNVS/fcondp2 | 202 | 5.7 | 52.0 | 48.2 | Oil production platform |
13 | Schenk_AFE/af_shell3 | 505 | 9.0 | 93.6 | 52.2 | Sheet metal forming |
14 | DNVS/troll | 214 | 6.1 | 64.2 | 55.9 | Structural analysis |
15 | AMD/G3_circuit | 1586 | 4.6 | 97.8 | 57.0 | Circuit simulation |
16 | GHS_psdef/bmwcra_1 | 149 | 5.4 | 69.8 | 60.8 | Automotive crankshaft |
17 | DNVS/halfb | 225 | 6.3 | 65.9 | 70.4 | Half-breadth barge |
18 | Um/2cubes_sphere | 102 | 0.9 | 45.0 | 74.9 | Electromagnetics |
19 | GHS_psdef/ldoor | 952 | 23.7 | 144.6 | 78.3 | Large door |
20 | DNVS/ship_003 | 122 | 4.1 | 60.2 | 81.0 | Ship structure |
21 | DNVS/fullb | 199 | 6.0 | 74.5 | 100.2 | Full-breadth barge |
22 | GHS_psdef/inline_1 | 504 | 18.7 | 172.9 | 144.4 | Inline skater |
23 | Chen/pkustk14 | 152 | 7.5 | 106.8 | 146.4 | Tall building |
24 | GHS_psdef/apache2 | 715 | 2.8 | 134.7 | 174.3 | 3D structural problem |
25 | Koutsovasilis/F1 | 344 | 13.6 | 173.7 | 218.8 | AUDI engine crankshaft |
26 | Oberwolfach/boneS10 | 915 | 28.2 | 278.0 | 281.6 | Bone micro-FEM |
27 | ND/nd12k | 36.0 | 7.1 | 116.5 | 505.0 | 3D mesh problem |
28 | JGD_Trefethen/Trefethen_20000 | 20.0 | 0.3 | 90.7 | 652.6 | Integer matrix |
29 | ND/nd24k | 72.0 | 14.4 | 321.6 | 2054.4 | 3D mesh problem |
30 | Janna/Flan_1565 | 1565 | 59.5 | 1477.9 | 3859.8 | 3D mechanical problem |
31 | Oberwolfach/bone010 | 987 | 36.3 | 1076.4 | 3876.2 | Bone micro-FEM |
32 | Janna/StocF-1465 | 1465 | 11.2 | 1126.1 | 4386.6 | Underground aquifer |
33 | GHS_psdef/audikw_1 | 944 | 39.3 | 1242.3 | 5804.1 | Automotive crankshaft |
34 | Janna/Fault_639 | 639 | 14.6 | 1144.7 | 8283.9 | Gas reservoir |
35 | Janna/Hook_1498 | 1498 | 31.2 | 1532.9 | 8891.3 | Steel hook |
36 | Janna/Emilia_923 | 923 | 21.0 | 1729.9 | 13661.1 | Gas reservoir |
37 | Janna/Geo_1438 | 1438 | 32.3 | 2467.4 | 18058.1 | Underground deformation |
38 | Janna/Serena | 1391 | 33.0 | 2761.7 | 30048.9 | Gas reservoir |
# | Name | n (103) |
nz(A) (106) |
nz(L) (106) |
Flops (109) |
Application/Description |
1 | Schmid/thermal2 | 1228 | 4.9 | 51.6 | 14.6 | Unstructured thermal FEM |
2 | Rothberg/gearbox | 154 | 4.6 | 37.1 | 20.6 | Aircraft flap actuator |
3 | DNVS/m_t1 | 97.6 | 4.9 | 34.2 | 21.9 | Tubular joint |
4 | Boeing/pwtk | 218 | 5.9 | 48.6 | 22.4 | Pressurised wind tunnel |
5 | Chen/pkustk13 | 94.9 | 3.4 | 30.4 | 25.9 | Machine element |
6 | GHS_psdef/crankseg_1 | 52.8 | 5.3 | 33.4 | 32.3 | Linear static analysis |
7 | Rothberg/cfd2 | 123 | 1.6 | 38.3 | 32.7 | CFD pressure matrix |
8 | DNVS/thread | 29.7 | 2.2 | 24.1 | 34.9 | Threaded connector |
9 | DNVS/shipsec8 | 115 | 3.4 | 35.9 | 38.1 | Ship section |
10 | DNVS/shipsec1 | 141 | 4.0 | 39.4 | 38.1 | Ship section |
11 | GHS_psdef/crankseg_2 | 63.8 | 7.1 | 43.8 | 46.7 | Linear static analysis |
12 | DNVS/fcondp2 | 202 | 5.7 | 52.0 | 48.2 | Oil production platform |
13 | Schenk_AFE/af_shell3 | 505 | 9.0 | 93.6 | 52.2 | Sheet metal forming |
14 | DNVS/troll | 214 | 6.1 | 64.2 | 55.9 | Structural analysis |
15 | AMD/G3_circuit | 1586 | 4.6 | 97.8 | 57.0 | Circuit simulation |
16 | GHS_psdef/bmwcra_1 | 149 | 5.4 | 69.8 | 60.8 | Automotive crankshaft |
17 | DNVS/halfb | 225 | 6.3 | 65.9 | 70.4 | Half-breadth barge |
18 | Um/2cubes_sphere | 102 | 0.9 | 45.0 | 74.9 | Electromagnetics |
19 | GHS_psdef/ldoor | 952 | 23.7 | 144.6 | 78.3 | Large door |
20 | DNVS/ship_003 | 122 | 4.1 | 60.2 | 81.0 | Ship structure |
21 | DNVS/fullb | 199 | 6.0 | 74.5 | 100.2 | Full-breadth barge |
22 | GHS_psdef/inline_1 | 504 | 18.7 | 172.9 | 144.4 | Inline skater |
23 | Chen/pkustk14 | 152 | 7.5 | 106.8 | 146.4 | Tall building |
24 | GHS_psdef/apache2 | 715 | 2.8 | 134.7 | 174.3 | 3D structural problem |
25 | Koutsovasilis/F1 | 344 | 13.6 | 173.7 | 218.8 | AUDI engine crankshaft |
26 | Oberwolfach/boneS10 | 915 | 28.2 | 278.0 | 281.6 | Bone micro-FEM |
27 | ND/nd12k | 36.0 | 7.1 | 116.5 | 505.0 | 3D mesh problem |
28 | JGD_Trefethen/Trefethen_20000 | 20.0 | 0.3 | 90.7 | 652.6 | Integer matrix |
29 | ND/nd24k | 72.0 | 14.4 | 321.6 | 2054.4 | 3D mesh problem |
30 | Janna/Flan_1565 | 1565 | 59.5 | 1477.9 | 3859.8 | 3D mechanical problem |
31 | Oberwolfach/bone010 | 987 | 36.3 | 1076.4 | 3876.2 | Bone micro-FEM |
32 | Janna/StocF-1465 | 1465 | 11.2 | 1126.1 | 4386.6 | Underground aquifer |
33 | GHS_psdef/audikw_1 | 944 | 39.3 | 1242.3 | 5804.1 | Automotive crankshaft |
34 | Janna/Fault_639 | 639 | 14.6 | 1144.7 | 8283.9 | Gas reservoir |
35 | Janna/Hook_1498 | 1498 | 31.2 | 1532.9 | 8891.3 | Steel hook |
36 | Janna/Emilia_923 | 923 | 21.0 | 1729.9 | 13661.1 | Gas reservoir |
37 | Janna/Geo_1438 | 1438 | 32.3 | 2467.4 | 18058.1 | Underground deformation |
38 | Janna/Serena | 1391 | 33.0 | 2761.7 | 30048.9 | Gas reservoir |
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