Simulating solidification in metals at high pressure: The drive to petascale computing

Streitz, Frederick H.; Glosli, James N.; Patel, Mehul V.; Chan, Betty; Yates, Robert K.; Supinski, Bronis R. de; Sexton, James; Gunnels, John A.

doi:10.1088/1742-6596/46/1/037

Cited by 28 publications

(26 citation statements)

References 26 publications

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“…As in other recent Ta4 MGPT applications [2,4,6,21,28,31,36,37], all of the melt methods discussed below apply the Ta6.8x potentials using the advanced matrix representation of MGPT [6], as implemented in the parallel molecular dynamics code ddcMD [39]. In ddcMD, the angular functions L, P, and M in Eqs.…”

Section: B Methods Of Melt Calculationmentioning

confidence: 99%

Polymorphism and melt in high-pressure tantalum

2012

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Recent small-cell (< 150-atom) quantum molecular dynamics (QMD) simulations for Ta based on density functional theory (DFT) have predicted a hexagonal omega (hex-ω) phase more stable than the normal bcc phase at high temperature (T) and pressure (P) above 70 GPa [Burakovsky et al., Phys. Rev. Lett. 104, 255702 (2010)]. Here we examine possible high-T , P polymorphism in Ta with complementary DFT-based model generalized pseudopotential theory (MGPT) multi-ion interatomic potentials, which allow accurate treatment of much larger system sizes (up to ~ 80000 atoms). We focus on candidate bcc, A15, fcc, hcp, and hex-ω phases for the high-T , P phase diagram to 420 GPa, studying the mechanical and relative thermodynamic stability of these phases for both small and large computational cells. Our MGPT potentials fully capture the T = 0 DFT energetics of these phases, while MGPT-MD simulations demonstrate that the higher-energy fcc, hcp and hex-ω structures are only mechanically stabilized at high temperature by large, size-dependent, anharmonic vibrational effects, with the stability of the hex-ω phase also being found to be a sensitive function of its c / a ratio. Both twophase and Z-method melting techniques have been used in MGPT-MD simulations to determine relative phase stability and its size dependence. In the large-cell limit, the twophase method yields accurate equilibrium melt curves for all five phases, with bcc producing the highest melt temperatures at all pressures and hence being the most stable phase of those considered. The two-phase bcc melt curve is also in good agreement with dynamic experimental data as well as with the MGPT melt curve calculated from bcc and 2 liquid free energies. In contrast, we find that the Z method produces only an upper bound to the equilibrium melt curve in the large-cell limit. For the bcc and hex-ω structures, however, this is a close upper bound within 5% of the two-phase results, although for the A15, fcc, and hcp structures, the Z-melt curves are 25-35% higher in temperature than the two-phase results. Nonetheless, the Z method has allowed us to study melt size effects in detail. We find these effects to be either small or modest for the cubic bcc, A15, and fcc structures, but to have a large impact on the hexagonal hcp and hex-ω melt curves, which are dramatically pushed above that of bcc for simulation cells less than 150 atoms. The melt size effects are driven by and closely correlated with similar size effects on the mechanical stability and the vibrational anharmonicity. We further show that for the same simulation cell sizes and choice of c / a ratio, the MGPT-MD bcc and hex-ω melt curves are in good agreement with the QMD results, so the QMD prediction is confirmed in the small-cell limit. But in the large-cell limit, the MGPT-MD hex-ω melt curve is always lowered below that of bcc for any choice of c / a , so bcc is the most stable phase.We conclude that for the non-bcc Ta phases studied, one requires simulation cells of at least 250-500 atoms to be free ...

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Section: B Methods Of Melt Calculationmentioning

confidence: 99%

Polymorphism and melt in high-pressure tantalum

2012

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“…It has been shown that, under specific circumstances, adding computing units might hamper applications completion time, as a larger node count implies a higher probability of reliability issues. This directly translates into a lower efficiency of the machine, which equates to a lower scientific throughput [Streitz et al 2006]. It is estimated that the MTTF of High Performance Computing (HPC) systems might drop to about one hour in the near future [Cappello 2009].…”

Section: Introductionmentioning

confidence: 99%

Algorithm-Based Fault Tolerance for Dense Matrix Factorizations, Multiple Failures and Accuracy

Bouteiller

Hérault

Bosilca

et al. 2015

ACM Trans. Parallel Comput.

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Dense matrix factorizations, such as LU, Cholesky and QR, are widely used for scientific applications that require solving systems of linear equations, eigenvalues and linear least squares problems. Such computations are normally carried out on supercomputers, whose ever-growing scale induces a fast decline of the Mean Time To Failure (MTTF). This paper proposes a new hybrid approach, based on Algorithm-Based Fault Tolerance (ABFT), to help matrix factorizations algorithms survive fail-stop failures. We consider extreme conditions, such as the absence of any reliable node and the possibility of losing both data and checksum from a single failure. We will present a generic solution for protecting the right factor, where the updates are applied, of all above mentioned factorizations. For the left factor, where the panel has been applied, we propose a scalable checkpointing algorithm. This algorithm features high degree of checkpointing parallelism and cooperatively utilizes the checksum storage leftover from the right factor protection. The fault-tolerant algorithms derived from this hybrid solution is applicable to a wide range of dense matrix factorizations, with minor modifications. Theoretical analysis shows that the fault tolerance overhead decreases inversely to the scaling in the number of computing units and the problem size. Experimental results of LU and QR factorization on the Kraken (Cray XT5) supercomputer validate the theoretical evaluation and confirm negligible overhead, with-and without-errors. Applicability to tolerate multiple failures and accuracy after multiple recovery is also considered.

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“…It has been shown that, under specific circumstances, adding computing units might increases applications completion time, as a larger node count implies a higher probability of reliability issues. This directly translates into a lower efficiency of the machine, which equates to a lower scientific throughput [24]. It is estimated that the MTTF of High Performance Computing (HPC) systems might drop to about one hour in the near future [7].…”

Section: Introductionmentioning

confidence: 99%

Algorithm-based fault tolerance for dense matrix factorizations

Bouteiller

Bosilca

et al. 2012

Proceedings of the 17th ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming

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Dense matrix factorizations, like LU, Cholesky and QR, are widely used for scientific applications that require solving systems of linear equations, eigenvalues and linear least squares problems. Such computations are normally carried out on supercomputers, whose ever-growing scale induces a fast decline of the Mean Time To Failure (MTTF). This paper proposes a new hybrid approach, based on Algorithm-Based Fault Tolerance (ABFT), to help matrix factorizations algorithms survive fail-stop failures. We consider extreme conditions, such as the absence of any reliable component and the possibility of loosing both data and checksum from a single failure. We will present a generic solution for protecting the right factor, where the updates are applied, of all above mentioned factorizations. For the left factor, where the panel has been applied, we propose a scalable checkpointing algorithm. This algorithm features high degree of checkpointing parallelism and cooperatively utilizes the checksum storage leftover from the right factor protection. The fault-tolerant algorithms derived from this hybrid solution is applicable to a wide range of dense matrix factorizations, with minor modifications. Theoretical analysis shows that the fault tolerance overhead sharply decreases with the scaling in the number of computing units and the problem size. Experimental results of LU and QR factorization on the Kraken (Cray XT5) supercomputer validate the theoretical evaluation and confirm negligible overhead, with-and without-errors.

show abstract

Simulating solidification in metals at high pressure: The drive to petascale computing

Cited by 28 publications

References 26 publications

Polymorphism and melt in high-pressure tantalum

Polymorphism and melt in high-pressure tantalum

Algorithm-Based Fault Tolerance for Dense Matrix Factorizations, Multiple Failures and Accuracy

Algorithm-based fault tolerance for dense matrix factorizations

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