Elemental

Poulson, Jack; Marker, Bryan; Geijn, Robert A.; Hammond, Jeff R.; Romero, Nichols A.

doi:10.1145/2427023.2427030

Cited by 149 publications

(28 citation statements)

References 27 publications

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“…Therefore, we calculate the compact SVDĴ ¼ U r S r V T r , which requires memory of OðN d N m Þ and is relatively fast because 2N d ≪ N m . Using a new distributed library for dense linear algebra (Poulson et al, 2012) Distance (km) Distance (km) Figure 13. The 50% PSF width for the model shown in Figure 8b and the field acquisition geometry.…”

Section: Sensitivity and Resolution Analysismentioning

confidence: 99%

3D inversion and resolution analysis of land-based CSEM data from the Ketzin CO2 storage formation

2014

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We evaluated 3D inversion of land controlled-source electromagnetic (CSEM) data collected across the Ketzin CO 2 storage formation. A newly developed, parallel and distributed 3D inversion code, which is based on a direct forward solver, has been used. This inversion scheme allowed us to calculate the Jacobian matrix explicitly within a reasonable time and use it to calculate regularization parameters, inspect survey coverage, and carry out resolution analysis. After demonstrating that the magnetic field components are sensitive to conductors only, whereas the electric field components are sensitive to all features of interest, we continued to work with electric field data only. Estimates of data uncertainty obtained from robust processing were used for automated data preselection and weighting during inversion. We tested different regularization techniques and a range of starting models to explore the model space and assess the influence of regularization on the inversion images. We further demonstrated an approach for handling numerical singularities due to sources located inside the inversion domain. We estimated survey coverage, horizontal and vertical resolution, and depth penetration using cumulative sensitivity, point spread functions, and depth-resolution plots. Based on data fit analysis, we determined a preferred subsurface conductivity model, which we compared to an independent regional structural geologic model, and we provided an interpretation for the structures resolved. The inversion approach we used provides robust results in good agreement with known geology, offers new possibilities for model assessment, and should be transferable to other CSEM data sets.

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Section: Sensitivity and Resolution Analysismentioning

confidence: 99%

3D inversion and resolution analysis of land-based CSEM data from the Ketzin CO2 storage formation

2014

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“…The Elemental library [22] was incorporated into NEMO5 to perform a highly-efficient parallel diagonal- isation of the Hamiltonian and an unfolding algorithm was developed and integrated to unfold the band structure as it was calculated. The supercell tight-binding calculation generates a folded band structure, where this loss of a continuous E(k) relation complicates most forms of analysis.…”

Section: Methodsmentioning

confidence: 99%

Unfolding the band structure of GaAsBi

Maspero

Sweeney

Florescu

2016

J. Phys.: Condens. Matter

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Abstract. Typical supercell approaches used to investigate the electronic properties of GaAs (1−x) Bi (x) produce highly accurate, but folded, band structures. Using a highly optimized algorithm, we unfold the band structure to an approximate E(k) relation associated with an effective Brillouin zone. The dispersion relations we generate correlate strongly with experimental results, confirming that a regime of band gap energy greater than the spin-orbit-splitting energy is reached at around 10% bismuth fraction. We also demonstrate the effectiveness of the unfolding algorithm throughout the Brillouin zone (BZ), which is key to enabling transition rate calculations, such as Auger recombination rates. Finally, we show the effect of disorder on the effective masses and identify approximate values for the effective mass of the conduction band and valence bands for bismuth concentrations from 0-12%.

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“…3) Software : We compared SIPs with Elemental because of its proven performance. However, there are other libraries, such as ELPA, which have also been shown to scale on thousands of cores . Obviously, using different libraries or improvements in these libraries can change the crossover point.…”

Section: Comparisons With Other Methodsmentioning

confidence: 99%

“…Therefore, it is useful to determine this crossover point to identify which method should be preferred for different matrix sizes and sparsities. We compare SIPs with the generalized eigenvalue solver with a dense matrix storage in the recently developed linear algebra library, Elemental, [61,62] which has been shown [61,63] to have a better parallel performance compared to ScaLapack. [64] Our comparison is based on the computational time to find all of the eigensolutions in an interval corresponding to 60% (DNW, BDC) to 70% (CNT) of the spectrum.…”

Section: Comparisons With Other Methodsmentioning

confidence: 99%

Shift‐and‐invert parallel spectral transformation eigensolver: Massively parallel performance for density‐functional based tight‐binding

et al. 2015

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The Shift-and-invert parallel spectral transformations (SIPs), a computational approach to solve sparse eigenvalue problems, is developed for massively parallel architectures with exceptional parallel scalability and robustness. The capabilities of SIPs are demonstrated by diagonalization of density-functional based tight-binding (DFTB) Hamiltonian and overlap matrices for single-wall metallic carbon nanotubes, diamond nanowires, and bulk diamond crystals. The largest (smallest) example studied is a 128,000 (2000) atom nanotube for which ∼330,000 (∼5600) eigenvalues and eigenfunctions are obtained in ∼190 (∼5) seconds when parallelized over 266,144 (16,384) Blue Gene/Q cores. Weak scaling and strong scaling of SIPs are analyzed and the performance of SIPs is compared with other novel methods. Different matrix ordering methods are investigated to reduce the cost of the factorization step, which dominates the time-to-solution at the strong scaling limit. A parallel implementation of assembling the density matrix from the distributed eigenvectors is demonstrated.

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Elemental

Cited by 149 publications

References 27 publications

3D inversion and resolution analysis of land-based CSEM data from the Ketzin CO2 storage formation

3D inversion and resolution analysis of land-based CSEM data from the Ketzin CO2 storage formation

Unfolding the band structure of GaAsBi

Shift‐and‐invert parallel spectral transformation eigensolver: Massively parallel performance for density‐functional based tight‐binding

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