Implementación paralela de métodos de Krylov con reinicio para problemas de valores propios y singulares

Esta tesis aborda la paralelización de los métodos de Krylov con reinicio para problemas de valores propios y valores singulares (SVD). Estos métodos son de naturaleza iterativa y resultan adecuados para encontrar unos pocos valores propios o singulares de problemas dispersos. El procedimiento de ortogonalización suele ser la parte más costosa de este tipo de métodos, por lo que ha recibido especial atención en esta tesis, proponiendo y validando nuevos algoritmos para mejorar sus prestaciones paralelas. La implementación se ha realizado en el marco de la librería SLEPc, que proporciona una interfaz orientada a objetos para la resolución iterativa de problemas de valores propios o singulares. SLEPc está basada en la librería PETSc, que dispone de implementaciones paralelas de métodos iterativos para la resolución de sistemas lineales, precondicionadores, matrices dispersas y vectores. Ambas librerías están optimizadas para su ejecución en máquinas paralelas de memoria distribuida y con problemas dispersos de gran dimensión. Esta implementación incorpora los métodos para valores propios de Arnoldi con reinicio explícito, de Lanczos (incluyendo variantes semiortogonales) con reinicio explícito, y versiones de Krylov-Schur (equivalente al reinicio implícito) para problemas no Hermitianos y Hermitianos (Lanczos con reinicio grueso). Estos métodos comparten una interfaz común, permitiendo su comparación de forma sencilla, característica que no está disponible en otras implementaciones. Las mismas técnicas utilizadas para problemas de valores propios se han adaptado a los métodos de Golub-Kahan-Lanczos con reinicio explícito y grueso para problemas de valores singulares, de los que no existe ninguna otra implementación paralela con paso de mensajes. Cada uno de los métodos se ha validado mediante una batería de pruebas con matrices procedentes de aplicaciones reales. Las prestaciones paralelas se han medido en máquinas tipo cluster, comprobando una buena escalabilidad incTomás Domínguez, A. (2009). Implementación paralela de métodos de Krylov con reinicio para problemas de valores propios y singulares [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/5082Palanci

Tall-and-skinny QR factorization with approximate Householder reflectors on graphics processors

[EN] We present a novel method for the QR factorization of large tall-and-skinny matrices that introduces an approximation technique for computing the Householder vectors. This approach is very competitive on a hybrid platform equipped with a graphics processor, with a performance advantage over the conventional factorization due to the reduced amount of data transfers between the graphics accelerator and the main memory of the host. Our experiments show that, for tall¿skinny matrices, the new approach outperforms the code in MAGMA by a large margin, while it is very competitive for square matrices when the memory transfers and CPU computations are the bottleneck of the Householder QR factorizationThis research was supported by the Project TIN2017-82972-R from the MINECO (Spain) and the EU H2020 Project 732631 "OPRECOMP. Open Transprecision Computing".Tomás Domínguez, AE.; Quintana-Ortí, ES. (2020). Tall-and-skinny QR factorization with approximate Householder reflectors on graphics processors. The Journal of Supercomputing (Online). 76(11):8771-8786. https://doi.org/10.1007/s11227-020-03176-3S877187867611Abdelfattah A, Haidar A, Tomov S, Dongarra J (2018) Analysis and design techniques towards high-performance and energy-efficient dense linear solvers on GPUs. IEEE Trans Parallel Distrib Syst 29(12):2700–2712. https://doi.org/10.1109/TPDS.2018.2842785Ballard G, Demmel J, Grigori L, Jacquelin M, Knight N, Nguyen H (2015) Reconstructing Householder vectors from tall-skinny QR. J Parallel Distrib Comput 85:3–31. https://doi.org/10.1016/j.jpdc.2015.06.003Barrachina S, Castillo M, Igual FD, Mayo R, Quintana-Ortí ES (2008) Solving dense linear systems on graphics processors. In: Luque E, Margalef T, Benítez D (eds) Euro-Par 2008—parallel processing. Springer, Heidelberg, pp 739–748Benson AR, Gleich DF, Demmel J (2013) Direct QR factorizations for tall-and-skinny matrices in MapReduce architectures. In: 2013 IEEE International Conference on Big Data, pp 264–272. https://doi.org/10.1109/BigData.2013.6691583Businger P, Golub GH (1965) Linear least squares solutions by householder transformations. Numer Math 7(3):269–276. https://doi.org/10.1007/BF01436084Demmel J, Grigori L, Hoemmen M, Langou J (2012) Communication-optimal parallel and sequential QR and LU factorizations. SIAM J Sci Comput 34(1):206–239. https://doi.org/10.1137/080731992Dongarra J, Du Croz J, Hammarling S, Duff IS (1990) A set of level 3 basic linear algebra subprograms. ACM Trans Math Softw 16(1):1–17. https://doi.org/10.1145/77626.79170Drmač Z, Bujanović Z (2008) On the failure of rank-revealing qr factorization software—a case study. ACM Trans Math Softw 35(2):12:1–12:28. https://doi.org/10.1145/1377612.1377616Fukaya T, Nakatsukasa Y, Yanagisawa Y, Yamamoto Y (2014) CholeskyQR2: A simple and communication-avoiding algorithm for computing a tall-skinny QR factorization on a large-scale parallel system. In: 2014 5th workshop on latest advances in scalable algorithms for large-scale systems, pp 31–38. https://doi.org/10.1109/ScalA.2014.11Fukaya T, Kannan R, Nakatsukasa Y, Yamamoto Y, Yanagisawa Y (2018) Shifted CholeskyQR for computing the QR factorization of ill-conditioned matrices, arXiv:1809.11085Golub G, Van Loan C (2013) Matrix computations. Johns Hopkins studies in the mathematical sciences. Johns Hopkins University Press, BaltimoreGunter BC, van de Geijn RA (2005) Parallel out-of-core computation and updating the QR factorization. ACM Trans Math Softw 31(1):60–78. https://doi.org/10.1145/1055531.1055534Joffrain T, Low TM, Quintana-Ortí ES, Rvd Geijn, Zee FGV (2006) Accumulating householder transformations, revisited. ACM Trans Math Softw 32(2):169–179. https://doi.org/10.1145/1141885.1141886Puglisi C (1992) Modification of the householder method based on the compact WY representation. SIAM J Sci Stat Comput 13(3):723–726. https://doi.org/10.1137/0913042Saad Y (2003) Iterative methods for sparse linear systems, 3rd edn. Society for Industrial and Applied Mathematics, PhiladelphiaSchreiber R, Van Loan C (1989) A storage-efficient WY representation for products of householder transformations. SIAM J Sci Comput 10(1):53–57. https://doi.org/10.1137/0910005Stathopoulos A, Wu K (2001) A block orthogonalization procedure with constant synchronization requirements. SIAM J Sci Comput 23(6):2165–2182. https://doi.org/10.1137/S1064827500370883Strazdins P (1998) A comparison of lookahead and algorithmic blocking techniques for parallel matrix factorization. Tech. Rep. TR-CS-98-07, Department of Computer Science, The Australian National University, Canberra 0200 ACT, AustraliaTomás Dominguez AE, Quintana Orti ES (2018) Fast blocking of householder reflectors on graphics processors. In: 2018 26th Euromicro International Conference on Parallel, Distributed and Network-Based Processing (PDP), pp 385–393. https://doi.org/10.1109/PDP2018.2018.00068Volkov V, Demmel JW (2008) LU, QR and Cholesky factorizations using vector capabilities of GPUs. Tech. Rep. 202, LAPACK Working Note. http://www.netlib.org/lapack/lawnspdf/lawn202.pdfYamamoto Y, Nakatsukasa Y, Yanagisawa Y, Fukaya T (2015) Roundoff error analysis of the Cholesky QR2 algorithm. Electron Trans Numer Anal 44:306–326Yamazaki I, Tomov S, Dongarra J (2015) Mixed-precision Cholesky QR factorization and its case studies on multicore CPU with multiple GPUs. SIAM J Sci Comput 37(3):C307–C330. https://doi.org/10.1137/14M097377

Electromagnetic interaction between a laser beam and semiconductor nanowires deposited on different substrates: Raman enhancement in Si Nanowires

Raman scattering of Si nanowires (NWs) presents antenna effects. The electromagnetic resonance depends on the electromagnetic coupling of the system laser/NW/substrate. The antenna effect of the Raman signal was measured in individual NWs deposited on different substrates, and also free standing NWs in air. The one phonon Raman band in NWs can reach high intensities depending on the system configuration; values of Raman intensity per unit volume more than a few hundred times with respect to bulk substrate can be obtainedRaman scattering of Si nanowires (NWs) presents antenna effects. The electromagnetic resonance depends on the electromagnetic coupling of the system laser/NW/substrate. The antenna effect of the Raman signal was measured in individual NWs deposited on different substrates, and also free standing NWs in air. The one phonon Raman band in NWs can reach high intensities depending on the system configuration; values of Raman intensity per unit volume more than a few hundred times with respect to bulk substrate can be obtaine

Individualization and Electrical Characterization of SiGe Nanowires

SiGe nanowires of different Ge atomic fractions up to 15% were grown and ex-situ n-type doped by diffusion from a solid source in contact with the sample. The phenomenon of dielectrophoresis was used to locate single nanowires between pairs of electrodes in order to carry out electrical measurements. The measured resistance of the as-grown nanowires is very high, but it decreases more than three orders of magnitude upon doping, indicating that the doping procedure used has been effectiv

SiGe nanowires grown by LPCVD using Ga-Au catalysts

The use of Ga-Au alloys as metal catalysts for the growth of SiGe nanowires has been investigated. The grown nanowires are cylindrical and straight, with a defect-free crystalline structure, sharp nanowire-droplet interfaces and an almost constant Ge atomic fraction throughout all their length. These features represent significant improvements over the results obtained using pure A

SiGe/Si nanowire axial heterostructures grown by LPCVD using Ga-Au

The use of Ga-Au alloys of different compositions as metal catalysts for the growth of abrupt SiGe/Si nanowire axial heterostructures has been investigated. The heterostructures grown in a continuous process by just switching the gas precursors, show uniform nanowire diameters, almost abrupt compositional changes and no defects between the different sections. These features represent significant improvements over the results obtained using pure Au

Place-Based Education and Heritage Education in in-service teacher training: research on teaching practices in secondary schools in Galicia (NW Spain)

This paper analyses what occurs when in-service secondary teachers face a new subject, Landscape and Sustainability. Recently implemented in Galicia (NW Spain), this subject has no strong curricular constrictions. It is opened to diverse contents that can be integrated into Social Sciences. It promotes an environmental, social and critical consciousness. The hypothesis was that teachers may present deficiencies when approaching a subject which, due to its characteristics, requires training extending beyond disciplinary knowledge, thus impeding better performance and a greater degree of learning among pupils. The study was organised in three axes: (a) observation of the teaching and learning process in schools (n = 3); (b) teacher’s conceptions (n = 38) on the subject, its context and their pupils’ learning; and (c) pupils’ reflections (n = 70) derived from their learning process. The objectives were: (1) to elaborate a theoretical substantiation for the subject and, in accordance with it, making a critical analysis of the practices observed; (2) to analyse how teachers conceive the subject; and (3) to analyse the pupils’ reflections regarding the experience and to what extent they acquire social, civic and/or academic skills. The methodology was qualitative, using in the data analysis a quantitative perspective too. The instruments used were the participant observation, interviews, a closed questionnaire and a semi-opened questionnaire. The results are presented in a descriptive-interpretative way, but also quantitative. It can be advanced that teachers designed the subject in line with Place-Based Education and Heritage Education, but the lack of specific training in those theories ends up blurring their holistic approach in the nearby places. Teachers show similar conceptions about the subject and its teaching process. And the majority of students value positively the methodology used in the initiatives and acquire a socio-critical consciousnessS

Nanostructures with Group IV nanocrystals obtained by LPCVD and thermal annealing of SiGeO layers

Nanocrystals embedded in an oxide matrix have been fabricated by annealing SiGeO films deposited by LPCVD. The composition of the oxide layers and its evolution after annealing as well as the presence and nature of nanocrystals in the films have been studied by several experimental techniques. The results are analyzed and discussed in terms of the main deposition parameters and the annealing temperature

Interaction between a laser beam and semiconductor nanowires: application to the raman spectrum of Si nanowires

One presents in this work the study of the interaction between a focused laser beam and Si nanowires (NWs). The NWs heating induced by the laser beam is studied by solving the heat transfer equation by finite element methods (FEM). This analysis permits to establish the temperature distribution inside the NW when it is excited by the laser beam. The overheating is dependent on the dimensions of the NW, both the diameter and the length. When performing optical characterisation of NWs using focused laser beams, one has to consider the temperature increase introduced by the laser beam. An important issue concerns the fact that the NW's diameter has subwavelength dimensions, and is also smaller than the focused laser beam. The analysis of the thermal behaviour of the NWs under the excitation with the laser beam permits the interpretation of the Raman spectrum of Si NWs. It is demonstrated that the temperature increase induced by the laser beam plays a major role in shaping the Raman spectrum of Si NWs

Interaction between a laser beam and semiconductor nanowires: application to the raman spectrum of Si nanowires

One presents in this work the study of the interaction between a focused laser beam and Si nanowires (NWs). The NWs heating induced by the laser beam is studied by solving the heat transfer equation by finite element methods (fem). This analysis permits to establish the temperature distribution inside the NW when it is excited by the laser beam. The overheating is dependent on the dimensions of the NW, both the diameter and the length. When performing optical characterization of the NWs using focused laser beams, one has to consider the temperature increase introduced by the laser beam. An important issue concerns the fact that the NWs diameter has subwavelength dimensions, and is also smaller than the focused laser beam. The analysis of the thermal behaviour of the NWs under the excitation with the laser beam permits the interpretation of the Raman spectra of Si NWs, where it is demonstrated that temperature induced by the laser beam play a major role in shaping the Raman spectrum of Si NW