Tensor Numerical Methods in Quantum Chemistry: from Hartree-Fock Energy to Excited States

We resume the recent successes of the grid-based tensor numerical methods and discuss their prospects in real-space electronic structure calculations. These methods, based on the low-rank representation of the multidimensional functions and integral operators, led to entirely grid-based tensor-structured 3D Hartree-Fock eigenvalue solver. It benefits from tensor calculation of the core Hamiltonian and two-electron integrals (TEI) in $O(n\log n)$ complexity using the rank-structured approximation of basis functions, electron densities and convolution integral operators all represented on 3D $n\times n\times n$ Cartesian grids. The algorithm for calculating TEI tensor in a form of the Cholesky decomposition is based on multiple factorizations using algebraic 1D ``density fitting`` scheme. The basis functions are not restricted to separable Gaussians, since the analytical integration is substituted by high-precision tensor-structured numerical quadratures. The tensor approaches to post-Hartree-Fock calculations for the MP2 energy correction and for the Bethe-Salpeter excited states, based on using low-rank factorizations and the reduced basis method, were recently introduced. Another direction is related to the recent attempts to develop a tensor-based Hartree-Fock numerical scheme for finite lattice-structured systems, where one of the numerical challenges is the summation of electrostatic potentials of a large number of nuclei. The 3D grid-based tensor method for calculation of a potential sum on a $L\times L\times L$ lattice manifests the linear in $L$ computational work, $O(L)$, instead of the usual $O(L^3 \log L)$ scaling by the Ewald-type approaches

Computational Physics on Graphics Processing Units

The use of graphics processing units for scientific computations is an emerging strategy that can significantly speed up various different algorithms. In this review, we discuss advances made in the field of computational physics, focusing on classical molecular dynamics, and on quantum simulations for electronic structure calculations using the density functional theory, wave function techniques, and quantum field theory.Comment: Proceedings of the 11th International Conference, PARA 2012, Helsinki, Finland, June 10-13, 201

Overview of Large-Scale Computing: The Past, the Present, and the Future

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Hybrid energy storage systems via power electronic converters

In recent years, many research lines have focused their efforts on improving energy efficiency and developing renewable energy sources. In this context, the use of energy storage systems is on the rise, as they can contribute to the integration of renewables to the main electrical grid. However, energy storage systems are divided into high energy or high power devices. Due to the lack of a solution covering both aspects, researchers are forced to find alternatives. The hybridization of different energy storage technologies is presented as a suitable solution for this problem, since it combines high power and high energy within the same system. The main goal of this thesis is the design and implementation of a hybrid energy storage system (HESS), capable of improving the performance provided by a single storage technology. As a first step in this direction, this document reviews and classifies the most relevant HESS topologies found in the literature. This allows a better understanding of the drawbacks and benefits of each configuration. To ensure the optimal use of this HESS, it is essential to design a suitable energy management strategy and a proper power electronic converter control. To this end, the control structure has been analyzed from different approaches. On the one hand there would be the classic multilevel control structure, which usually consists of three levels among which are the operating constraints, the power sharing and at the lowest level the control of the converter. On the other hand there would be the single level control structure in which both, the power distribution and the control of the converter, are integrated within the same level by using modern MPC control algorithms. Finally, three different case studies are presented to show the practical application of the developed control strategies together with the main conclusions of the thesis.Azken urteetan, ikerketa-lerro askok eraginkortasun energetikoa hobetzeko eta energia berriztagarriak garatzeko ahaleginak egin dituzte. Testuinguru honetan, energia metatze sistemen erabilera geroz eta handiagoa da, berriztagarrien integrazioa sare elektrikoarekin erraztu dezaketelako. Hala ere, energia altuko edo potentzia altuko metatze sistemak bakarrik aukeratu daitezke. Horregatik, ikertzaileek alternatiba berriak bilatzera behartuta daude. Energia metatze sistema desberdinen hibridazioa, arazo horri irtenbidea ematen dio. Honekin, potentzia eta energia maila altuak sistema bakar batetan batu daitezke. Tesi honen helburu nagusia, energia metatze sistema hibrido (HESS sigla, ingelesetik Hybrid Energy Storage System) bat diseinatzea eta inplementatzea da. Sistema honek, teknologia bakar batek eskaintzen duen errendimendua hobetzeko gai izan beharko luke. Lehen urratsa bezala, dokumentu honek literaturan aurkitutako topologia hibrido garrantzitsuenak laburbildu eta batzen ditu. Honi esker, konfigurazio bakoitzaren abantaila eta desabantailak hobeto ulertzea ahal da. HESS honen erabilera optimoa bermatzeko, ezinbestekoa da energia kudeatzeko estrategia on bat diseinatzea bihurgailu elektronikoaren kontrol egokiarekin batera. Horretarako, kontrol egitura ikuspegi desberdinetatik aztertuko da. Alde batetik, maila anitzeko kontrol egitura klasikoa egongo litzateke, normalean hiru mailaz osatua dagoena. Goi mailan funtzionamendu eta segurtasun mugak egongo lirateke, erdiko mailan potentzia banaketa, eta azkenik bihurgailuaren maila baxuko kontrola. Bestalde, maila bakarreko kontrol egitura egongo litzateke non mugak, potentzia banaketa eta bihurgailuaren kontrola maila berean integratzen dira kontrol iragarleko algoritmoen bidez (MPC). Azkenik, hiru kasu desberdin aurkezten dira garatutako kontrolen aplikazio praktikoa erakusteko tesiaren ondorio nagusiekin batera.En los últimos años, numerosas líneas de investigación han centrado sus esfuerzos en mejorar la eficiencia energética junto con el desarrollo de fuentes de generación renovables. En este contexto, el uso de sistemas de almacenamiento de energía está al alza, ya que estos pueden contribuir a la integración de las renovables en la red eléctrica convencional. Sin embargo, la necesidad de elegir entre dispositivos de alta energía o alta potencia, obliga a los investigadores a buscar otras alternativas. La hibridación de diferentes sistemas de almacenamiento se presenta como una solución apropiada para este problema, ya que combina alta energía y alta potencia dentro de un mismo sistema. El objetivo principal de esta tesis es el diseño e implementación de un sistema híbrido de almacenamiento de energía (sigla HESS, del inglés Hybrid Energy Storage System), capaz de mejorar las prestaciones que proporcionaría el uso de una única tecnología. Como primer paso en esta dirección, en este documento resume y clasifica las topologías de hibridación más relevantes encontradas en la literatura. Esto permite una mejor comprensión de los beneficios e inconvenientes de cada configuración. Para garantizar el uso óptimo de dicho HESS, es esencial diseñar una estrategia adecuada de gestión de energía junto con un control óptimo del convertidor electrónico de potencia. Para lograr este fin, la estructura de control ha sido analizada desde diferentes enfoques. Por un lado se encontraría la estructura de control multinivel clásica, la cual generalmente consta de tres niveles. En el nivel más alto se encontrarían las restricciones operativas y de seguridad, en el intermedio se encontraría la división de potencia, y por último el control de nivel bajo del convertidor. Por otro lado, se encontraría la estructura de control de un único nivel, en la que tanto las restricciones, el reparto de potencia y el control del convertidor se integran dentro del mismo nivel mediante algoritmos de control predictivo (MPC). Finalmente, se presentan tres casos de estudio para mostrar la aplicación práctica de las estrategias de control desarrolladas junto con las principales conclusiones de la tesis

Real-Space Mesh Techniques in Density Functional Theory

This review discusses progress in efficient solvers which have as their foundation a representation in real space, either through finite-difference or finite-element formulations. The relationship of real-space approaches to linear-scaling electrostatics and electronic structure methods is first discussed. Then the basic aspects of real-space representations are presented. Multigrid techniques for solving the discretized problems are covered; these numerical schemes allow for highly efficient solution of the grid-based equations. Applications to problems in electrostatics are discussed, in particular numerical solutions of Poisson and Poisson-Boltzmann equations. Next, methods for solving self-consistent eigenvalue problems in real space are presented; these techniques have been extensively applied to solutions of the Hartree-Fock and Kohn-Sham equations of electronic structure, and to eigenvalue problems arising in semiconductor and polymer physics. Finally, real-space methods have found recent application in computations of optical response and excited states in time-dependent density functional theory, and these computational developments are summarized. Multiscale solvers are competitive with the most efficient available plane-wave techniques in terms of the number of self-consistency steps required to reach the ground state, and they require less work in each self-consistency update on a uniform grid. Besides excellent efficiencies, the decided advantages of the real-space multiscale approach are 1) the near-locality of each function update, 2) the ability to handle global eigenfunction constraints and potential updates on coarse levels, and 3) the ability to incorporate adaptive local mesh refinements without loss of optimal multigrid efficiencies.Comment: 70 pages, 11 figures. To be published in Reviews of Modern Physic

Technology for large space systems: A special bibliography with indexes (supplement 03)

A bibliography containing 217 abstracts addressing the technology for large space systems is presented. State of the art and advanced concepts concerning interactive analysis and design, structural concepts, control systems, electronics, advanced materials, assembly concepts, propulsion, solar power satellite systems, and flight experiments are represented

The Partial Elements Equivalent Circuit Method: The State Of The Art

This year marks about half a century since the birth of the technique known as the partial element equivalent circuit modeling approach. This method was initially conceived to model the behavior of interconnect-type problems for computer-integrated circuits. An important industrial requirement was the computation of general inductances in integrated circuits and packages. Since then, the advances in methods and applications made it suitable for modeling a large class of electromagnetic problems, especially in the electromagnetic compatibility (EMC)/signal and power integrity (SI/PI) areas. The purpose of this article is to present an overview of all aspects of the method, from its beginning to the present day, with special attention to the developments that have made it suitable for EMC/SI/PI problems

Three real-space discretization techniques in electronic structure calculations

A characteristic feature of the state-of-the-art of real-space methods in electronic structure calculations is the diversity of the techniques used in the discretization of the relevant partial differential equations. In this context, the main approaches include finite-difference methods, various types of finite-elements and wavelets. This paper reports on the results of several code development projects that approach problems related to the electronic structure using these three different discretization methods. We review the ideas behind these methods, give examples of their applications, and discuss their similarities and differences.Comment: 39 pages, 10 figures, accepted to a special issue of "physica status solidi (b) - basic solid state physics" devoted to the CECAM workshop "State of the art developments and perspectives of real-space electronic structure techniques in condensed matter and molecular physics". v2: Minor stylistic and typographical changes, partly inspired by referee comment