A domain-specific language and matrix-free stencil code for investigating electronic properties of Dirac and topological materials

We introduce PVSC-DTM (Parallel Vectorized Stencil Code for Dirac and Topological Materials), a library and code generator based on a domain-specific language tailored to implement the specific stencil-like algorithms that can describe Dirac and topological materials such as graphene and topological insulators in a matrix-free way. The generated hybrid-parallel (MPI+OpenMP) code is fully vectorized using Single Instruction Multiple Data (SIMD) extensions. It is significantly faster than matrix-based approaches on the node level and performs in accordance with the roofline model. We demonstrate the chip-level performance and distributed-memory scalability of basic building blocks such as sparse matrix-(multiple-) vector multiplication on modern multicore CPUs. As an application example, we use the PVSC-DTM scheme to (i) explore the scattering of a Dirac wave on an array of gate-defined quantum dots, to (ii) calculate a bunch of interior eigenvalues for strong topological insulators, and to (iii) discuss the photoemission spectra of a disordered Weyl semimetal.Comment: 16 pages, 2 tables, 11 figure

Closed-Form Expressions for the Radiation Properties of Nanoloops in the Terahertz, Infrared and Optical Regimes

This work was supported in part by the Spanish Ministry of Education through the Commission Fulbright Program “Salvador de Madariaga” under Grant PR X14/00320, in part by the Spanish and Andalusian Research Programs under Grant TEC2013-48414-C3-01 and Grant P12-TIC-1442, and in part by the Center for Nanoscale Science, NSF Materials Research Science a nd Engineering Center, under Award DMR-1420620Since the pioneering work of Heinrich Hertz, perfect-electric conductor (PEC) loop antennas for RF appli- cations have been studied extensively. Meanwhile, nanoloops are promising in the optical regime for their applications in a wide range of emerging technologies. Unfortunately, analytical expressions for the radiation properties of conducting loops have not been extended to the optical regime. This paper presents closed-form expressions for the electric fields, total radiated power, directivity, and gain for thin-wire nanoloops operating in the terahertz, infrared and optical regimes. This is accomplished by extending the formulation for PEC loops to include the effects of dispersion and loss. The expressions derived for a gold nanoloop are implemented and the results agree well with full-wave computational simulations, but with a speed increase of more than 300 × . This allows the scientist or engineer to quickly prototype designs and gain a deeper understanding of the underlying physics. Moreover, through rapid numerical experimentation, these closed-form expressions made possible the discovery that broadband superdirectivity occurs naturally for nanoloops of a specific size and material composition. This is an unexpected and potentially transformative result that does not occur for PEC loops. Additionally, the Appendices give useful guidelines on how to efficiently compute the required integrals.Spanish Ministry of Education through the Commission Fulbright Program “Salvador de Madariaga” under Grant PR X14/00320Spanish and Andalusian Research Programs under Grant TEC2013-48414-C3-01 and Grant P12-TIC-1442Center for Nanoscale Science, NSF Materials Research Science a nd Engineering Center, under Award DMR-142062

High-precision computation of uniform asymptotic expansions for special functions

In this dissertation, we investigate new methods to obtain uniform asymptotic expansions for the numerical evaluation of special functions to high-precision. We shall first present the theoretical and computational fundamental aspects required for the development and ultimately implementation of such methods. Applying some of these methods, we obtain efficient new convergent and uniform expansions for numerically evaluating the confluent hypergeometric functions and the Lerch transcendent at high-precision. In addition, we also investigate a new scheme of computation for the generalized exponential integral, obtaining on the fastest and most robust implementations in double-precision floating-point arithmetic. In this work, we aim to combine new developments in asymptotic analysis with fast and effective open-source implementations. These implementations are comparable and often faster than current open-source and commercial stateof-the-art software for the evaluation of special functions.Esta tesis presenta nuevos métodos para obtener expansiones uniformes asintóticas, para la evaluación numérica de funciones especiales en alta precisión. En primer lugar, se introducen fundamentos teóricos y de carácter computacional necesarios para el desarrollado y posterior implementación de tales métodos. Aplicando varios de dichos métodos, se obtienen nuevas expansiones uniformes convergentes para la evaluación numérica de las funciones hipergeométricas confluentes y de la función transcendental de Lerch. Por otro lado, se estudian nuevos esquemas de computo para evaluar la integral exponencial generalizada, desarrollando una de las implementaciones más eficientes y robustas en aritmética de punto flotante de doble precisión. En este trabajo, se combinan nuevos desarrollos en análisis asintótico con implementaciones rigurosas, distribuidas en código abierto. Las implementaciones resultantes son comparables, y en ocasiones superiores, a las soluciones comerciales y de código abierto actuales, que representan el estado de la técnica en el campo de la evaluación de funciones especiales

High-precision computation of uniform asymptotic expansions for special functions

In this dissertation, we investigate new methods to obtain uniform asymptotic expansions for the numerical evaluation of special functions to high-precision. We shall first present the theoretical and computational fundamental aspects required for the development and ultimately implementation of such methods. Applying some of these methods, we obtain efficient new convergent and uniform expansions for numerically evaluating the confluent hypergeometric functions and the Lerch transcendent at high-precision. In addition, we also investigate a new scheme of computation for the generalized exponential integral, obtaining on the fastest and most robust implementations in double-precision floating-point arithmetic. In this work, we aim to combine new developments in asymptotic analysis with fast and effective open-source implementations. These implementations are comparable and often faster than current open-source and commercial stateof-the-art software for the evaluation of special functions.Esta tesis presenta nuevos métodos para obtener expansiones uniformes asintóticas, para la evaluación numérica de funciones especiales en alta precisión. En primer lugar, se introducen fundamentos teóricos y de carácter computacional necesarios para el desarrollado y posterior implementación de tales métodos. Aplicando varios de dichos métodos, se obtienen nuevas expansiones uniformes convergentes para la evaluación numérica de las funciones hipergeométricas confluentes y de la función transcendental de Lerch. Por otro lado, se estudian nuevos esquemas de computo para evaluar la integral exponencial generalizada, desarrollando una de las implementaciones más eficientes y robustas en aritmética de punto flotante de doble precisión. En este trabajo, se combinan nuevos desarrollos en análisis asintótico con implementaciones rigurosas, distribuidas en código abierto. Las implementaciones resultantes son comparables, y en ocasiones superiores, a las soluciones comerciales y de código abierto actuales, que representan el estado de la técnica en el campo de la evaluación de funciones especiales.Postprint (published version

Analytical Expressions for the Mutual Coupling of Loop Antennas Valid from the RF to Optical Regimes

Arrays of circular loop antennas are commonly employed at radio frequencies for communications and geo- physical sensing, while also holding enormous potential in the optical regime for applications such as solar energy harvesting. Exact analytical expressions exist for predicting the mutual coupling between a variety of antennas, including dipoles and slots. However, due to the complexity of the integrals involved, analytical expressions for evaluating the coupling between loop antennas have not been previously available. This paper presents straightforward analytical expressions for efficient calculation of the coupling between two circular loops at arbitrary locations. The theory is extended to the optical regime by taking into account the dispersion and loss of the material comprising the loop antenna. These analytical expressions provide insight into the physics underlying the mutual coupling phenomenon. Along with the approximate analytical expressions, a useful pseudo-analytical representation is developed which is more exact, especially in the near-field regime, and can be easily and efficiently evaluated in MATLAB via numerical integration. It is shown that full-wave simulations for a two-element array of nanoloops can take up to six hours, while the corresponding analytical and pseudo-analytical implementations derived here take less than a minute.This work was supported in part by the Spanish Ministry of Education- Commission Fulbright Program “Salvador de Madariaga” for sponsoring the join t research collaboration under Grant PRX14/00320, in part by the Spanish and A ndalusian research programs Grant TEC2013-48414-C3-01 and Grant P12-TIC-1442, in part by the Center for Nanoscale Science, and in part by an NSF Materials Research Science and Engineering Center under Grant DMR-142062

Infrastructures and Compilation Strategies for the Performance of Computing Systems

This document presents our main contributions to the field of compilation, and more generally to the quest of performance ofcomputing systems.It is structured by type of execution environment, from static compilation (execution of native code), to JIT compilation, and purelydynamic optimization. We also consider interpreters. In each chapter, we give a focus on the most relevant contributions.Chapter 2 describes our work about static compilation. It covers a long time frame (from PhD work 1995--1998 to recent work on real-timesystems and worst-case execution times at Inria in 2015) and various positions, both in academia and in the industry.My research on JIT compilers started in the mid-2000s at STMicroelectronics, and is still ongoing. Chapter 3 covers the results we obtained on various aspects of JIT compilers: split-compilation, interaction with real-time systems, and obfuscation.Chapter 4 reports on dynamic binary optimization, a research effort started more recently, in 2012. This considers the optimization of a native binary (without source code), while it runs. It incurs significant challenges but also opportunities.Interpreters represent an alternative way to execute code. Instead of native code generation, an interpreter executes an infinite loop thatcontinuously reads a instruction, decodes it and executes its semantics. Interpreters are much easier to develop than compilers,they are also much more portable, often requiring a simple recompilation. The price to pay is the reduced performance. Chapter 5presents some of our work related to interpreters.All this research often required significant software infrastructures for validation, from early prototypes to robust quasi products, andfrom open-source to proprietary. We detail them in Chapter 6.The last chapter concludes and gives some perspectives