57 research outputs found
Abstractions and performance optimisations for finite element methods
Finding numerical solutions to partial differential equations (PDEs) is an essential task in the discipline of scientific computing.
In designing software tools for this task, one of the ultimate goals is to balance the needs for generality, ease to use and high performance.
Domain-specific systems based on code generation techniques,
such as Firedrake,
attempt to address this problem with a design consisting of
a hierarchy of abstractions,
where the users can specify the mathematical problems via a high-level,
descriptive interface,
which is progressively lowered through the intermediate abstractions.
Well-designed abstraction layers are essential to enable performing code transformations and optimisations robustly and efficiently,
generating high-performance code without user intervention.
This thesis discusses several topics on the design of the abstraction layers of Firedrake,
and presents the benefit of its software architecture by providing examples of various optimising code transformations at the appropriate abstraction layers.
In particular, we discuss the advantage of describing the local assembly stage of a finite element solver in an intermediate representation based on symbolic tensor algebra.
We successfully lift specific loop optimisations,
previously implemented by rewriting ASTs of the local assembly kernels, to this higher-level tensor language,
improving the compilation speed and optimisation effectiveness.
The global assembly phase involves the application of local assembly kernels on a collection of entities of an unstructured mesh.
We redesign the abstraction to express the global assembly loop nests
using tools and concepts based on the polyhedral model.
This enables us to implement the cross-element vectorisation algorithm that delivers stable vectorisation performance on CPUs automatically.
This abstraction also improves the portability of Firedrake,
as we demonstrate targeting GPU devices transparently from the same software stack.Open Acces
Dense and sparse parallel linear algebra algorithms on graphics processing units
Una línea de desarrollo seguida en el campo de la supercomputación es el uso de procesadores de propósito específico para acelerar determinados tipos de cálculo. En esta tesis estudiamos el uso de tarjetas gráficas como aceleradores de la computación y lo aplicamos al ámbito del álgebra lineal. En particular trabajamos con la biblioteca SLEPc para resolver problemas de cálculo de autovalores en matrices de gran dimensión, y para aplicar funciones de matrices en los cálculos de aplicaciones científicas. SLEPc es una biblioteca paralela que se basa en el estándar MPI y está desarrollada con la premisa de ser escalable, esto es, de permitir resolver problemas más grandes al aumentar las unidades de procesado.
El problema lineal de autovalores, Ax = lambda x en su forma estándar, lo abordamos con el uso de técnicas iterativas, en concreto con métodos de Krylov, con los que calculamos una pequeña porción del espectro de autovalores. Este tipo de algoritmos se basa en generar un subespacio de tamaño reducido (m) en el que proyectar el problema de gran dimensión (n), siendo m << n. Una vez se ha proyectado el problema, se resuelve este mediante métodos directos, que nos proporcionan aproximaciones a los autovalores del problema inicial que queríamos resolver. Las operaciones que se utilizan en la expansión del subespacio varían en función de si los autovalores deseados están en el exterior o en el interior del espectro. En caso de buscar autovalores en el exterior del espectro, la expansión se hace mediante multiplicaciones matriz-vector. Esta operación la realizamos en la GPU, bien mediante el uso de bibliotecas o mediante la creación de funciones que aprovechan la estructura de la matriz. En caso de autovalores en el interior del espectro, la expansión requiere resolver sistemas de ecuaciones lineales. En esta tesis implementamos varios algoritmos para la resolución de sistemas de ecuaciones lineales para el caso específico de matrices con estructura tridiagonal a bloques, que se ejecutan en GPU.
En el cálculo de las funciones de matrices hemos de diferenciar entre la aplicación directa de una función sobre una matriz, f(A), y la aplicación de la acción de una función de matriz sobre un vector, f(A)b. El primer caso implica un cálculo denso que limita el tamaño del problema. El segundo permite trabajar con matrices dispersas grandes, y para resolverlo también hacemos uso de métodos de Krylov. La expansión del subespacio se hace mediante multiplicaciones matriz-vector, y hacemos uso de GPUs de la misma forma que al resolver autovalores. En este caso el problema proyectado comienza siendo de tamaño m, pero se incrementa en m en cada reinicio del método. La resolución del problema proyectado se hace aplicando una función de matriz de forma directa. Nosotros hemos implementado varios algoritmos para calcular las funciones de matrices raíz cuadrada y exponencial, en las que el uso de GPUs permite acelerar el cálculo.One line of development followed in the field of supercomputing is the use of specific purpose processors to speed up certain types of computations. In this thesis we study the use of graphics processing units as computer accelerators and apply it to the field of linear algebra. In particular, we work with the SLEPc library to solve large scale eigenvalue problems, and to apply matrix functions in scientific applications. SLEPc is a parallel library based on the MPI standard and is developed with the premise of being scalable, i.e. to allow solving larger problems by increasing the processing units.
We address the linear eigenvalue problem, Ax = lambda x in its standard form, using iterative techniques, in particular with Krylov's methods, with which we calculate a small portion of the eigenvalue spectrum. This type of algorithms is based on generating a subspace of reduced size (m) in which to project the large dimension problem (n), being m << n. Once the problem has been projected, it is solved by direct methods, which provide us with approximations of the eigenvalues of the initial problem we wanted to solve. The operations used in the expansion of the subspace vary depending on whether the desired eigenvalues are from the exterior or from the interior of the spectrum. In the case of searching for exterior eigenvalues, the expansion is done by matrix-vector multiplications. We do this on the GPU, either by using libraries or by creating functions that take advantage of the structure of the matrix. In the case of eigenvalues from the interior of the spectrum, the expansion requires solving linear systems of equations. In this thesis we implemented several algorithms to solve linear systems of equations for the specific case of matrices with a block-tridiagonal structure, that are run on GPU.
In the computation of matrix functions we have to distinguish between the direct application of a matrix function, f(A), and the action of a matrix function on a vector, f(A)b. The first case involves a dense computation that limits the size of the problem. The second allows us to work with large sparse matrices, and to solve it we also make use of Krylov's methods. The expansion of subspace is done by matrix-vector multiplication, and we use GPUs in the same way as when solving eigenvalues. In this case the projected problem starts being of size m, but it is increased by m on each restart of the method. The solution of the projected problem is done by directly applying a matrix function. We have implemented several algorithms to compute the square root and the exponential matrix functions, in which the use of GPUs allows us to speed up the computation.Una línia de desenvolupament seguida en el camp de la supercomputació és l'ús de processadors de propòsit específic per a accelerar determinats tipus de càlcul. En aquesta tesi estudiem l'ús de targetes gràfiques com a acceleradors de la computació i ho apliquem a l'àmbit de l'àlgebra lineal. En particular treballem amb la biblioteca SLEPc per a resoldre problemes de càlcul d'autovalors en matrius de gran dimensió, i per a aplicar funcions de matrius en els càlculs d'aplicacions científiques. SLEPc és una biblioteca paral·lela que es basa en l'estàndard MPI i està desenvolupada amb la premissa de ser escalable, açò és, de permetre resoldre problemes més grans en augmentar les unitats de processament.
El problema lineal d'autovalors, Ax = lambda x en la seua forma estàndard, ho abordem amb l'ús de tècniques iteratives, en concret amb mètodes de Krylov, amb els quals calculem una xicoteta porció de l'espectre d'autovalors. Aquest tipus d'algorismes es basa a generar un subespai de grandària reduïda (m) en el qual projectar el problema de gran dimensió (n), sent m << n. Una vegada s'ha projectat el problema, es resol aquest mitjançant mètodes directes, que ens proporcionen aproximacions als autovalors del problema inicial que volíem resoldre. Les operacions que s'utilitzen en l'expansió del subespai varien en funció de si els autovalors desitjats estan en l'exterior o a l'interior de l'espectre. En cas de cercar autovalors en l'exterior de l'espectre, l'expansió es fa mitjançant multiplicacions matriu-vector. Aquesta operació la realitzem en la GPU, bé mitjançant l'ús de biblioteques o mitjançant la creació de funcions que aprofiten l'estructura de la matriu. En cas d'autovalors a l'interior de l'espectre, l'expansió requereix resoldre sistemes d'equacions lineals. En aquesta tesi implementem diversos algorismes per a la resolució de sistemes d'equacions lineals per al cas específic de matrius amb estructura tridiagonal a blocs, que s'executen en GPU.
En el càlcul de les funcions de matrius hem de diferenciar entre l'aplicació directa d'una funció sobre una matriu, f(A), i l'aplicació de l'acció d'una funció de matriu sobre un vector, f(A)b. El primer cas implica un càlcul dens que limita la grandària del problema. El segon permet treballar amb matrius disperses grans, i per a resoldre-ho també fem ús de mètodes de Krylov. L'expansió del subespai es fa mitjançant multiplicacions matriu-vector, i fem ús de GPUs de la mateixa forma que en resoldre autovalors. En aquest cas el problema projectat comença sent de grandària m, però s'incrementa en m en cada reinici del mètode. La resolució del problema projectat es fa aplicant una funció de matriu de forma directa. Nosaltres hem implementat diversos algorismes per a calcular les funcions de matrius arrel quadrada i exponencial, en les quals l'ús de GPUs permet accelerar el càlcul.Lamas Daviña, A. (2018). Dense and sparse parallel linear algebra algorithms on graphics processing units [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/112425TESI
Cellular Automata
Modelling and simulation are disciplines of major importance for science and engineering. There is no science without models, and simulation has nowadays become a very useful tool, sometimes unavoidable, for development of both science and engineering. The main attractive feature of cellular automata is that, in spite of their conceptual simplicity which allows an easiness of implementation for computer simulation, as a detailed and complete mathematical analysis in principle, they are able to exhibit a wide variety of amazingly complex behaviour. This feature of cellular automata has attracted the researchers' attention from a wide variety of divergent fields of the exact disciplines of science and engineering, but also of the social sciences, and sometimes beyond. The collective complex behaviour of numerous systems, which emerge from the interaction of a multitude of simple individuals, is being conveniently modelled and simulated with cellular automata for very different purposes. In this book, a number of innovative applications of cellular automata models in the fields of Quantum Computing, Materials Science, Cryptography and Coding, and Robotics and Image Processing are presented
10th EASN International Conference on Innovation in Aviation & Space to the Satisfaction of the European Citizens
This Special Issue book contains selected papers from works presented at the 10th EASN (European Aeronautics Science Network) International Conference on Innovation in Aviation & Space, which was held from the 2nd until the 4th of September, 2020. About 350 remote participants contributed to a high-level scientific gathering providing some of the latest research results on the topic, as well as some of the latest relevant technological advancements. Eleven interesting articles, which cover a wide range of topics including characterization, analysis and design, as well as numerical simulation, are contained in this Special Issue
Annals of Scientific Society for Assembly, Handling and Industrial Robotics
This Open Access proceedings present a good overview of the current research landscape of industrial robots. The objective of MHI Colloquium is a successful networking at academic and management level. Thereby the colloquium is focussing on a high level academic exchange to distribute the obtained research results, determine synergetic effects and trends, connect the actors personally and in conclusion strengthen the research field as well as the MHI community. Additionally there is the possibility to become acquainted with the organizing institute. Primary audience are members of the scientific association for assembly, handling and industrial robots (WG MHI)
Making the most of imaging and spectroscopy in TEM: computer simulations for materials science problems
[eng] Transmission Electron Microscopy (TEM), since its first implementation by Ernst August Friedrich Ruska and Max Knoll in 1931, has been an essential technique in the nanoscience and nanotechnology field. In the beginning, the real resolution was just a small fraction of the potential resolution expected by the fact of using electrons as a “light” source. The wavelength of the electrons accelerated at hundreds of electronvolts would involve a subatomic resolution; however, all the aberrations related to electromagnetic lenses caused a dramatic decrease. In addition, the energy resolution was highly affected by the chromatic aberration of the electron beam. Nowadays, all these initial problems have been solved by the development of the image aberration correctors and the monochromators. Since atomic resolution together with 10 meV energy resolution are a reality for researchers, new and higher horizons have been set for the transmission electron microscopy, such as orbital imaging, phonon imaging, or real time atom monitoring amongst others. TEM could be described at its most fundamental as the analysis of the result of impacting electrons with a specific compound or structure. From, this impact different data can be obtained which can be rapidly classified between imaging and spectroscopy. With the recent increases in energy and spatial resolution, a huge amount of information can be directly extracted from very large experimental datasets; however, for a deeper understanding, most of the times the support from theoretical calculations is also needed. Solid state physics with quantum considerations can contribute to an accurate description of the studied systems.
Whereas in the past, materials science, solid state physics, quantum mechanics and chemistry were disciplines with a huge separation between them, nowadays they merge in the field of nanoscience and nanotechnology. When the object size is reduced to the nanoscale the quantum effects cannot be neglected anymore, any change on the synthesis can in turn change the structure which plays an essential role on the compound properties.
Thus, modelling has become an essential step in the materials synthesis and characterization. The knowledge of the structure allows to compute the interaction of the electrons with any well described crystalline structure and generate images and spectra comparable with experimental data, but not just as a check, but to gain deeper insight. The interaction of the electrons with matter must be computed by solving the Schrödinger equation of the electrons interacting with the sample. The sample, the system, can be considered as a periodic potential.
Imaging, measuring, modelling and manipulating matter are the basis of the promising field of nanoscience, and they can be carried out using a TEM, with the continuous support of theoretical calculations to obtain the most.
The present thesis uses three main types of calculations to interpret TEM data: atomic simulations applied to imaging, Boundary Element Method (BEM) based calculations for surface plasmon distributions and Density Functional Theory (DFT) for EELS analysis. Even if they will be presented separately, they are not independent; the essence is always the same but depending on the desired results different considerations are needed. The materials science problems solved through these kinds of simulations presented in the thesis are the analysis of CuPtB ordering effects in GaInP, the influence of oxygen vacancies in the EELS of Bi2O3, the consequences of the Fe3O4 Verwey transition in its electronic structure and how it is observed in EELS and, finally, the surface plasmon distribution in gold-nanodomes as a function of the dome shape.
To conclude, the simulations have been presented as an essential tool to complement TEM studies to link the experimental results with the most fundamental aspects which are determined by the structure of the studied materials.[cat] Aquesta tesi doctoral s'ha centrat en la realització de càlculs teòrics que permetin comprendre i extreure la major quantitat d'informació possible de les dades experimentals de microscòpia de transmissió d’electrons (TEM), i de les tècniques espectroscòpiques relacionades, concretament, l'espectroscòpia de pèrdua d’energia dels electrons (EELS). S’hi utilitzen tres tipus principals de càlculs per interpretar les dades del TEM: simulacions atòmiques aplicades a l'obtenció d'imatges, càlculs basats en el mètode d'elements de contorn (BEM) per a les distribucions de plasmons superficials i la teoria del funcional de la densitat (DFT) per a l'anàlisi d’EELS. Tot i que es presentin per separat, no són independents; l'essència sempre és la mateixa, però depenent dels resultats desitjats es necessiten diferents consideracions. En aquest sentit, primerament s'han presentat les bases físiques de diferents mètodes de simulació: simulació multislice per calcular imatges de contrast de número atòmic i de contrast de fase, càlculs (DFT) per calcular dades EELS de baixa pèrdua i de pèrdues profundes i, simulacions basades en BEM per a plasmons de superfície. Un cop presentades les bases, s’han resolt problemes de la ciència dels materials mitjançant aquest tipus de simulacions: l'anàlisi dels efectes d'ordenació del CuPtB al GaInP, la influència de les vacants d'oxigen a l'EELS del Bi2O3, les conseqüències de la transició Fe3O4 Verwey en la seva estructura electrònica i com s'observa a l'EELS i, finalment, la distribució de plasmons superficials als nanodoms d'or en funció de la forma de la cúpula. En resum, al llarg la tesi doctoral les simulacions han demostrat ser una eina essencial per complementar els estudis de TEM, per vincular els resultats experimentals amb els aspectes més fonamentals determinats per l'estructura dels materials estudiats
MC 2019 Berlin Microscopy Conference - Abstracts
Das Dokument enthält die Kurzfassungen der Beiträge aller Teilnehmer an der Mikroskopiekonferenz "MC 2019", die vom 01. bis 05.09.2019, in Berlin stattfand
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