25 research outputs found

    Brain and Human Body Modeling

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    This open access book describes modern applications of computational human modeling with specific emphasis in the areas of neurology and neuroelectromagnetics, depression and cancer treatments, radio-frequency studies and wireless communications. Special consideration is also given to the use of human modeling to the computational assessment of relevant regulatory and safety requirements. Readers working on applications that may expose human subjects to electromagnetic radiation will benefit from this book’s coverage of the latest developments in computational modelling and human phantom development to assess a given technology’s safety and efficacy in a timely manner. Describes construction and application of computational human models including anatomically detailed and subject specific models; Explains new practices in computational human modeling for neuroelectromagnetics, electromagnetic safety, and exposure evaluations; Includes a survey of modern applications for which computational human models are critical; Describes cellular-level interactions between the human body and electromagnetic fields

    Parallel Overlapping Schwarz Preconditioners for Incompressible Fluid Flow and Fluid-Structure Interaction Problems

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    Efficient methods for the approximation of solutions to incompressible fluid flow and fluid-structure interaction problems are presented. In particular, partial differential equations (PDEs) are derived from basic conservation principles. First, the incompressible Navier-Stokes equations for Newtonian fluids are introduced. This is followed by a consideration of solid mechanical problems. Both, the fluid equations and the equation for solid problems are then coupled and a fluid-structure interaction problem is constructed. Furthermore, a discretization by the finite element method for weak formulations of these problems is described. This spatial discretization of variables is followed by a discretization of the remaining time-dependent parts. An implementation of the discretizations and problems in a parallel C++ software environment is described. This implementation is based on the software package Trilinos. The parallel execution of a program is the essence of High Performance Computing (HPC). HPC clusters are, in general, machines with several tens of thousands of cores. The fastest current machine, as of the TOP500 list from November 2019, has over 2.4 million cores, while the largest machine possesses over 10 million cores. To achieve sufficient accuracy of the approximate solutions, a fine spatial discretization must be used. In particular, fine spatial discretizations lead to systems with large sparse matrices that have to be solved. Iterative preconditioned Krylov methods are among the most widely used and efficient solution strategies for these systems. Robust and efficient preconditioners which possess good scaling behavior for a parallel execution on several thousand cores are the main component. In this thesis, the focus is on parallel algebraic preconditioners for fluid and fluid-structure interaction problems. Therefore, monolithic overlapping Schwarz preconditioners for saddle point problems of Stokes and Navier-Stokes problems are presented. Monolithic preconditioners for incompressible fluid flow problems can significantly improve the convergence speed compared to preconditioners based on block factorizations. In order to obtain numerically scalable algorithms, coarse spaces obtained from the Generalized Dryja-Smith-Widlund (GDSW) and the Reduced dimension GDSW (RGDSW) approach are used. These coarse spaces can be constructed in an essentially algebraic way. Numerical results of the parallel implementation are presented for various incompressible fluid flow problems. Good scalability for up to 11 979 MPI ranks, which corresponds to the largest problem configuration fitting on the employed supercomputer, were achieved. A comparison of these monolithic approaches and commonly used block preconditioners with respect to time-to-solution is made. Similarly, the most efficient construction of two-level overlapping Schwarz preconditioners with GDSW and RGDSW coarse spaces for solid problems is reported. These techniques are then combined to efficiently solve fully coupled monolithic fluid-strucuture interaction problems

    Compiler Support for Operator Overloading and Algorithmic Differentiation in C++

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    Multiphysics software needs derivatives for, e.g., solving a system of non-linear equations, conducting model verification, or sensitivity studies. In C++, algorithmic differentiation (AD), based on operator overloading (overloading), can be used to calculate derivatives up to machine precision. To that end, the built-in floating-point type is replaced by the user-defined AD type. It overloads all required operators, and calculates the original value and the corresponding derivative based on the chain rule of calculus. While changing the underlying type seems straightforward, several complications arise concerning software and performance engineering. This includes (1) fundamental language restrictions of C++ w.r.t. user-defined types, (2) type correctness of distributed computations with the Message Passing Interface (MPI) library, and (3) identification and mitigation of AD induced overheads. To handle these issues, AD experts may spend a significant amount of time to enhance a code with AD, verify the derivatives and ensure optimal application performance. Hence, in this thesis, we propose a modern compiler-based tooling approach to support and accelerate the AD-enhancement process of C++ target codes. In particular, we make contributions to three aspects of AD. The initial type change - While the change to the AD type in a target code is conceptually straightforward, the type change often leads to a multitude of compiler error messages. This is due to the different treatment of built-in floating-point types and user-defined types by the C++ language standard. Previously legal code constructs in the target code subsequently violate the language standard when the built-in floating-point type is replaced with a user-defined AD type. We identify and classify these problematic code constructs and their root cause is shown. Solutions by localized source transformation are proposed. To automate this rather mechanical process, we develop a static code analyser and source transformation tool, called OO-Lint, based on the Clang compiler framework. It flags instances of these problematic code constructs and applies source transformations to make the code compliant with the requirements of the language standard. To show the overall relevance of complications with user-defined types, OO-Lint is applied to several well-known scientific codes, some of which have already been AD enhanced by others. In all of these applications, except the ones manually treated for AD overloading, problematic code constructs are detected. Type correctness of MPI communication - MPI is the de-facto standard for programming high performance, distributed applications. At the same time, MPI has a complex interface whose usage can be error-prone. For instance, MPI derived data types require manual construction by specifying memory locations of the underlying data. Specifying wrong offsets can lead to subtle bugs that are hard to detect. In the context of AD, special libraries exist that handle the required derivative book-keeping by replacing the MPI communication calls with overloaded variants. However, on top of the AD type change, the MPI communication routines have to be changed manually. In addition, the AD type fundamentally changes memory layout assumptions as it has a different extent than the built-in types. Previously legal layout assumptions have, thus, to be reverified. As a remedy, to detect any type-related errors, we developed a memory sanitizer tool, called TypeART, based on the LLVM compiler framework and the MPI correctness checker MUST. It tracks all memory allocations relevant to MPI communication to allow for checking the underlying type and extent of the typeless memory buffer address passed to any MPI routine. The overhead induced by TypeART w.r.t. several target applications is manageable. AD domain-specific profiling - Applying AD in a black-box manner, without consideration of the target code structure, can have a significant impact on both runtime and memory consumption. An AD expert is usually required to apply further AD-related optimizations for the reduction of these induced overheads. Traditional profiling techniques are, however, insufficient as they do not reveal any AD domain-specific metrics. Of interest for AD code optimization are, e.g., specific code patterns, especially on a function level, that can be treated efficiently with AD. To that end, we developed a static profiling tool, called ProAD, based on the LLVM compiler framework. For each function, it generates the computational graph based on the static data flow of the floating-point variables. The framework supports pattern analysis on the computational graph to identify the optimal application of the chain rule. We show the potential of the optimal application of AD with two case studies. In both cases, significant runtime improvements can be achieved when the knowledge of the code structure, provided by our tool, is exploited. For instance, with a stencil code, a speedup factor of about 13 is achieved compared to a naive application of AD and a factor of 1.2 compared to hand-written derivative code

    Dense and sparse parallel linear algebra algorithms on graphics processing units

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    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

    Proceedings of the International Micro Air Vehicles Conference and Flight Competition 2017 (IMAV 2017)

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    The IMAV 2017 conference has been held at ISAE-SUPAERO, Toulouse, France from Sept. 18 to Sept. 21, 2017. More than 250 participants coming from 30 different countries worldwide have presented their latest research activities in the field of drones. 38 papers have been presented during the conference including various topics such as Aerodynamics, Aeroacoustics, Propulsion, Autopilots, Sensors, Communication systems, Mission planning techniques, Artificial Intelligence, Human-machine cooperation as applied to drones

    Geometry–aware finite element framework for multi–physics simulations: an algorithmic and software-centric perspective

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    In finite element simulations, the handling of geometrical objects and their discrete representation is a critical aspect in both serial and parallel scientific software environments. The development of codes targeting such envinronments is subject to great development effort and man-hours invested. In this thesis we approach these issues from three fronts. First, stable and efficient techniques for the transfer of discrete fields between non matching volume or surface meshes are an essential ingredient for the discretization and numerical solution of coupled multi-physics and multi-scale problems. In particular L2-projections allows for the transfer of discrete fields between unstructured meshes, both in the volume and on the surface. We present an algorithm for parallelizing the assembly of the L2-transfer operator for unstructured meshes which are arbitrarily distributed among different processes. The algorithm requires no a priori information on the geometrical relationship between the different meshes. Second, the geometric representation is often a limiting factor which imposes a trade-off between how accurately the shape is described, and what methods can be employed for solving a system of differential equations. Parametric finite-elements and bijective mappings between polygons or polyhedra allow us to flexibly construct finite element discretizations with arbitrary resolutions without sacrificing the accuracy of the shape description. Such flexibility allows employing state-of-the-art techniques, such as geometric multigrid methods, on meshes with almost any shape.t, the way numerical techniques are represented in software libraries and approached from a development perspective, affect both usability and maintainability of such libraries. Completely separating the intent of high-level routines from the actual implementation and technologies allows for portable and maintainable performance. We provide an overview on current trends in the development of scientific software and showcase our open-source library utopia
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