Reproducibility, accuracy and performance of the Feltor code and library on parallel computer architectures

Feltor is a modular and free scientific software package. It allows developing platform independent code that runs on a variety of parallel computer architectures ranging from laptop CPUs to multi-GPU distributed memory systems. Feltor consists of both a numerical library and a collection of application codes built on top of the library. Its main target are two- and three-dimensional drift- and gyro-fluid simulations with discontinuous Galerkin methods as the main numerical discretization technique. We observe that numerical simulations of a recently developed gyro-fluid model produce non-deterministic results in parallel computations. First, we show how we restore accuracy and bitwise reproducibility algorithmically and programmatically. In particular, we adopt an implementation of the exactly rounded dot product based on long accumulators, which avoids accuracy losses especially in parallel applications. However, reproducibility and accuracy alone fail to indicate correct simulation behaviour. In fact, in the physical model slightly different initial conditions lead to vastly different end states. This behaviour translates to its numerical representation. Pointwise convergence, even in principle, becomes impossible for long simulation times. In a second part, we explore important performance tuning considerations. We identify latency and memory bandwidth as the main performance indicators of our routines. Based on these, we propose a parallel performance model that predicts the execution time of algorithms implemented in Feltor and test our model on a selection of parallel hardware architectures. We are able to predict the execution time with a relative error of less than 25% for problem sizes between 0.1 and 1000 MB. Finally, we find that the product of latency and bandwidth gives a minimum array size per compute node to achieve a scaling efficiency above 50% (both strong and weak)

Heterogeneous parallel algorithms for computational fluid dynamics on unstructured meshes

Frontiers of computational fluid dynamics (CFD) are constantly expanding and eagerly demanding more computational resources. Currently, we are experiencing an rapid evolution in the high performance computing systems driven by power consumption constraints. New HPC nodes incorporate accelerators that are used as math co-processors for increasing the throughput and the FLOP per watt ratio. On the other hand, multi-core CPUs have turned into energy efficient system-on-chip architectures. By doing so, the main components of the node are fused and integrated into a single chip reducing the energy costs. Nowadays, several institutions and governments are investing in the research and development of different aspects of HPC that could lead to the next generations of supercomputers. This initiatives have entitled the problem as the exascale challenge. This goal can only be achieved by incorporating major changes in computer architecture, memory design and network interfaces. The CFD community faces an important challenge: keep the pace at the rapid changes in the HPC resources. The codes and formulations need to be re-design in other to exploit the different levels of parallelism and complex memory hierarchies of the new heterogeneous systems. The main characteristics demanded to the new CFD software are: memory awareness, extreme concurrency, modularity and portability. This thesis is devoted to the study of a CFD algorithm re-factoring for the adoption of new technologies. Our application context is the solution of incompressible flows (DNS or LES) on unstructured meshes. The first approach was using GPUs for accelerating the Poisson solver, that is the most computational intensive part of our application. The positive results obtained in this first step motivated us to port the complete time integration phase of our application. This requires a major redesign of the code. We propose a portable implementation model for CFD applications. The main idea was substituting stencil data structures and kernels by algebraic storage formats and operators. By doing so, the algorithm was restructured into a minimal set of algebraic operations. The implementation strategy consisted in the creation of a low-level algebraic layer for computations on CPUs and GPUs, and a high-level user-friendly discretization layer for CPUs that is fully localized at the preprocessing stage where performance does not play an important role. As a result, at the time-integration phase the code relies only on three algebraic kernels: sparse-matrix-vector product (SpMV), linear combination of two vectors (AXPY) and dot product (DOT). Such a simple set of basic linear algebra operations naturally provides the desired portability to any computing architecture. Special attention was paid at the development of data structures compatibles with the stream processing model. A detailed performance analysis was studied in both sequential and parallel execution engaging up to 128 GPUs in a hybrid CPU/GPU supercomputer. Moreover, we tested the portable implementation model of TermoFluids code in the Mont-Blanc mobile-based supercomputer. The re-design of the kernels exploits a heterogeneous execution model using both computing devices CPU and GPU of the ARM-based nodes. The load balancing between the two computing devices exploits a tabu search strategy that tunes the workload distribution during the preprocessing stage. A comparison of the Mont-Blanc prototypes with high-end supercomputers in terms of the achieved net performance and energy consumption provided some guidelines of the behavior of CFD applications in ARM-based architectures. Finally, we present a memory aware auto-tuned Poisson solver for problems with one Fourier diagonalizable direction. This work was developed and tested in the BlueGene/Q Vesta supercomputer, and aims at demonstrating the relevance of vectorization and memory awareness for fully exploiting the modern energy efficient CPUs.Las fronteras de la dinámica de fluidos computacional (CFD) están en constante expansión y demandan más y más recursos computacionales. Actualmente, estamos experimentando una evolución en los sistemas de computación de alto rendimiento (HPC) impulsado por restricciones de consumo de energía. Los nuevos nodos HPC incorporan aceleradores que se utilizan como co-procesadores para incrementar el rendimiento y la relación FLOP por vatio. Por otro lado, CPUs multi-core se han convertido en arquitecturas system-on-chip. Hoy en día, varias instituciones y gobiernos están invirtiendo en la investigación y desarrollo de los diferentes aspectos de HPC que podrían llevar a las próximas generaciones de superordenadores. Estas iniciativas han titulado el problema como el "exascale challenge". Este objetivo sólo puede lograrse mediante la incorporación de cambios importantes en: la arquitectura de ordenador, diseño de la memoria y las interfaces de red. La comunidad de CFD se enfrenta a un reto importante: mantener el ritmo a los rápidos cambios en las infraestructuras de HPC. Los códigos y formulaciones necesitan ser rediseñados para explotar los diferentes niveles de paralelismo y complejas jerarquías de memoria de los nuevos sistemas heterogéneos. Las principales características exigidas al nuevo software CFD son: estructuras de datos, la concurrencia extrema, modularidad y portabilidad. Esta tesis está dedicada al estudio de un modelo de implementation CFD para la adopción de nuevas tecnologías. Nuestro contexto de aplicación es la solución de los flujos incompresibles (DNS o LES) en mallas no estructuradas. El primer enfoque se basó en utilizar GPUs para acelerar el solver de Poisson. Los resultados positivos obtenidos en este primer paso nos motivaron a la portabilidad completa de la fase de integración temporal de nuestra aplicación. Esto requiere un importante rediseño del código. Proponemos un modelo de implementacion portable para aplicaciones de CFD. La idea principal es sustituir las estructuras de datos de los stencils y kernels por formatos de almacenamiento algebraicos y operadores. La estrategia de implementación consistió en la creación de una capa algebraica de bajo nivel para los cálculos de CPU y GPU, y una capa de discretización fácil de usar de alto nivel para las CPU. Como resultado, la fase de integración temporal del código se basa sólo en tres funciones algebraicas: producto de una matriz dispersa con un vector (SPMV), combinación lineal de dos vectores (AXPY) y producto escalar (DOT). Además, se prestó especial atención en el desarrollo de estructuras de datos compatibles con el modelo stream processing. Un análisis detallado de rendimiento se ha estudiado tanto en ejecución secuencial y paralela utilizando hasta 128 GPUs en un superordenador híbrido CPU / GPU. Por otra parte, hemos probado el nuevo modelo de TermoFluids en el superordenador Mont-Blanc basado en tecnología móvil. El rediseño de las funciones explota un modelo de ejecución heterogénea utilizando tanto la CPU y la GPU de los nodos basados en arquitectura ARM. El equilibrio de carga entre las dos unidades de cálculo aprovecha una estrategia de búsqueda tabú que sintoniza la distribución de carga de trabajo durante la etapa de preprocesamiento. Una comparación de los prototipos Mont-Blanc con superordenadores de alta gama en términos de rendimiento y consumo de energía nos proporcionó algunas pautas del comportamiento de las aplicaciones CFD en arquitecturas basadas en ARM. Por último, se presenta una estructura de datos auto-sintonizada para el solver de Poisson en problemas con una dirección diagonalizable mediante una descomposicion de Fourier. Este trabajo fue desarrollado y probado en la superordenador BlueGene / Q Vesta, y tiene por objeto demostrar la relevancia de vectorización y las estructuras de datos para aprovechar plenamente las CPUs de los superodenadores modernos

Software for Exascale Computing - SPPEXA 2016-2019

This open access book summarizes the research done and results obtained in the second funding phase of the Priority Program 1648 "Software for Exascale Computing" (SPPEXA) of the German Research Foundation (DFG) presented at the SPPEXA Symposium in Dresden during October 21-23, 2019. In that respect, it both represents a continuation of Vol. 113 in Springer’s series Lecture Notes in Computational Science and Engineering, the corresponding report of SPPEXA’s first funding phase, and provides an overview of SPPEXA’s contributions towards exascale computing in today's sumpercomputer technology. The individual chapters address one or more of the research directions (1) computational algorithms, (2) system software, (3) application software, (4) data management and exploration, (5) programming, and (6) software tools. The book has an interdisciplinary appeal: scholars from computational sub-fields in computer science, mathematics, physics, or engineering will find it of particular interest

Towards Efficient and Scalable Discontinuous Galerkin Methods for Unsteady Flows

openNegli ultimi anni, la crescente disponibilit`a di risorse computazionali ha contribuito alla diffusione della fluidodinamica computazionale per la ricerca e per la progettazione industriale. Uno degli approcci pi promettenti si basa sul metodo agli elementi finiti discontinui di Galerkin (dG). Nell’ambito di queste metodologie, il contributo della tesi e' triplice. Innanzi- tutto, il lavoro introduce un algoritmo di parallelizzazione ibrida MPI/OpenMP per l’utilizzo efficiente di risorse di super calcolo. In secondo luogo, propone strategie di soluzione efficienti, scalabili e con limitata allocazione di memoria per la soluzione di problemi complessi. Infine, confronta le strategie di soluzione introdotte con nuove tecniche di discretizzazione dette “ibridizzabili”, su problemi riguardanti la soluzione delle equazioni di Navier–Stokes non stazionarie. L’efficienza computazionale e' stata valutata su casi di crescente complessita' riguardanti la simulazione della turbolenza. In primo luogo, e' stata considerata la convezione naturale di Rayleigh-Benard e il flusso turbolento in un canale a numeri di Reynolds moderatamente alti. Le strategie di soluzione proposte sono risultate fino a cinque volte piu` veloci rispetto ai metodi standard allocando solamente il 7% della memoria. In secondo luogo, e' stato analizzato il flusso attorno ad una piastra piana con bordo arrotondato sottoposta a diversi livelli di turbolenza in ingresso. Nonostante la maggiore complessità' dovuta all’uso di elementi curvi ed anisotropi, l’algoritmo proposto e' risultato oltre tre volte piu` veloce allocando il 15% della memoria rispetto ad un metodo standard. Concludendo, viene riportata la simulazione del “Boeing Rudimentary Landing Gear” a Re = 10^6. In tutti i casi i risultati ottenuti sono in ottimo accordo con i dati sperimentali e con precedenti simulazioni numeriche pubblicate in letteratura.In recent years the increasing availability of High Performance Computing (HPC) resources strongly promoted the widespread of high fidelity simulations, such as the Large Eddy Simulation (LES), for industrial research and design. One of the most promising approaches to those kind of simulations is based on the discontinuous Galerkin (dG) discretization method. The contribution of the thesis towards this research area is three-fold. First, the work introduces an efficient hybrid MPI/OpenMP parallelisation paradigm to fruitfully exploit large HPC facilities. Second, it reports efficient, scalable and memory saving solution strategies for stiff dG discretisations. Third, it compares those solution strategies, for the first time using the same numerical framework, to hybridizable discontinuous Galerkin (HDG) methods, including a novel implementation of a p-multigrid preconditioning approach, on unsteady flow problems involving the solution of the NavierStokes equations. The improvements in computational efficiency have been evaluated on cases of growing complexity involving large eddy simulations of turbulent flows. First, the Rayleigh-Benard convection problem and the turbulent channel flow at moderately high Reynolds numbers is presented. The solution strategies proposed resulted up to five times faster than standard matrix-based methods while al- locating the 7% of the memory. A second family of test cases involve the LES simulation of a rounded leading edge flat plate under different levels of free-stream turbulence. Although the increased stiffness of the iteration matrix due to the use of curved and stretched elements, the solver resulted more than three times faster while allocating the 15% of the memory if compared to standard methods. Finally, the large eddy simulation of the Boeing Rudimentary Landing Gear at Re = 10^6 is reported. In all the cases, a remarkable agreement with experimental data as well as previous numerical simulations is documented.INGEGNERIA INDUSTRIALEopenFranciolini, Matte

High-Performance Computing: Dos and Don’ts

Computational fluid dynamics (CFD) is the main field of computational mechanics that has historically benefited from advances in high-performance computing. High-performance computing involves several techniques to make a simulation efficient and fast, such as distributed memory parallelism, shared memory parallelism, vectorization, memory access optimizations, etc. As an introduction, we present the anatomy of supercomputers, with special emphasis on HPC aspects relevant to CFD. Then, we develop some of the HPC concepts and numerical techniques applied to the complete CFD simulation framework: from preprocess (meshing) to postprocess (visualization) through the simulation itself (assembly and iterative solvers)

A high-performance open-source framework for multiphysics simulation and adjoint-based shape and topology optimization

The first part of this thesis presents the advances made in the Open-Source software SU2, towards transforming it into a high-performance framework for design and optimization of multiphysics problems. Through this work, and in collaboration with other authors, a tenfold performance improvement was achieved for some problems. More importantly, problems that had previously been impossible to solve in SU2, can now be used in numerical optimization with shape or topology variables. Furthermore, it is now exponentially simpler to study new multiphysics applications, and to develop new numerical schemes taking advantage of modern high-performance-computing systems. In the second part of this thesis, these capabilities allowed the application of topology optimiza- tion to medium scale fluid-structure interaction problems, using high-fidelity models (nonlinear elasticity and Reynolds-averaged Navier-Stokes equations), which had not been done before in the literature. This showed that topology optimization can be used to target aerodynamic objectives, by tailoring the interaction between fluid and structure. However, it also made ev- ident the limitations of density-based methods for this type of problem, in particular, reliably converging to discrete solutions. This was overcome with new strategies to both guarantee and accelerate (i.e. reduce the overall computational cost) the convergence to discrete solutions in fluid-structure interaction problems.Open Acces

From Piz Daint to the Stars: Simulation of Stellar Mergers using High-Level Abstractions

We study the simulation of stellar mergers, which requires complex simulations with high computational demands. We have developed Octo-Tiger, a finite volume grid-based hydrodynamics simulation code with Adaptive Mesh Refinement which is unique in conserving both linear and angular momentum to machine precision. To face the challenge of increasingly complex, diverse, and heterogeneous HPC systems, Octo-Tiger relies on high-level programming abstractions. We use HPX with its futurization capabilities to ensure scalability both between nodes and within, and present first results replacing MPI with libfabric achieving up to a 2.8x speedup. We extend Octo-Tiger to heterogeneous GPU-accelerated supercomputers, demonstrating node-level performance and portability. We show scalability up to full system runs on Piz Daint. For the scenario's maximum resolution, the compute-critical parts (hydrodynamics and gravity) achieve 68.1% parallel efficiency at 2048 nodes.Comment: Accepted at SC1