Optimisation of computational fluid dynamics applications on multicore and manycore architectures

This thesis presents a number of optimisations used for mapping the underlying computational patterns of finite volume CFD applications onto the architectural features of modern multicore and manycore processors. Their effectiveness and impact is demonstrated in a block-structured and an unstructured code of representative size to industrial applications and across a variety of processor architectures that make up contemporary high-performance computing systems. The importance of vectorization and the ways through which this can be achieved is demonstrated in both structured and unstructured solvers together with the impact that the underlying data layout can have on performance. The utility of auto-tuning for ensuring performance portability across multiple architectures is demonstrated and used for selecting optimal parameters such as prefetch distances for software prefetching or tile sizes for strip mining/loop tiling. On the manycore architectures, running more than one thread per physical core is found to be crucial for good performance on processors with in-order core designs but not required on out-of-order architectures. For architectures with high-bandwidth memory packages, their exploitation, whether explicitly or implicitly, is shown to be imperative for best performance. The implementation of all of these optimisations led to application speed-ups ranging between 2.7X and 3X on the multicore CPUs and 5.7X to 24X on the manycore processors.Open Acces

Real-Time Simulation and Prognosis of Smoke Propagation in Compartments Using a GPU

The evaluation of life safety in buildings in case of fire is often based on smoke spread calculations. However, recent simulation models – in general, based on computational fluid dynamics – often require long execution times or high-performance computers to achieve simulation results in or faster than real-time. Therefore, the objective of this study is the development of a concept for the real-time and prognosis simulation of smoke propagation in compartments using a graphics processing unit (GPU). The developed concept is summarized in an expandable open source software basis, called JuROr (Jülich's Real-time simulation within ORPHEUS). JuROr simulates buoyancy-driven, turbulent smoke spread based on a reduced modeling approach using finite differences and a Large Eddy Simulation turbulence model to solve the incompressible Navier-Stokes and energy equations. This reduced model is fully adapted to match the target hardware of highly parallel computer architectures. Thereby, the code is written in the object-oriented programming language C++ and the pragma-based programming model OpenACC. This model ensures to maintain a single source code, which can be executed in serial and parallel on various architectures. Further, the study provides a proof of JuROr's concept to balance sufficient accuracy and practicality. First, the code was successfully verified using unit and (semi-) analytical tests. Then, the underlying model was validated by comparing the numerical results to the experimental results of scenarios relevant for fire protection. Thereby, verification and validation showed acceptable accuracy for JuROr's application. Lastly, the performance criteria of JuROr – being real-time and prognosis capable with comparable performance across various architectures – was successfully evaluated. Here, JuROr also showed high speedup results on a GPU and faster time-to-solution compared to the established Fire Dynamics Simulator. These results show JuROr's practicality.Die Bewertung der Personensicherheit bei Feuer in Gebäuden basiert häufig auf Berechnungen zur Rauchausbreitung. Bisherige Simulationsmodelle – im Allgemeinen basierend auf numerischer Strömungsdynamik – erfordern jedoch lange Ausführungszeiten oder Hochleistungsrechner, um Simulationsergebnisse in und schneller als Echtzeit liefern zu können. Daher ist das Ziel dieser Arbeit die Entwicklung eines Konzeptes für die Echtzeit- und Prognosesimulation der Rauchausbreitung in Gebäuden mit Hilfe eines Grafikprozessors (GPU). Zusammengefasst ist das entwickelte Konzept in einer erweiterbaren Open-Source-Software, genannt JuROr (Jülich's Real-time Simulation in ORPHEUS). JuROr simuliert die Ausbreitung von auftriebsgetriebenem, turbulentem Rauch basierend auf einem reduzierten Modellierungsansatz mit finiten Differenzen und einem Large Eddy Simulation Turbulenzmodell, um inkompressible Navier- Stokes und Energiegleichungen zu lösen. Das reduzierte Modell ist voll- ständig angepasst an hochparallele Computerarchitekturen. Dabei ist der Code implementiert mit C++ und OpenACC. Dies hat den Vorteil mit nur einem Quellcode verschiedenste serielle und parallele Ausführungen des Programms für unterschiedliche Architekturen erstellen zu können. Die Studie liefert weiterhin einen Konzeptnachweis dafür, ausreichende Genauigkeit und Praktikabilität im Gleichgewicht zu halten. Zunächst wurde der Code erfolgreich mit Modul- und (semi-) analytischen Tests verifiziert. Dann wurde das zugrundeliegende Modell durch einen Vergleich der numerischen mit den experimentellen Ergebnissen für den Brandschutz relevanter Szenarien validiert. Die Verifizierung und Validierung zeigten dabei ausreichende Genauigkeit für JuROr. Zuletzt, wurden die Kriterien von JuROr – echtzeit- und prognosefähig zu sein mit vergleichbarer Leistung auf unterschiedlichsten Architekturen – erfolgreich geprüft. Zudem zeigte JuROr hohe Beschleunigungseffekte auf einer GPU und schnellere Lösungszeiten im Vergleich zum etablierten Fire Dynamics Simulator. Diese Ergebnisse zeigen JuROr's Praktikabilität

Polyhedral+Dataflow Graphs

This research presents an intermediate compiler representation that is designed for optimization, and emphasizes the temporary storage requirements and execution schedule of a given computation to guide optimization decisions. The representation is expressed as a dataflow graph that describes computational statements and data mappings within the polyhedral compilation model. The targeted applications include both the regular and irregular scientific domains. The intermediate representation can be integrated into existing compiler infrastructures. A specification language implemented as a domain specific language in C++ describes the graph components and the transformations that can be applied. The visual representation allows users to reason about optimizations. Graph variants can be translated into source code or other representation. The language, intermediate representation, and associated transformations have been applied to improve the performance of differential equation solvers, or sparse matrix operations, tensor decomposition, and structured multigrid methods

CFDNet: a deep learning-based accelerator for fluid simulations

CFD is widely used in physical system design and optimization, where it is used to predict engineering quantities of interest, such as the lift on a plane wing or the drag on a motor vehicle. However, many systems of interest are prohibitively expensive for design optimization, due to the expense of evaluating CFD simulations. To render the computation tractable, reduced-order or surrogate models are used to accelerate simulations while respecting the convergence constraints provided by the higher-fidelity solution. This paper introduces CFDNet -- a physical simulation and deep learning coupled framework, for accelerating the convergence of Reynolds Averaged Navier-Stokes simulations. CFDNet is designed to predict the primary physical properties of the fluid including velocity, pressure, and eddy viscosity using a single convolutional neural network at its core. We evaluate CFDNet on a variety of use-cases, both extrapolative and interpolative, where test geometries are observed/not-observed during training. Our results show that CFDNet meets the convergence constraints of the domain-specific physics solver while outperforming it by 1.9 - 7.4x on both steady laminar and turbulent flows. Moreover, we demonstrate the generalization capacity of CFDNet by testing its prediction on new geometries unseen during training. In this case, the approach meets the CFD convergence criterion while still providing significant speedups over traditional domain-only models.Comment: It has been accepted and almost published in the International Conference in Supercomputing (ICS) 202

Automatische Codegenerierung für Massiv Parallele Applikationen in der Numerischen Strömungsmechanik

Solving partial differential equations (PDEs) is a fundamental challenge in many application domains in industry and academia alike. With increasingly large problems, efficient and highly scalable implementations become more and more crucial. Today, facing this challenge is more difficult than ever due to the increasingly heterogeneous hardware landscape. One promising approach is developing domain‐specific languages (DSLs) for a set of applications. Using code generation techniques then allows targeting a range of hardware platforms while concurrently applying domain‐specific optimizations in an automated fashion. The present work aims to further the state of the art in this field. As domain, we choose PDE solvers and, in particular, those from the group of geometric multigrid methods. To avoid having a focus too broad, we restrict ourselves to methods working on structured and patch‐structured grids. We face the challenge of handling a domain as complex as ours, while providing different abstractions for diverse user groups, by splitting our external DSL ExaSlang into multiple layers, each specifying different aspects of the final application. Layer 1 is designed to resemble LaTeX and allows inputting continuous equations and functions. Their discretization is expressed on layer 2. It is complemented by algorithmic components which can be implemented in a Matlab‐like syntax on layer 3. All information provided to this point is summarized on layer 4, enriched with particulars about data structures and the employed parallelization. Additionally, we support automated progression between the different layers. All ExaSlang input is processed by our jointly developed Scala code generation framework to ultimately emit C++ code. We particularly focus on how to generate applications parallelized with, e.g., MPI and OpenMP that are able to run on workstations and large‐scale cluster alike. We showcase the applicability of our approach by implementing simple test problems, like Poisson’s equation, as well as relevant applications from the field of computational fluid dynamics (CFD). In particular, we implement scalable solvers for the Stokes, Navier‐Stokes and shallow water equations (SWE) discretized using finite differences (FD) and finite volumes (FV). For the case of Navier‐Stokes, we also extend our implementation towards non‐uniform grids, thereby enabling static mesh refinement, and advanced effects such as the simulated fluid being non‐Newtonian and non‐isothermal

Leveraging performance of 3D finite difference schemes in large scientific computing simulations

Gone are the days when engineers and scientists conducted most of their experiments empirically. During these decades, actual tests were carried out in order to assess the robustness and reliability of forthcoming product designs and prove theoretical models. With the advent of the computational era, scientific computing has definetely become a feasible solution compared with empirical methods, in terms of effort, cost and reliability. Large and massively parallel computational resources have reduced the simulation execution times and have improved their numerical results due to the refinement of the sampled domain. Several numerical methods coexist for solving the Partial Differential Equations (PDEs). Methods such as the Finite Element (FE) and the Finite Volume (FV) are specially well suited for dealing with problems where unstructured meshes are frequent. Unfortunately, this flexibility is not bestowed for free. These schemes entail higher memory latencies due to the handling of irregular data accesses. Conversely, the Finite Difference (FD) scheme has shown to be an efficient solution for problems where the structured meshes suit the domain requirements. Many scientific areas use this scheme due to its higher performance. This thesis focuses on improving FD schemes to leverage the performance of large scientific computing simulations. Different techniques are proposed such as the Semi-stencil, a novel algorithm that increases the FLOP/Byte ratio for medium- and high-order stencils operators by reducing the accesses and endorsing data reuse. The algorithm is orthogonal and can be combined with techniques such as spatial- or time-blocking, adding further improvement. New trends on Symmetric Multi-Processing (SMP) systems -where tens of cores are replicated on the same die- pose new challenges due to the exacerbation of the memory wall problem. In order to alleviate this issue, our research is focused on different strategies to reduce pressure on the cache hierarchy, particularly when different threads are sharing resources due to Simultaneous Multi-Threading (SMT). Several domain decomposition schedulers for work-load balance are introduced ensuring quasi-optimal results without jeopardizing the overall performance. We combine these schedulers with spatial-blocking and auto-tuning techniques, exploring the parametric space and reducing misses in last level cache. As alternative to brute-force methods used in auto-tuning, where a huge parametric space must be traversed to find a suboptimal candidate, performance models are a feasible solution. Performance models can predict the performance on different architectures, selecting suboptimal parameters almost instantly. In this thesis, we devise a flexible and extensible performance model for stencils. The proposed model is capable of supporting multi- and many-core architectures including complex features such as hardware prefetchers, SMT context and algorithmic optimizations. Our model can be used not only to forecast execution time, but also to make decisions about the best algorithmic parameters. Moreover, it can be included in run-time optimizers to decide the best SMT configuration based on the execution environment. Some industries rely heavily on FD-based techniques for their codes. Nevertheless, many cumbersome aspects arising in industry are still scarcely considered in academia research. In this regard, we have collaborated in the implementation of a FD framework which covers the most important features that an HPC industrial application must include. Some of the node-level optimization techniques devised in this thesis have been included into the framework in order to contribute in the overall application performance. We show results for a couple of strategic applications in industry: an atmospheric transport model that simulates the dispersal of volcanic ash and a seismic imaging model used in Oil & Gas industry to identify hydrocarbon-rich reservoirs.Atrás quedaron los días en los que ingenieros y científicos realizaban sus experimentos empíricamente. Durante esas décadas, se llevaban a cabo ensayos reales para verificar la robustez y fiabilidad de productos venideros y probar modelos teóricos. Con la llegada de la era computacional, la computación científica se ha convertido en una solución factible comparada con métodos empíricos, en términos de esfuerzo, coste y fiabilidad. Los supercomputadores han reducido el tiempo de las simulaciones y han mejorado los resultados numéricos gracias al refinamiento del dominio. Diversos métodos numéricos coexisten para resolver las Ecuaciones Diferenciales Parciales (EDPs). Métodos como Elementos Finitos (EF) y Volúmenes Finitos (VF) están bien adaptados para tratar problemas donde las mallas no estructuradas son frecuentes. Desafortunadamente, esta flexibilidad no se confiere de forma gratuita. Estos esquemas conllevan latencias más altas debido al acceso irregular de datos. En cambio, el esquema de Diferencias Finitas (DF) ha demostrado ser una solución eficiente cuando las mallas estructuradas se adaptan a los requerimientos. Esta tesis se enfoca en mejorar los esquemas DF para impulsar el rendimiento de las simulaciones en la computación científica. Se proponen diferentes técnicas, como el Semi-stencil, un nuevo algoritmo que incrementa el ratio de FLOP/Byte para operadores de stencil de orden medio y alto reduciendo los accesos y promoviendo el reuso de datos. El algoritmo es ortogonal y puede ser combinado con técnicas como spatial- o time-blocking, añadiendo mejoras adicionales. Las nuevas tendencias hacia sistemas con procesadores multi-simétricos (SMP) -donde decenas de cores son replicados en el mismo procesador- plantean nuevos retos debido a la exacerbación del problema del ancho de memoria. Para paliar este problema, nuestra investigación se centra en estrategias para reducir la presión en la jerarquía de cache, particularmente cuando diversos threads comparten recursos debido a Simultaneous Multi-Threading (SMT). Introducimos diversos planificadores de descomposición de dominios para balancear la carga asegurando resultados casi óptimos sin poner en riesgo el rendimiento global. Combinamos estos planificadores con técnicas de spatial-blocking y auto-tuning, explorando el espacio paramétrico y reduciendo los fallos en la cache de último nivel. Como alternativa a los métodos de fuerza bruta usados en auto-tuning donde un espacio paramétrico se debe recorrer para encontrar un candidato, los modelos de rendimiento son una solución factible. Los modelos de rendimiento pueden predecir el rendimiento en diferentes arquitecturas, seleccionando parámetros suboptimos casi de forma instantánea. En esta tesis, ideamos un modelo de rendimiento para stencils flexible y extensible. El modelo es capaz de soportar arquitecturas multi-core incluyendo características complejas como prefetchers, SMT y optimizaciones algorítmicas. Nuestro modelo puede ser usado no solo para predecir los tiempos de ejecución, sino también para tomar decisiones de los mejores parámetros algorítmicos. Además, puede ser incluido en optimizadores run-time para decidir la mejor configuración SMT. Algunas industrias confían en técnicas DF para sus códigos. Sin embargo, no todos los aspectos que aparecen en la industria han sido sometidos a investigación. En este aspecto, hemos diseñado e implementado desde cero una infraestructura DF que cubre las características más importantes que una aplicación industrial debe incluir. Algunas de las técnicas de optimización propuestas en esta tesis han sido incluidas para contribuir en el rendimiento global a nivel industrial. Mostramos resultados de un par de aplicaciones estratégicas para la industria: un modelo de transporte atmosférico que simula la dispersión de ceniza volcánica y un modelo de imagen sísmica usado en la industria del petroleo y gas para identificar reservas ricas en hidrocarburo

Automated cache optimisations of stencil computations for partial differential equations

This thesis focuses on numerical methods that solve partial differential equations. Our focal point is the finite difference method, which solves partial differential equations by approximating derivatives with explicit finite differences. These partial differential equation solvers consist of stencil computations on structured grids. Stencils for computing real-world practical applications are patterns often characterised by many memory accesses and non-trivial arithmetic expressions that lead to high computational costs compared to simple stencils used in much prior proof-of-concept work. In addition, the loop nests to express stencils on structured grids may often be complicated. This work is highly motivated by a specific domain of stencil computations where one of the challenges is non-aligned to the structured grid ("off-the-grid") operations. These operations update neighbouring grid points through scatter and gather operations via non-affine memory accesses, such as {A[B[i]]}. In addition to this challenge, these practical stencils often include many computation fields (need to store multiple grid copies), complex data dependencies and imperfect loop nests. In this work, we aim to increase the performance of stencil kernel execution. We study automated cache-memory-dependent optimisations for stencil computations. This work consists of two core parts with their respective contributions.The first part of our work tries to reduce the data movement in stencil computations of practical interest. Data movement is a dominant factor affecting the performance of high-performance computing applications. It has long been a target of optimisations due to its impact on execution time and energy consumption. This thesis tries to relieve this cost by applying temporal blocking optimisations, also known as time-tiling, to stencil computations. Temporal blocking is a well-known technique to enhance data reuse in stencil computations. However, it is rarely used in practical applications but rather in theoretical examples to prove its efficacy. Applying temporal blocking to scientific simulations is more complex. More specifically, in this work, we focus on the application context of seismic and medical imaging. In this area, we often encounter scatter and gather operations due to signal sources and receivers at arbitrary locations in the computational domain. These operations make the application of temporal blocking challenging. We present an approach to overcome this challenge and successfully apply temporal blocking.In the second part of our work, we extend the first part as an automated approach targeting a wide range of simulations modelled with partial differential equations. Since temporal blocking is error-prone, tedious to apply by hand and highly complex to assimilate theoretically and practically, we are motivated to automate its application and automatically generate code that benefits from it. We discuss algorithmic approaches and present a generalised compiler pipeline to automate the application of temporal blocking. These passes are written in the Devito compiler. They are used to accelerate the computation of stencil kernels in areas such as seismic and medical imaging, computational fluid dynamics and machine learning. \href{www.devitoproject.org}{Devito} is a Python package to implement optimised stencil computation (e.g., finite differences, image processing, machine learning) from high-level symbolic problem definitions. Devito builds on \href{www.sympy.org}{SymPy} and employs automated code generation and just-in-time compilation to execute optimised computational kernels on several computer platforms, including CPUs, GPUs, and clusters thereof. We show how we automate temporal blocking code generation without user intervention and often achieve better time-to-solution. We enable domain-specific optimisation through compiler passes and offer temporal blocking gains from a high-level symbolic abstraction. These automated optimisations benefit various computational kernels for solving real-world application problems.Open Acces

Communication-avoiding optimizations for large-scale unstructured-mesh applications with OP2

This thesis presents data movement-reducing and communication-avoiding optimizations and their practicable implementation for large-scale unstructured-mesh numerical simulation applications. Utilizing the high-level abstractions of the OP2 domain-specific library, we reason about techniques for reduced communications across a consecutive sequence of loops – a loop-chain. The optimizations are explored for shared-memory systems where multiple processors share a common memory space and distributed-memory systems that comprise separate memory spaces across multiple nodes. We elucidate the challenges when executing unstructured-mesh applications on large-scale high-performance systems that are specifically related to data sharing and movement, synchronization, and communication among processes. A key feature of the work is to mitigate these problems for real-world, large-scale applications and computing kernels, bringing together proven and effective techniques within a DSL framework. On shared-memory systems, We explore cache-blocking tiling, a key technique for exploiting data locality, in unstructured-mesh applications by integrating the SLOPE library, a cache-blocking tiling library, with OP2. For distributed-memory systems, we analyze the trade-off between increased redundant computation in place of data movement and design a new communication-avoiding back-end for OP2 that applies these techniques automatically to any OP2 application targeting CPUs and GPUs. The communication-avoiding optimizations are applied to two non-trivial applications, including the OP2 version of Rolls Royce’s production CFD application, Hydra, on problem sizes representative of real-world workloads. Results demonstrate how, for select configurations, the new communication-avoiding back-end provides between 30 – 65% runtime reductions for the loop-chains in these applications on both an HPE Cray EX system and an NVIDIA V100 GPU cluster. We model and examine the determinants and characteristics of a given unstructured-mesh loop-chain that lead to performance benefits with communication-avoidance techniques, providing insights into the general feasibility and profitability of using the optimizations for this class of applications