arXiv subjects

Harald Köstler

Publications and source records attributed to Harald Köstler.

At least 37 records · Page 2Linked to original sources

arXiv2024

Towards Code Generation for Octree-Based Multigrid Solvers

This paper presents a novel method designed to generate multigrid solvers optimized for octree-based software frameworks. Our approach focuses on accurately capturing local features within a domain while leveraging the efficiency inherent in multigrid techniques. We outline the essential steps involved in generating specialized kernels for local refinement and communication routines, integrating on-the-fly interpolations to seamlessly transfer information between refinement levels. For this purpose, we established a software coupling via an automatic fusion of generated multigrid solvers and communication kernels with manual implementations of complex octree data structures and algorithms often found in established software frameworks. We demonstrate the effectiveness of our method through numerical experiments with different interpolation orders. Large-scale benchmarks conducted on the SuperMUC-NG CPU cluster underscore the advantages of our approach, offering a comparison against a reference implementation to highlight the benefits of our method and code generation in general.

cs.CE↗

arXiv2024

Code Generation and Performance Engineering for Matrix-Free Finite Element Methods on Hybrid Tetrahedral Grids

This paper introduces a code generator designed for node-level optimized, extreme-scalable, matrix-free finite element operators on hybrid tetrahedral grids. It optimizes the local evaluation of bilinear forms through various techniques including tabulation, relocation of loop invariants, and inter-element vectorization - implemented as transformations of an abstract syntax tree. A key contribution is the development, analysis, and generation of efficient loop patterns that leverage the local structure of the underlying tetrahedral grid. These significantly enhance cache locality and arithmetic intensity, mitigating bandwidth-pressure associated with compute-sparse, low-order operators. The paper demonstrates the generator's capabilities through a comprehensive educational cycle of performance analysis, bottleneck identification, and emission of dedicated optimizations. For three differential operators ($-Δ$, $-\nabla \cdot (k(\mathbf{x})\, \nabla\,)$, $α(\mathbf{x})\, \mathbf{curl}\ \mathbf{curl} + β(\mathbf{x}) $), we determine the set of most effective optimizations. Applied by the generator, they result in speed-ups of up to 58$\times$ compared to reference implementations. Detailed node-level performance analysis yields matrix-free operators with a throughput of 1.3 to 2.1 GDoF/s, achieving up to 62% peak performance on a 36-core Intel Ice Lake socket. Finally, the solution of the curl-curl problem with more than a trillion ($ 10^{12}$) degrees of freedom on 21504 processes in less than 50 seconds demonstrates the generated operators' performance and extreme-scalability as part of a full multigrid solver.

cs.CE↗

arXiv2024

A Continuous Benchmarking Infrastructure for High-Performance Computing Applications

For scientific software, especially those used for large-scale simulations, achieving good performance and efficiently using the available hardware resources is essential. It is important to regularly perform benchmarks to ensure the efficient use of hardware and software when systems are changing and the software evolves. However, this can become quickly very tedious when many options for parameters, solvers, and hardware architectures are available. We present a continuous benchmarking strategy that automates benchmarking new code changes on high-performance computing clusters. This makes it possible to track how each code change affects the performance and how it evolves.

cs.PF↗

arXiv2023

waLBerla-wind: a lattice-Boltzmann-based high-performance flow solver for wind energy applications

This article presents the development of a new wind turbine simulation software to study wake flow physics. To this end, the design and development of waLBerla-wind, a new simulator based on the lattice-Boltzmann method that is known for its excellent performance and scaling properties, will be presented. Here it will be used for large eddy simulations (LES) coupled with actuator wind turbine models. Due to its modular software design, waLBerla-wind is flexible and extensible with regard to turbine configurations. Additionally it is performance portable across different hardware architectures, another critical design goal. The new solver is validated by presenting force distributions and velocity profiles and comparing them with experimental data and a vortex solver. Furthermore, waLBerla-wind's performance is \revision{compared to a theoretical peak performance}, and analysed with weak and strong scaling benchmarks on CPU and GPU systems. This analysis demonstrates the suitability for large-scale applications and future cost-effective full wind farm simulations.

cs.CE↗

arXiv2023

p-adaptive discontinuous Galerkin method for the shallow water equations on heterogeneous computing architectures

Heterogeneous computing and exploiting integrated CPU-GPU architectures has become a clear current trend since the flattening of Moore's Law. In this work, we propose a numerical and algorithmic re-design of a p-adaptive quadrature-free discontinuous Galerkin method (DG) for the shallow water equations (SWE). Our new approach separates the computations of the non-adaptive (lower-order) and adaptive (higher-order) parts of the discretization form each other. Thereby, we can overlap computations of the lower-order and the higher-order DG solution components. Furthermore, we investigate execution times of main computational kernels and use automatic code generation to optimize their distribution between the CPU and GPU. Several setups, including a prototype of a tsunami simulation in a tide-driven flow scenario, are investigated, and the results show that significant performance improvements can be achieved in suitable setups.

cs.MS↗

arXiv2023

AI Driven Near Real-time Locational Marginal Pricing Method: A Feasibility and Robustness Study

Accurate price predictions are essential for market participants in order to optimize their operational schedules and bidding strategies, especially in the current context where electricity prices become more volatile and less predictable using classical approaches. The Locational Marginal Pricing (LMP) pricing mechanism is used in many modern power markets, where the traditional approach utilizes optimal power flow (OPF) solvers. However, for large electricity grids this process becomes prohibitively time-consuming and computationally intensive. Machine learning (ML) based predictions could provide an efficient tool for LMP prediction, especially in energy markets with intermittent sources like renewable energy. This study evaluates the performance of popular machine learning and deep learning models in predicting LMP on multiple electricity grids. The accuracy and robustness of these models in predicting LMP is assessed considering multiple scenarios. The results show that ML models can predict LMP 4-5 orders of magnitude faster than traditional OPF solvers with 5-6\% error rate, highlighting the potential of ML models in LMP prediction for large-scale power models with the assistance of hardware infrastructure like multi-core CPUs and GPUs in modern HPC clusters.

cs.CE↗

arXiv2023

Particle-resolved simulation of antidunes in free-surface flows

The interaction of supercritical turbulent flows with granular sediment beds is challenging to study both experimentally and numerically; this challenging task has hampered the advances in understanding antidunes, the most characteristic bedform of supercritical flows. This article presents the first numerical attempt to simulate upstream-migrating antidunes with geometrically resolved particles and a liquid-gas interface. Our simulations provide data at a resolution higher than laboratory experiments, and they can therefore provide new insights into the mechanisms of antidune migration and contribute to a deeper understanding of the underlying physics. To manage the simulations' computational costs and physical complexity, we employ the cumulant lattice Boltzmann method in conjunction with a discrete element method for particle interactions, as well as a volume of fluid scheme to track the deformable free surface of the fluid. By reproducing two flow configurations of previous experiments (Pascal et al., Earth Surf. Proc. Land., vol. 46(9), 2021, 1750-1765), we demonstrate that our approach is robust and accurately predicts the antidunes' amplitude, wavelength, and celerity. Furthermore, the simulated wall-shear stress, a key parameter governing sediment transport, is in excellent agreement with the experimental measurements. The highly resolved data of fluid and particle motion from our simulation approach open new perspectives for detailed studies of morphodynamics in shallow supercritical flows.

physics.flu-dyn↗

arXiv2023

MD-Bench: Engineering the in-core performance of short-range molecular dynamics kernels from state-of-the-art simulation packages

Molecular dynamics (MD) simulations provide considerable benefits for the investigation and experimentation of systems at atomic level. Their usage is widespread into several research fields, but their system size and timescale are also crucially limited by the computing power they can make use of. Performance engineering of MD kernels is therefore important to understand their bottlenecks and point out possible improvements. For that reason, we developed MD-Bench, a proxy-app for short-range MD kernels that implements state-of-the-art algorithms from multiple production applications such as LAMMPS and GROMACS. MD-Bench is intended to have simpler, understandable and extensible source code, as well as to be transparent and suitable for teaching, benchmarking and researching MD algorithms. In this paper we introduce MD-Bench, describe its design and structure and implemented algorithms. Finally, we show five usage examples of MD-Bench and describe how these are useful to have a deeper understanding of MD kernels from a performance point of view, also exposing some interesting performance insights.

physics.chem-ph↗

arXiv2022

MD-Bench: A generic proxy-app toolbox for state-of-the-art molecular dynamics algorithms

Proxy-apps, or mini-apps, are simple self-contained benchmark codes with performance-relevant kernels extracted from real applications. Initially used to facilitate software-hardware co-design, they are a crucial ingredient for serious performance engineering, especially when dealing with large-scale production codes. MD-Bench is a new proxy-app in the area of classical short-range molecular dynamics. In contrast to existing proxy-apps in MD (e.g. miniMD and coMD) it does not resemble a single application code, but implements state-of-the art algorithms from multiple applications (currently LAMMPS and GROMACS). The MD-Bench source code is understandable, extensible and suited for teaching, benchmarking and researching MD algorithms. Primary design goals are transparency and simplicity, a developer is able to tinker with the source code down to the assembly level. This paper introduces MD-Bench, explains its design and structure, covers implemented optimization variants, and illustrates its usage on three examples.

physics.comp-ph↗

arXiv2022

Evolving Generalizable Multigrid-Based Helmholtz Preconditioners with Grammar-Guided Genetic Programming

Solving the indefinite Helmholtz equation is not only crucial for the understanding of many physical phenomena but also represents an outstandingly-difficult benchmark problem for the successful application of numerical methods. Here we introduce a new approach for evolving efficient preconditioned iterative solvers for Helmholtz problems with multi-objective grammar-guided genetic programming. Our approach is based on a novel context-free grammar, which enables the construction of multigrid preconditioners that employ a tailored sequence of operations on each discretization level. To find solvers that generalize well over the given domain, we propose a custom method of successive problem difficulty adaption, in which we evaluate a preconditioner's efficiency on increasingly ill-conditioned problem instances. We demonstrate our approach's effectiveness by evolving multigrid-based preconditioners for a two-dimensional indefinite Helmholtz problem that outperform several human-designed methods for different wavenumbers up to systems of linear equations with more than a million unknowns.

math.NA↗

arXiv2021

Deep Learning for Real-Time Aerodynamic Evaluations of Arbitrary Vehicle Shapes

The aerodynamic optimization process of cars requires multiple iterations between aerodynamicists and stylists. Response Surface Modeling and Reduced-Order Modeling are commonly used to eliminate the overhead due to Computational Fluid Dynamics, leading to faster iterations. However, a primary drawback of these models is that they can work only on the parametrized geometric features they were trained with. This study evaluates if deep learning models can predict the drag coefficient for an arbitrary input geometry without explicit parameterization. We use two similar data sets based on the publicly available DrivAer geometry for training. We use a modified U-Net architecture that uses Signed Distance Fields to represent the input geometries. Our models outperform the existing models by at least 11% in prediction accuracy for the drag coefficient. We achieved this improvement by combining multiple data sets that were created using different parameterizations, which is not possible with the methods currently used. We have also shown that it is possible to predict velocity fields and drag coefficient concurrently and that simple data augmentation methods can improve the results. In addition, we have performed an occlusion sensitivity study on our models to understand what information is used to make predictions. From the occlusion sensitivity study, we showed that the models were able to identify the geometric features and have discovered that the model has learned to exploit the global information present in the SDF. In contrast to the currently operational method, where design changes are restricted to the initially defined parameters, this study brings surrogate models one step closer to the long-term goal of having a model that can be used for approximate aerodynamic evaluation of unseen, arbitrary vehicle shapes, thereby providing complete design freedom to the vehicle stylists.

cs.CE↗

arXiv2021

Known Operator Learning and Hybrid Machine Learning in Medical Imaging -- A Review of the Past, the Present, and the Future

In this article, we perform a review of the state-of-the-art of hybrid machine learning in medical imaging. We start with a short summary of the general developments of the past in machine learning and how general and specialized approaches have been in competition in the past decades. A particular focus will be the theoretical and experimental evidence pro and contra hybrid modelling. Next, we inspect several new developments regarding hybrid machine learning with a particular focus on so-called known operator learning and how hybrid approaches gain more and more momentum across essentially all applications in medical imaging and medical image analysis. As we will point out by numerous examples, hybrid models are taking over in image reconstruction and analysis. Even domains such as physical simulation and scanner and acquisition design are being addressed using machine learning grey box modelling approaches. Towards the end of the article, we will investigate a few future directions and point out relevant areas in which hybrid modelling, meta learning, and other domains will likely be able to drive the state-of-the-art ahead.

cs.LG↗

arXiv2020

tinyMD: A Portable and Scalable Implementation for Pairwise Interactions Simulations

This paper investigates the suitability of the AnyDSL partial evaluation framework to implement tinyMD: an efficient, scalable, and portable simulation of pairwise interactions among particles. We compare tinyMD with the miniMD proxy application that scales very well on parallel supercomputers. We discuss the differences between both implementations and contrast miniMD's performance for single-node CPU and GPU targets, as well as its scalability on SuperMUC-NG and Piz Daint supercomputers. Additionaly, we demonstrate tinyMD's flexibility by coupling it with the waLBerla multi-physics framework. This allow us to execute tinyMD simulations using the load-balancing mechanism implemented in waLBerla.

cs.PF↗

arXiv2020

lbmpy: Automatic code generation for efficient parallel lattice Boltzmann methods

Lattice Boltzmann methods are a popular mesoscopic alternative to macroscopic computational fluid dynamics solvers. Many variants have been developed that vary in complexity, accuracy, and computational cost. Extensions are available to simulate multi-phase, multi-component, turbulent, or non-Newtonian flows. In this work we present lbmpy, a code generation package that supports a wide variety of different methods and provides a generic development environment for new schemes as well. A high-level domain-specific language allows the user to formulate, extend and test various lattice Boltzmann schemes. The method specification is represented in a symbolic intermediate representation. Transformations that operate on this intermediate representation optimize and parallelize the method, yielding highly efficient lattice Boltzmann compute kernels not only for single- and two-relaxation-time schemes but also for multi-relaxation-time, cumulant, and entropically stabilized methods. An integration into the HPC framework waLBerla makes massively parallel, distributed simulations possible, which is demonstrated through scaling experiments on the SuperMUC-NG supercomputing system

cs.MS↗

arXiv2019

Optimizing Geometric Multigrid Methods with Evolutionary Computation

For many linear and nonlinear systems that arise from the discretization of partial differential equations the construction of an efficient multigrid solver is a challenging task. Here we present a novel approach for the optimization of geometric multigrid methods that is based on evolutionary computation, a generic program optimization technique inspired by the principle of natural evolution. A multigrid solver is represented as a tree of mathematical expressions which we generate based on a tailored grammar. The quality of each solver is evaluated in terms of convergence and compute performance using automated local Fourier analysis (LFA) and roofline performance modeling, respectively. Based on these objectives a multi-objective optimization is performed using strongly typed genetic programming with a non-dominated sorting based selection. To evaluate the model-based prediction and to target concrete applications, scalable implementations of an evolved solver can be automatically generated with the ExaStencils framework. We demonstrate our approach by constructing multigrid solvers for the steady-state heat equation with constant and variable coefficients that consistently perform better than common V- and W-cycles.

math.NA↗

arXiv2019

waLBerla: A block-structured high-performance framework for multiphysics simulations

Programming current supercomputers efficiently is a challenging task. Multiple levels of parallelism on the core, on the compute node, and between nodes need to be exploited to make full use of the system. Heterogeneous hardware architectures with accelerators further complicate the development process. waLBerla addresses these challenges by providing the user with highly efficient building blocks for developing simulations on block-structured grids. The block-structured domain partitioning is flexible enough to handle complex geometries, while the structured grid within each block allows for highly efficient implementations of stencil-based algorithms. We present several example applications realized with waLBerla, ranging from lattice Boltzmann methods to rigid particle simulations. Most importantly, these methods can be coupled together, enabling multiphysics simulations. The framework uses meta-programming techniques to generate highly efficient code for CPUs and GPUs from a symbolic method formulation. To ensure software quality and performance portability, a continuous integration toolchain automatically runs an extensive test suite encompassing multiple compilers, hardware architectures, and software configurations.

cs.DC↗

arXiv2019

Towards whole program generation of quadrature-free discontinuous Galerkin methods for the shallow water equations

The shallow water equations (SWE) are a commonly used model to study tsunamis, tides, and coastal ocean circulation. However, there exist various approaches to discretize and solve them efficiently. Which of them is best for a certain scenario is often not known and, in addition, depends heavily on the used HPC platform. From a simulation software perspective, this places a premium on the ability to adapt easily to different numerical methods and hardware architectures. One solution to this problem is to apply code generation techniques and to express methods and specific hardware-dependent implementations on different levels of abstraction. This allows for a separation of concerns and makes it possible, e.g., to exchange the discretization scheme without having to rewrite all low-level optimized routines manually. In this paper, we show how code for an advanced quadrature-free discontinuous Galerkin (DG) discretized shallow water equation solver can be generated. Here, we follow the multi-layered approach from the ExaStencils project that starts from the continuous problem formulation, moves to the discrete scheme, spells out the numerical algorithms, and, finally, maps to a representation that can be transformed to a distributed memory parallel implementation by our in-house Scala-based source-to-source compiler. Our contributions include: A new quadrature-free discontinuous Galerkin formulation, an extension of the class of supported computational grids, and an extension of our toolchain allowing to evaluate discrete integrals stemming from the DG discretization implemented in Python. As first results we present the whole toolchain and also demonstrate the convergence of our method for higher order DG discretizations.

cs.MS↗

arXiv2018

A Scalable and Extensible Checkpointing Scheme for Massively Parallel Simulations

Realistic simulations in engineering or in the materials sciences can consume enormous computing resources and thus require the use of massively parallel supercomputers. The probability of a failure increases both with the runtime and with the number of system components. For future exascale systems it is therefore considered critical that strategies are developed to make software resilient against failures. In this article, we present a scalable, distributed, diskless, and resilient checkpointing scheme that can create and recover snapshots of a partitioned simulation domain. We demonstrate the efficiency and scalability of the checkpoint strategy for simulations with up to $40$ billion computational cells executing on more than $400$ billion floating point values. A checkpoint creation is shown to require only a few seconds and the new checkpointing scheme scales almost perfectly up to more than $260\,000$ ($2^{18}$) processes. To recover from a diskless checkpoint during runtime, we realize the recovery algorithms using ULFM MPI. The checkpointing mechanism is fully integrated in a state-of-the-art high-performance multi-physics simulation framework. We demonstrate the efficiency and robustness of the method with a realistic phase-field simulation originating in the material sciences and with a lattice Boltzmann method implementation.

cs.DC↗