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At least 127 records · Page 7

Algorithm for solving the linear Cauchy problem for large systems of ordinary differential equations with the use of parallel computations

An algorithm for solving the linear Cauchy problem for large systems of ordinary differential equations is presented. The algorithm for systems of first-order differential equations is implemented in the EDELWEISS code with the possibility of parallel computations on supercomputers employing the MPI (Message Passing Interface) standard for the data exchange between parallel processes. The solution is represented by a series of orthogonal polynomials on the interval [0, 1]. The algorithm is characterized by simplicity and the possibility to solve nonlinear problems with a correction of the operator in accordance with the solution obtained in the previous iterative process.

74 ATOMIC AND MOLECULAR PHYSICS↗

Conservative Multimoment Transport along Characteristics for Discontinuous Galerkin Methods

A set of algorithms based on characteristic discontinuous Galerkin methods is presented for tracer transport on the sphere. The algorithms are designed to reduce message passing interface communication volume per unit of simulated time relative to current methods generally, and to the spectral element scheme employed by the U.S. Department of Energy's Exascale Earth System Model (E3SM) specifically. Two methods are developed to enforce discrete mass conservation when the transport schemes are coupled to a separate dynamics solver; constrained transport and Jacobian-combined transport. A communication-efficient method is introduced to enforce tracer consistency between the transport scheme and dynamics solver; this method also provides the transport scheme's shape preservation capability. A subset of the algorithms derived here is implemented in E3SM and shown to improve transport performance by a factor of 2.2 for the model's standard configuration with 40 tracers at the strong scaling limit of one element per core. Read More: https://epubs.siam.org/doi/10.1137/18M1165943

97 MATHEMATICS AND COMPUTING↗

Scalable Asynchronous Domain Decomposition Solvers

We discuss how parallel implementations of linear iterative solvers generally alternate between phases of data exchange and phases of local computation. Increasingly large problem sizes and more heterogeneous compute architectures make load balancing and the design of low latency network interconnects that are able to satisfy the communication requirements of linear solvers very challenging tasks. In particular, global communication patterns such as inner products become increasingly limiting at scale. We explore the use of asynchronous communication based on one-sided Message Passing Interface primitives in the context of domain decomposition solvers. In particular, a scalable asynchronous two-level Schwarz method is presented. We discuss practical issues encountered in the development of a scalable solver and show experimental results obtained on a state-of-the-art supercomputer system that illustrate the benefits of asynchronous solvers in load balanced as well as load imbalanced scenarios. Using the novel method, we can observe speedups of up to four times over its classical synchronous equivalent.

97 MATHEMATICS AND COMPUTING↗

Space-Time Block Preconditioning for Incompressible Flow

Parallel-in-time methods have become increasingly popular in the simulation of time-dependent numerical PDEs, allowing for the efficient use of additional message passing interface processes when spatial parallelism saturates. Most methods treat the solution and parallelism in space and time separately. In contrast, all-at-once methods solve the full space-time system directly, largely treating time as simply another spatial dimension. All-at-once methods offer a number of benefits over separate treatment of space and time, most notably significantly increased parallelism and faster time to solution (when applicable). However, the development of fast, scalable all-at-once methods has largely been limited to time-dependent (advection-)diffusion problems. This paper introduces the concept of space-time block preconditioning for the all-at-once solution of incompressible flow. By extending well-known concepts of spatial block preconditioning to the space-time setting, we develop a block preconditioner whose application requires the solution of a space-time (advection-)diffusion equation in the velocity block, coupled with a pressure Schur complement approximation consisting of independent spatial solves at each time-step, and a space-time matrix-vector multiplication. The new method is tested on four classical models in incompressible flow. Finally, the results indicate perfect scalability in refinement of spatial and temporal mesh spacing, perfect scalability in nonlinear Picard iteration count when applied to a nonlinear Navier--Stokes problem, and minimal overhead in terms of number of preconditioner applications compared with sequential time-stepping.

97 MATHEMATICS AND COMPUTING↗

FROSch Preconditioners for Land Ice Simulations of Greenland and Antarctica

Numerical simulations of Greenland and Antarctic ice sheets involve the solution of large-scale highly nonlinear systems of equations on complex shallow geometries. This work is concerned with the construction of Schwarz preconditioners for the solution of the associated tangent problems, which are challenging for solvers mainly because of the strong anisotropy of the meshes and wildly changing boundary conditions that can lead to poorly constrained problems on large portions of the domain. In this study, two-level generalized Dryja--Smith--Widlund (GDSW)--type Schwarz preconditioners are applied to different land ice problems, i.e., a velocity problem, a temperature problem, as well as the coupling of the former two problems. We employ the message passing interface (MPI)--parallel implementation of multilevel Schwarz preconditioners provided by the package FROSch (fast and robust Schwarz) from the Trilinos library. The strength of the proposed preconditioner is that it yields out-of-the-box scalable and robust preconditioners for the single physics problems. To the best of our knowledge, this is the first time two-level Schwarz preconditioners have been applied to the ice sheet problem and a scalable preconditioner has been used for the coupled problem. The preconditioner for the coupled problem differs from previous monolithic GDSW preconditioners in the sense that decoupled extension operators are used to compute the values in the interior of the subdomains. Additionally, several approaches for improving the performance, such as reuse strategies and shared memory OpenMP parallelization, are explored. In our numerical study we target both uniform meshes of varying resolution for the Antarctic ice sheet as well as nonuniform meshes for the Greenland ice sheet. We present several weak and strong scaling studies confirming the robustness of the approach and the parallel scalability of the FROSch implementation. Among the highlights of the numerical results are a weak scaling study for up to 32,K processor cores (8,K MPI ranks and 4 OpenMP threads) and 566,M degrees of freedom for the velocity problem as well as a strong scaling study for up to 4,K processor cores (and MPI ranks) and 68,M degrees of freedom for the coupled problem.

97 MATHEMATICS AND COMPUTING↗

End-to-end data movement using MPI-IO over routed terabits infrastructures. In: NDM '13 Proceedings of the Third International Workshop on Network-Aware Data Management, Article No. 9

Scientific discovery is nowadays driven by large-scale simulations running on massively parallel high-performance computing (HPC) systems. These applications each generate a large amount of data, which then needs to be post-processed for example for data mining or visualization. Unfortunately, the computing platform used for post processing might be different from the one on which the data is initially generated, introducing the challenge of moving large amount of data between computing platforms. This is especially challenging when these two platforms are geographically separated since the data needs to be moved between computing facilities. This is even more critical when scientists tightly couple their domain specific applications with a post processing application. The paper presents a solution for the data transfer between MPI applications using a dedicated wide area network (WAN) terabit infrastructure. The proposed solution is based on parallel access to data files and the Message Passing Interface (MPI) over the Common Communication Infrastructure (CCI) for the data transfer over a routed infrastructure. In the context of this research, the Energy Sciences Network (ESnet) of the U.S. Department of Energy (DOE) is targeted for the transfer of data between DOE national laboratories.

Vallée, Geoffroy↗

A Case for Application Oblivious Energy-Efficient MPI Runtime

Power has become the major impediment in designing large scale high-end systems. Message Passing Interface (MPI) is the {\em de facto} communication interface used as the back-end for designing applications, programming models and runtime for these systems. Slack --- the time spent by an MPI process in a single MPI call --- provides a potential for energy and power savings, if an appropriate power reduction technique such as core-idling/Dynamic Voltage and Frequency Scaling (DVFS) can be applied without perturbing application's execution time. Existing techniques that exploit slack for power savings assume that application behavior repeats across iterations/executions. However, an increasing use of adaptive, data-dependent workloads combined with system factors (OS noise, congestion) makes this assumption invalid. This paper proposes and implements Energy Aware MPI (EAM) --- an application-oblivious energy-efficient MPI runtime. EAM uses a combination of communication models of common MPI primitives (point-to-point, collective, progress, blocking/non-blocking) and an online observation of slack for maximizing energy efficiency. Each power lever incurs time overhead, which must be amortized over slack to minimize degradation. When predicted communication time exceeds a lever overhead, the lever is used {\em as soon as possible} --- to maximize energy efficiency. When mis-prediction occurs, the lever(s) are used automatically at specific intervals for amortization. We implement EAM using MVAPICH2 and evaluate it on ten applications using up to 4096 processes. Our performance evaluation on an InfiniBand cluster indicates that EAM can reduce energy consumption by 5--41\% in comparison to the default approach, with negligible (less than 4\% in all cases) performance loss.

Venkatesh, Akshay↗

Communication Characterization and Optimization of Applications Using Topology-Aware Task Mapping on Large Supercomputers

On large supercomputers, the job scheduling systems may assign a non-contiguous node allocation for user applications depending on available resources. With parallel applications using MPI (Message Passing Interface), the default process ordering does not take into account the actual physical node layout available to the application. This contributes to non-locality in terms of physical network topology and impacts communication performance of the application. In order to mitigate such performance penalties, this work describes techniques to identify suitable task mapping that takes the layout of the allocated nodes as well as the application's communication behavior into account. During the first phase of this research, we instrumented and collected performance data to characterize communication behavior of critical US DOE (United States - Department of Energy) applications using an augmented version of the mpiP tool. Subsequently, we developed several reordering methods (spectral bisection, neighbor join tree etc.) to combine node layout and application communication data for optimized task placement. We developed a tool called mpiAproxy to facilitate detailed evaluation of the various reordering algorithms without requiring full application executions. This work presents a comprehensive performance evaluation (14,000 experiments) of the various task mapping techniques in lowering communication costs on Titan, the leadership class supercomputer at Oak Ridge National Laboratory.

97 MATHEMATICS AND COMPUTING↗

Adding Fault Tolerance to NPB Benchmarks Using ULFM

In the world of high-performance computing, fault tolerance and application resilience are becoming some of the primary concerns because of increasing hardware failures and memory corruptions. While the research community has been investigating various options, from system-level solutions to application-level solutions, standards such as the Message Passing Interface (MPI) are also starting to include such capabilities. The current proposal for MPI fault tolerant is centered around the User-Level Failure Mitigation (ULFM) concept, which provides means for fault detection and recovery of the MPI layer. This approach does not address application-level recovery, which is currently left to application developers. In this work, we present a modification of some of the benchmarks of the NAS parallel benchmark (NPB) to include support of the ULFM capabilities as well as application-level strategies and mechanisms for application-level failure recovery. As such, we present: (i) an application-level library to "checkpoint" and restore data, (ii) extensions of NPB benchmarks for fault tolerance based on different strategies, (iii) a fault injection tool, and (iv) some preliminary results that show the impact of such fault tolerant strategies on the application execution.

97 MATHEMATICS AND COMPUTING↗

Production Application Performance Data Streaming for System Monitoring

In this article, we present an approach to streaming collection of application performance data. Practical application performance tuning and troubleshooting in production high-performance computing (HPC) environments requires an understanding of how applications interact with the platform, including (but not limited to) parallel programming libraries such as Message Passing Interface (MPI). Several profiling and tracing tools exist that collect heavy runtime data traces either in memory (released only at application exit) or on a file system (imposing an I/O load that may interfere with the performance being measured). Although these approaches are beneficial in development stages and post-run analysis, a systemwide and low-overhead method is required to monitor deployed applications continuously. This method must be able to collect information at both the application and system levels to yield a complete performance picture. In our approach, an application profiler collects application event counters. A sampler uses an efficient inter-process communication method to periodically extract the application counters and stream them into an infrastructure for performance data collection. We implement a tool-set based on our approach and integrate it with the Lightweight Distributed Metric Service (LDMS) system, a monitoring system used on large-scale computational platforms. LDMS provides the infrastructure to create and gather streams of performance data in a low overhead manner. We demonstrate our approach using applications implemented with MPI, as it is one of the most common standards for the development of large-scale scientific applications. We utilize our tool-set to study the impact of our approach on an open source HPC application, Nalu. Our tool-set enables us to efficiently identify patterns in the behavior of the application without source-level knowledge. We leverage LDMS to collect system-level performance data and explore the correlation between the system and application events. Finally, we demonstrate how our tool-set can help detect anomalies with a low latency. We run tests on two different architectures: a system enabled with Intel Xeon Phi and another system equipped with Intel Xeon processor. Our overhead study shows our method imposes at most 0.5% CPU usage overhead on the application in realistic deployment scenarios.

59 BASIC BIOLOGICAL SCIENCES↗

A Sparse Distributed Gigascale Resolution Material Point Method

In this paper, we present a four-layer distributed simulation system and its adaptation to the Material Point Method (MPM). The system is built upon a performance portable C++ programming model targeting major High-Performance-Computing (HPC) platforms. A key ingredient of our system is a hierarchical block-tile-cell sparse grid data structure that is distributable to an arbitrary number of Message Passing Interface (MPI) ranks. We additionally propose strategies for efficient dynamic load balance optimization to maximize the efficiency of MPI tasks. Our simulation pipeline can easily switch among backend programming models, including OpenMP and CUDA, and can be effortlessly dispatched onto supercomputers and the cloud. Finally, we construct benchmark experiments and ablation studies on supercomputers and consumer workstations in a local network to evaluate the scalability and load balancing criteria. We demonstrate massively parallel, highly scalable, and gigascale resolution MPM simulations of up to 1.01 billion particles for less than 323.25 seconds per frame with 8 OpenSSH-connected workstations.

97 MATHEMATICS AND COMPUTING↗

Optimizing Communication in 2D Grid-Based MPI Applications at Exascale

The new reality of exascale computing faces many challenges in achieving optimal performance on large numbers of nodes. A key challenge is the efficient utilization of the message-passing interface (MPI), a critical component for process communication. This paper explores communication optimization strategies to harness the GPU-accelerated architectures of these supercomputers. We focus on MPI applications where processors form a two-dimensional process grid, a common arrangement in applications involving dense matrix operations. This configuration offers a unique opportunity to implement innovative strategies to improve performance and maintain effective load distribution. We study two applications— Dist-FW (Apsp:all-pair-shortest-path) and HPL-MxP (LU factorization with Mixed precision)—on two accelerated systems: Summit (IBM Power and NVIDIA V100) and Frontier (AMD EPYC and MI250X). These supercomputers are operated by the Oak Ridge Leadership Computing Facility (OLCF) and are currently ranked #1 and #5 on the Top500 list. We show how to scale up both applications to exascale levels and tackle the MPI challenges related to implementation, synchronization, and performance. We also compare the performance of several communication strategies at an unprecedented scale. Accurately predicting application performance becomes crucial for cost reduction as the computational scale grows. To address this, we suggest a hyperbolic model as a better alternative to the traditional one-sided asymptotic model for predicting future application performance at such large scales.

Lu, Hao↗

ChatMPI: LLM-Driven MPI Code Generation for HPC Workloads

The Message Passing Interface (MPI) standard plays a crucial role in enabling scientific applications for parallel computing and is an essential component in high-performance computing (HPC). However, implementing MPI code manually—especially applying a proper domain decomposition and communication pattern—is a challenging and error-prone task. We present ChatMPI, an AI assistant for MPI parallelization of sequential C codes. In our analysis, we focus on testing six essential HPC workloads, which are based on Basic Linear Algebra Subprograms levels 1, 2, and 3 as well as sparse, stencil, and iterative operations. We analyze the process of creating ChatMPI by using the ChatHPC library. This lightweight large language model (LLM)–based infrastructure enables HPC experts to efficiently create and supervise trustworthy AI capabilities for critical HPC software tasks. We study the data required for training (fine-tuning) ChatMPI to generate parallel codes that not only use MPI syntax correctly but also apply HPC techniques to reduce memory communication and maximize performance by using proper work decomposition. With a relatively small training dataset composed of a few dozen prompts and fewer than 15 minutes of fine-tuning on one node equipped with two NVIDIA H100 GPUs, ChatMPI elevates trustworthiness for MPI code generation of current LLMs (e.g., Code Llama, ChatGPT-4o and ChatGPT 5). Additionally, we evaluate the performance of the MPI codes generated by ChatMPI in comparison with the ones generated by ChatGPT-4o and ChatGPT-5. The codes generated by ChatMPI provide up to a 4 × boost in performance by using better problem decomposition, communication patterns, and HPC techniques (e.g., communication avoiding).

Valero Lara, Pedro [ORNL] (ORCID:0000000214794310)↗

Determination of performance characteristics of scientific applications on IBM Blue Gene/Q

The IBM Blue Gene®/Q platform presents scientists and engineers with a rich set of hardware features such as 16 cores per chip sharing a Level 2 cache, a wide SIMD (single-instruction, multiple-data) unit, a five-dimensional torus network, and hardware support for collective operations. Especially important is the feature related to cores that have four “hardware threads,” which makes it possible to hide latencies and obtain a high fraction of the peak issue rate from each core. All of these hardware resources present unique performance-tuning opportunities on Blue Gene/Q. We provide an overview of several important applications and solvers and study them on Blue Gene/Q using performance counters and Message Passing Interface profiles. We also discuss how Blue Gene/Q tools help us understand the interaction of the application with the hardware and software layers and provide guidance for optimization. Furthermore, on the basis of our analysis, we discuss code improvement strategies targeting Blue Gene/Q. Information about how these algorithms map to the Blue Gene® architecture is expected to have an impact on future system design as we move to the exascale era.

97 MATHEMATICS AND COMPUTING↗

Porting a 3D seismic modeling code (SW4) to CORAL machines

Seismic waves fourth order (SW4) solves the seismic wave equations on Cartesian and curvilinear grids using large compute clusters with O (100,000) cores. In this article we discuss the porting of SW4 to run on the CORAL architecture using the RAJA performance portability abstraction layer. The performances of key kernels using RAJA and CUDA are compared to estimate the performance penalty of using the portability abstraction layer. Code changes required for efficiency on GPUs and minimizing time spent in Message Passing Interface (MPI) are discussed. This article describes a path for efficiently porting large code bases to GPU-based machines while avoiding the pitfalls of a new architecture in the early stages of its deployment. Current bottlenecks in the code are discussed along with possible architectural or software mitigations. SW4 runs 28× faster on one 4-GPU CORAL node than on a CTS-1 node (Dual Intel Xeon E5-2695 v4). SW4 is now in routine use on problems of unprecedented resolution (203 billion grid points) and scale on 1,200 nodes of Summit.

97 MATHEMATICS AND COMPUTING↗

MPI Runtime Error Detection with MUST: Advances in Deadlock Detection

The widely used Message Passing Interface (MPI) is complex and rich. As a result, application developers require automated tools to avoid and to detect MPI programming errors. We present the Marmot Umpire Scalable Tool (MUST) that detects such errors with significantly increased scalability. We present improvements to our graph-based deadlock detection approach for MPI, which cover future MPI extensions. Our enhancements also check complex MPI constructs that no previous graph-based detection approach handled correctly. Finally, we present optimizations for the processing of MPI operations that reduce runtime deadlock detection overheads. Existing approaches often require 𝒪( p ) analysis time per MPI operation, for p processes. We empirically observe that our improvements lead to sub-linear or better analysis time per operation for a wide range of real world applications.

Hilbrich, Tobias↗

High-Performance Design Patterns for Modern Fortran

This paper presents ideas for using coordinate-free numerics in modern Fortran to achieve code flexibility in the partial differential equation (PDE) domain. We also show how Fortran, over the last few decades, has changed to become a language well-suited for state-of-the-art software development. Fortran’s new coarray distributed data structure, the language’s class mechanism, and its side-effect-free, pure procedure capability provide the scaffolding on which we implement HPC software. These features empower compilers to organize parallel computations with efficient communication. We present some programming patterns that support asynchronous evaluation of expressions comprised of parallel operations on distributed data. We implemented these patterns using coarrays and the message passing interface (MPI). We compared the codes’ complexity and performance. The MPI code is much more complex and depends on external libraries. The MPI code on Cray hardware using the Cray compiler is 1.5–2 times faster than the coarray code on the same hardware. The Intel compiler implements coarrays atop Intel’s MPI library with the result apparently being 2–2.5 times slower than manually coded MPI despite exhibiting nearly linear scaling efficiency. As compilers mature and further improvements to coarrays comes in Fortran 2015, we expect this performance gap to narrow.

Haveraaen, Magne↗

Livermore Random I/O Testbench

LRIOT is a test bench framework that is designed to generate sophisticated I/O rates that can stress high-performance memory and storage systems, such as non-volatile random access memories (NVRAM)and storage class memory. Furthermore, LRIOT provides the capabilities to mix multiple types of concurrency, namely threading and task parallelism, as well as distributed execution using Message Passing Interface (MPI) libraries. It will be used by algorithm designers to generate access patterns that mimic their application's behavior, and by system designers to test high-performance NVRAM storage.

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