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DOE OSTI2022

Xyce™ Parallel Electronic Simulator Users' Guide (V.7.6)

This manual describes the use of the Xyce™ Parallel Electronic Simulator. Xyce™ has been designed as a SPICE-compatible, high-performance analog circuit simulator, and has been written to support the simulation needs of the Sandia National Laboratories electrical designers. This development has focused on improving capability over the current state-of-the-art in the following areas: (1) Capability to solve extremely large circuit problems by supporting large-scale parallel computing platforms (up to thousands of processors). This includes support for most popular parallel and serial computers. (2) A differential-algebraic-equation (DAE) formulation, which better isolates the device model package from solver algorithms. This allows one to develop new types of analysis without requiring the implementation of analysis-specific device models. (3) Device models that are specifically tailored to meet Sandia's needs, including some radiation-aware devices (for Sandia users only). (4) Object-oriented code design and implementation using modern coding practices. Xyce™ is a parallel code in the most general sense of the phrase—a message passing parallel implementation—which allows it to run efficiently a wide range of computing platforms. These include serial, shared-memory and distributed-memory parallel platforms. Attention has been paid to the specific nature of circuit-simulation problems to ensure that optimal parallel eficiency is achieved as the number of processors grows.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Xyce™ Parallel Electronic Simulator Users’ Guide, Version 7.8

This manual describes the use of the Xyce Parallel Electronic Simulator. Xyce has been designed as a SPICE-compatible, high-performance analog circuit simulator, and has been written to support the simulation needs of the Sandia National Laboratories electrical designers. This development has focused on improving capability over the current state-of-the-art in the following areas: (1) Capability to solve extremely large circuit problems by supporting large-scale parallel computing platforms (up to thousands of processors). This includes support for most popular parallel and serial computers. (2) A differential-algebraic-equation (DAE) formulation, which better isolates the device model package from solver algorithms. This allows one to develop new types of analysis without requiring the implementation of analysis-specific device models. (3) Device models that are specifically tailored to meet Sandia’s needs, including some radiation-aware devices (for Sandia users only). (4) Object-oriented code design and implementation using modern coding practices. Xyce is a parallel code in the most general sense of the phrase — a message passing parallel implementation — which allows it to run efficiently a wide range of computing platforms. These include serial, shared-memory and distributed-memory parallel platforms. Attention has been paid to the specific nature of circuit-simulation problems to ensure that optimal parallel efficiency is achieved as the number of processors grows.

42 ENGINEERING↗

DOE OSTI2024

Efficient Parallelization of Irregular Applications on GPU Architectures

With the enlarging computation capacity of general Graphics Processing Units (GPUs), leveraging GPUs to accelerate parallel applications has become a critical topic in academia and industry. However, a wide range of irregular applications with the computation-/memory-intensive nature cannot easily achieve high GPU utilization. The challenges mainly involve the following aspects: first, data dependence leads to coarse-grained kernel and inefficient parallelism; second, heavy GPU memory usage may cause frequent memory evictions and extra overhead of I/O; third, specific computation patterns produce memory redundancies; last, workload balance and data reusability conjunctly benefit the overall performance, but there may exist a dynamic trade-off between them. Targeting these challenges, this dissertation proposes multiple optimizations to accelerate two real-world applications: many-body correlation functions to simulate nuclear physics in a large-scale scientific system; the other is the eALS-based matrix factorization recommendation system. To accelerate the calculations of many-body correlation functions, this dissertation presents three frameworks in GPU memory management and multi-GPU scheduling. Firstly, an optimized systematic GPU memory management framework, MemHC, utilizes a series of new memory reduction designs in GPU memory allocation, CPU/GPU communications, and GPU memory oversubscription. Secondly, an enhanced multi-GPU scheduling framework, MICCO, particularly by taking both data dimension (e.g., data reuse and data eviction) and computation dimension into account. MICCO designs a heuristic scheduling algorithm and a machine learning-based regression model to generate the optimal settings of a proposed new concept to manage the trade-off. Thirdly, a locality-aware multi-GPU scheduling framework. This scheduler leverages pipeline batch generation with a looking-ahead strategy by building local dependency graphs for memory transfer reduction and better data reuse, achieving up to 79.92% memory cost reduction and 1.67x speedup. To parallelize the eALS-based recommendation system, this dissertation proposes an efficient CPU/GPU heterogeneous recommendation system, HEALS. HEALS employs newly designed architecture-adaptive data formats to achieve load balance and good data locality on CPU and GPU. To mitigate the data dependence, HEALS presents a CPU/GPU collaboration model for both task parallelism and data parallelism with multiple kernel computation optimizations. In summary, this dissertation efficiently accelerates two typical irregular applications on GPUs by building four frameworks, including CPU/GPU collaboration, GPU memory management, and multi-GPU scheduling.

Wang, Qihan↗

DOE OSTI2021

Revisiting Huffman Coding: Toward Extreme Performance on Modern GPU Architectures

Today's high-performance computing (HPC) applications are producing vast volumes of data, which are challenging to store and transfer efficiently during the execution, such that data compression is becoming a critical technique to mitigate the storage burden and data movement cost. Huffman coding is arguably the most efficient Entropy coding algorithm in information theory, such that it could be found as a fundamental step in many modern compression algorithms such as DEFLATE. On the other hand, today's HPC applications are more and more relying on the accelerators such as GPU on supercomputers, while Huffman encoding suffers from low throughput on GPUs, resulting in a significant bottleneck in the entire data processing. In this paper, we propose and implement an efficient Huffman encoding approach based on modern GPU architectures, which addresses two key challenges: (1) how to parallelize the entire Huffman encoding algorithm, including codebook construction, and (2) how to fully utilize the high memory-bandwidth feature of modern GPU architectures. The detailed contribution is fourfold. (1) We develop an efficient parallel codebook construction on GPUs that scales effectively with the number of input symbols. (2) We propose a novel reduction based encoding scheme that can efficiently merge the codewords on GPUs. (3) We optimize the overall GPU performance by leveraging the state-of-the-art CUDA APIs such as Cooperative Groups. (4) We evaluate our Huffman encoder thoroughly using six real-world application datasets on two advanced GPUs and compare with our implemented multi-threaded Huffman encoder. Experiments show that our solution can improve the encoding throughput by up to 5.0x and 6.8x on NVIDIA RTX 5000 and V100, respectively, over the state-of-the-art GPU Huffman encoder, and by up to 3.3x over the multi-thread encoder on two 28-core Xeon Platinum 8280 CPUs.

Tian, Jiannan↗

DOE OSTI2021

Revisiting Huffman Coding: Toward Extreme Performance on Modern GPU Architectures

Today's high-performance computing (HPC) applications are producing vast volumes of data, which are challenging to store and transfer efficiently during the execution, such that data compression is becoming a critical technique to mitigate the storage burden and data movement cost. Huffman coding is arguably the most efficient Entropy coding algorithm in information theory, such that it could be found as a fundamental step in many modern compression algorithms such as DEFLATE. On the other hand, today's HPC applications are more and more relying on the accelerators such as GPU on supercomputers, while Huffman encoding suffers from low throughput on GPUs, resulting in a significant bottleneck in the entire data processing. In this paper, we propose and implement an efficient Huffman encoding approach based on modern GPU architectures, which addresses two key challenges: (1) how to parallelize the entire Huffman encoding algorithm, including codebook construction, and (2) how to fully utilize the high memory-bandwidth feature of modern GPU architectures. The detailed contribution is fourfold. (1) We develop an efficient parallel codebook construction on GPUs that scales effectively with the number of input symbols. (2) We propose a novel reduction based encoding scheme that can efficiently merge the codewords on GPUs. (3) We optimize the overall GPU performance by leveraging the state-of-the-art CUDA APIs such as Cooperative Groups. (4) We evaluate our Huffman encoder thoroughly using six real-world application datasets on two advanced GPUs and compare with our implemented multithreaded Huffman encoder. Experiments show that our solution can improve the encoding throughput by up to 5.0× and 6.8× on NVIDIA RTX 5000 and V100, respectively, over the state-of-the-art GPU Huffman encoder, and by up to 3.3× over the multithread encoder on two 28-core Xeon Platinum 8280 CPUs.

Tian, Jiannan↗

DOE OSTI2021

Porting HEP Parameterized Calorimeter Simulation Code to GPUs

The High Energy Physics (HEP) experiments, such as those at the Large Hadron Collider (LHC), traditionally consume large amounts of CPU cycles for detector simulations and data analysis, but rarely use compute accelerators such as GPUs. As the LHC is upgraded to allow for higher luminosity, resulting in much higher data rates, purely relying on CPUs may not provide enough computing power to support the simulation and data analysis needs. As a proof of concept, we investigate the feasibility of porting a HEP parameterized calorimeter simulation code to GPUs. We have chosen to use FastCaloSim, the ATLAS fast parametrized calorimeter simulation. While FastCaloSim is sufficiently fast such that it does not impose a bottleneck in detector simulations overall, significant speed-ups in the processing of large samples can be achieved from GPU parallelization at both the particle (intra-event) and event levels; this is especially beneficial in conditions expected at the high-luminosity LHC, where extremely high per-event particle multiplicities will result from the many simultaneous proton-proton collisions. We report our experience with porting FastCaloSim to NVIDIA GPUs using CUDA. A preliminary Kokkos implementation of FastCaloSim for portability to other parallel architectures is also described.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2017

PARALLEL PERTURBATION MODEL FOR CYCLE TO CYCLE VARIABILITY PPM4CCV

This code consists of a Fortran 90 implementation of the parallel perturbation model to compute cyclic variability in spark ignition (SI) engines. Cycle-to-cycle variability (CCV) is known to be detrimental to SI engine operation resulting in partial burn and knock, and result in an overall reduction in the reliability of the engine. Numerical prediction of cycle-to-cycle variability (CCV) in SI engines is extremely challenging for two key reasons: (i) high-fidelity methods such as large eddy simulation (LES) are required to accurately capture the in-cylinder turbulent flow field, and (ii) CCV is experienced over long timescales and hence the simulations need to be performed for hundreds of consecutive cycles. In the new technique, the strategy is to perform multiple parallel simulations, each of which encompasses 2-3 cycles, by effectively perturbing the simulation parameters such as the initial and boundary conditions. The PPM4CCV code is a pre-processing code and can be coupled with any engine CFD code. PPM4CCV was coupled with Converge CFD code and a 10-time speedup was demonstrated over the conventional multi-cycle LES in predicting the CCV for a motored engine. Recently, the model is also being applied to fired engines including port fuel injected (PFI) and direct injection spark ignition engines and the preliminary results are very encouraging.

Ameen, Muhsin Mohammed↗

DOE OSTI2024

Boosting RDataFrame performance with transparent bulk event processing

RDataFrame is ROOT’s high-level interface for Python and C++ data analysis. Since it first became available, RDataFrame adoption has grown steadily and it is now poised to be a major component of analysis software pipelines for LHC Run 3 and beyond. Thanks to its design inspired by declarative programming principles, RDataFrame enables the development of highperformance, highly parallel analyses without requiring expert knowledge of multi-threading and I/O: user logic is expressed in terms of self-contained, small computation kernels tied together by a high-level API. This design completely decouples analysis logic from its actual execution, and opens several interesting avenues for workflow optimization. In particular, in this work we explore the benefits of moving internal data processing from an event-by-event to a bulkby-bulk loop. This refactoring dramatically reduces the framework’s runtime overheads; in collaboration with the I/O layer it improves data access patterns; it exposes information that optimizing compilers might use to auto-vectorize the invocation of user-defined computations; finally, while existing user-facing interfaces remain unaffected, it becomes possible to additionally offer interfaces that explicitly expose bulks of events, useful e.g. for the injection of GPU kernels into the analysis workflow. In order to inform similar future R&D, design challenges will be presented, as well as an investigation of the relevant timememory trade-off backed by novel performance benchmarks.

Guiraud, Enrico↗

DOE OSTI2020

UQpy: A general purpose Python package and development environment for uncertainty quantification

In this paper, we present the UQpy software toolbox, an open-source Python package for general uncertainty quantification (UQ) in mathematical and physical systems. The software serves as both a user-ready toolbox that includes many of the latest methods for UQ in computational modeling and a convenient development environment for Python programmers advancing the field of UQ. The paper presents an introduction to the software's architecture and existing capabilities, divided in the code in a set of modules centered around different UQ tasks such as sampling methods, generation of random processes and random fields, probabilistic inverse modeling, reliability analysis, surrogate modeling, and active learning. The paper also highlights the importance of the RunModel module, which is used to drive simulations in the uncertainty analyses performed in UQpy. This module conveniently allows the user to define computational models directly in Python, or to run simulations from a third-party software in serial or in parallel. To illustrate the various capabilities, two examples are tracked throughout the paper and analyzed repeatedly for various UQ tasks. The first is a Python model solving a nonlinear structural dynamics problem, used to illustrate UQpy's capabilities in sampling and forward propagation of high dimensional random vectors (stochastic processes), and probabilistic inference. The second model is a third-party Abaqus finite element model solving the thermomechanical response of a beam structure. This example is used to illustrate UQpy's capabilities in variance reduction sampling techniques, reliability analysis, surrogate modeling and active learning techniques.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Structural Simluation Toolkit (SST) v.12.0

The Structural Simulation Toolkit (SST) was developed to explore innovations in highly concurrent computing systems where the instruction set architecture (ISA), micro-architecture, and memory interact with the programming model and communications system. The package provides a fully modular design for extensive exploration of an individual system parameter as well as a parallel simulation environment based on message passing interface (MPI) which enable a high level of performance as well as the ability to look at large systems. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

Rodrigues, ArunF.↗

DOE OSTI2016

Extreme-scale Algorithms and Solver Resilience

A widening gap exists between the peak performance of high-performance computers and the performance achieved by complex applications running on these platforms. Over the next decade, extreme-scale systems will present major new challenges to algorithm development that could amplify this mismatch in such a way that it prevents the productive use of future DOE Leadership computers due to the following; Extreme levels of parallelism due to multicore processors; An increase in system fault rates requiring algorithms to be resilient beyond just checkpoint/restart; Complex memory hierarchies and costly data movement in both energy and performance; Heterogeneous system architectures (mixing CPUs, GPUs, etc.); and Conflicting goals of performance, resilience, and power requirements.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2016

FY 2016 Fusion Energy Sciences (FES) Theory and Simulation Performance Target

Annual target: Predicting the magnitude and scaling of the divertor heat load width in magnetically confined burning plasmas is a high priority for the fusion program and ITER. One of the key unresolved physics issues is what sets the heat flux width at the entrance to the divertor region. Perform massively parallel simulations using 3D edge kinetic and fluid codes to determine the parameter dependence of the heat load width at the divertor entrance and compute the divertor plate heat flux applicable to moderate particle recycling conditions. Comparisons will be made with data from DIII-D, NSTX-U, and C-Mod.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

ECP ST Capability Assessment Report (CAR) for VTK-m (FY20)

The ECP/VTK-m project is providing the core capabilities to perform scientific visualization on Exascale architectures. The ECP/VTK-m project fills the critical feature gap of performing visualization and analysis on processors like graphics-based processors. The results of this project will be delivered in tools like ParaView, Vislt, and Ascent as well as in stand-alone form. Moreover, these projects are depending on this ECP effort to be able to make effective use of ECP architectures. One of the biggest recent changes in high-performance computing is the increasing use of accelerators. Accelerators contain processing cores that independently are inferior to a core in a typical CPU, but these cores are replicated and grouped such that their aggregate execution provides a very high computation rate at a much lower power. Current and future CPU processors also require much more explicit parallelism. Each successive version of the hardware packs more cores into each processor, and technologies like hyper threading and vector operations require even more parallel processing to leverage each core's full potential. VTK-m is a toolkit of scientific visualization algorithms for emerging processor architectures. VTK-m supports the fine-grained concurrency for data analysis and visualization algorithms required to drive extreme scale computing by providing abstract models for data and execution that can be applied to a variety of algorithms across many different processor architectures. The ECP/VTK-m project is building up the VTK-m codebase with the necessary visualization algorithm implementations that run across the varied hardware platforms to be leveraged at the Exascale. We will be working with other ECP projects, such as ALPINE, to integrate the new VTK-m code into production software to enable visualization on our HPC systems.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

LibERI—A portable and performant multi-GPU accelerated library for electron repulsion integrals via OpenMP offloading and standard language parallelism

A portable and performant graphics processing unit (GPU)-accelerated library for electron repulsion integral (ERI) evaluation, named LibERI, has been developed and implemented via directive-based (e.g., OpenMP and OpenACC) and standard language parallelism (e.g., Fortran DO CONCURRENT). Offloaded ERIs consist of integrals over low and high contraction s, p, and d functions using the rotated-axis and Rys quadrature methods. GPU codes are factorized based on previous developments with two layers of integral screening and quartet presorting. In this work, the density screening is moved to the GPU to enhance the computational efficacy for large molecular systems. Here, the L-shells in the Pople basis set are also separated into pure S and P shells to increase the ERI homogeneity and reduce atomic operations and the memory footprint. LibERI is compatible with any quantum chemistry drivers supporting the MolSSI Driver Interface. Benchmark calculations of LibERI interfaced with the GAMESS software package were carried out on various GPU architectures and molecular systems. The results show that the LibERI performance is comparable to other state-of-the-art GPU-accelerated codes (e.g., TeraChem and GMSHPC) and, in some cases, outperforms conventionally developed ERI CUDA kernels (e.g., QUICK) while fully maintaining portability.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Asynchronous Iterative Solvers for Extreme-Scale Computing

The Asynchronous Iterative Solvers for Extreme-Scale Computing (AsyncIS) project aims to explore more efficient numerical algorithms by decreasing their overhead. AsyncIS does this by replacing the outer Krylov subspace solver with an asynchronous optimized Schwarz method, thereby removing the global synchronization and bulk synchronous operations typically used in numerical codes. AsyncIS—a U.S. Department of Energy (DOE)-funded collaboration between Georgia Tech, the University of Tennessee, Knoxville, Temple University, and Sandia National Laboratories—also focuses on the development and optimization of asynchronous preconditioners (i.e., preconditioners that are generated and/or applied in an asynchronous fashion). The novel preconditioning algorithms that provide fine-grained parallelism enable preconditioned Krylov solvers to run efficiently on large-scale distributed systems and manycore accelerators like GPUs.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2017

Accelerating gravitational microlensing simulations using the Xeon Phi coprocessor

Recently Graphics Processing Units (GPUs) have been used to speed up very CPU-intensive gravitational microlensing simulations. In this work, we use the Xeon Phi coprocessor to accelerate such simulations and compare its performance on a microlensing code with that of NVIDIA's GPUs. For the selected set of parameters evaluated in our experiment, we find that the speedup by Intel's Knights Corner coprocessor is comparable to that by NVIDIA's Fermi family of GPUs with compute capability 2.0, but less significant than GPUs with higher compute capabilities such as the Kepler. However, the very recently released second generation Xeon Phi, Knights Landing, is about 5.8 times faster than the Knights Corner, and about 2.9 times faster than the Kepler GPU used in our simulations. Here, we conclude that the Xeon Phi is a very promising alternative to GPUs for modern high performance microlensing simulations. LESS

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2014

TH-E-18A-01: Developments in Monte Carlo Methods for Medical Imaging

Monte Carlo simulation methods are widely used in medical physics research and are starting to be implemented in clinical applications such as radiation therapy planning systems. Monte Carlo simulations offer the capability to accurately estimate quantities of interest that are challenging to measure experimentally while taking into account the realistic anatomy of an individual patient. Traditionally, practical application of Monte Carlo simulation codes in diagnostic imaging was limited by the need for large computational resources or long execution times. However, recent advancements in high-performance computing hardware, combined with a new generation of Monte Carlo simulation algorithms and novel postprocessing methods, are allowing for the computation of relevant imaging parameters of interest such as patient organ doses and scatter-to-primaryratios in radiographic projections in just a few seconds using affordable computational resources. Programmable Graphics Processing Units (GPUs), for example, provide a convenient, affordable platform for parallelized Monte Carlo executions that yield simulation times on the order of 10{sup 7} xray/ s. Even with GPU acceleration, however, Monte Carlo simulation times can be prohibitive for routine clinical practice. To reduce simulation times further, variance reduction techniques can be used to alter the probabilistic models underlying the x-ray tracking process, resulting in lower variance in the results without biasing the estimates. Other complementary strategies for further reductions in computation time are denoising of the Monte Carlo estimates and estimating (scoring) the quantity of interest at a sparse set of sampling locations (e.g. at a small number of detector pixels in a scatter simulation) followed by interpolation. Beyond reduction of the computational resources required for performing Monte Carlo simulations in medical imaging, the use of accurate representations of patient anatomy is crucial to the virtual generation of medical images and accurate estimation of radiation dose and other imaging parameters. For this, detailed computational phantoms of the patient anatomy must be utilized and implemented within the radiation transport code. Computational phantoms presently come in one of three format types, and in one of four morphometric categories. Format types include stylized (mathematical equation-based), voxel (segmented CT/MR images), and hybrid (NURBS and polygon mesh surfaces). Morphometric categories include reference (small library of phantoms by age at 50th height/weight percentile), patient-dependent (larger library of phantoms at various combinations of height/weight percentiles), patient-sculpted (phantoms altered to match the patient's unique outer body contour), and finally, patient-specific (an exact representation of the patient with respect to both body contour and internal anatomy). The existence and availability of these phantoms represents a very important advance for the simulation of realistic medical imaging applications using Monte Carlo methods. New Monte Carlo simulation codes need to be thoroughly validated before they can be used to perform novel research. Ideally, the validation process would involve comparison of results with those of an experimental measurement, but accurate replication of experimental conditions can be very challenging. It is very common to validate new Monte Carlo simulations by replicating previously published simulation results of similar experiments. This process, however, is commonly problematic due to the lack of sufficient information in the published reports of previous work so as to be able to replicate the simulation in detail. To aid in this process, the AAPM Task Group 195 prepared a report in which six different imaging research experiments commonly performed using Monte Carlo simulations are described and their results provided. The simulation conditions of all six cases are provided in full detail, with all necessary data on material composition, source, geometry, scoring and other parameters provided. The results of these simulations when performed with the four most common publicly available Monte Carlo packages are also provided in tabular form. The Task Group 195 Report will be useful for researchers needing to validate their Monte Carlo work, and for trainees needing to learn Monte Carlo simulation methods. In this symposium we will review the recent advancements in highperformance computing hardware enabling the reduction in computational resources needed for Monte Carlo simulations in medical imaging. We will review variance reduction techniques commonly applied in Monte Carlo simulations of medical imaging systems and present implementation strategies for efficient combination of these techniques with GPU acceleration. Trade-offs involved in Monte Carlo acceleration by means of denoising and “sparse sampling” will be discussed. A method for rapid scatter correction in cone-beam CT (<5 min/scan) will be presented as an illustration of the simulation speeds achievable with optimized Monte Carlo simulations. We will also discuss the development, availability, and capability of the various combinations of computational phantoms for Monte Carlo simulation of medical imaging systems. Finally, we will review some examples of experimental validation of Monte Carlo simulations and will present the AAPM Task Group 195 Report. Learning Objectives: Describe the advances in hardware available for performing Monte Carlo simulations in high performance computing environments. Explain variance reduction, denoising and sparse sampling techniques available for reduction of computational time needed for Monte Carlo simulations of medical imaging. List and compare the computational anthropomorphic phantoms currently available for more accurate assessment of medical imaging parameters in Monte Carlo simulations. Describe experimental methods used for validation of Monte Carlo simulations in medical imaging. Describe the AAPM Task Group 195 Report and its use for validation and teaching of Monte Carlo simulations in medical imaging.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2018

OpenMP in VASP: Threading and SIMD

Abstract The Vienna Ab initio Simulation Package (VASP) is a widely used electronic structure code that originally exploits process‐level parallelism through the Message Passing Interface (MPI) for work distribution within and across nodes. Architectural changes of modern parallel processors urge programmers to address thread‐ and data‐level parallelism as well to benefit most from the available compute resources within a node. We describe for VASP how to approach for an MPI + OpenMP parallelization including data‐level parallelism through OpenMP SIMD constructs together with a generic high‐level vector coding scheme. We can demonstrate an improved scalability of VASP and more than 20% gain over the MPI‐only version as well as a 2× increased performance of collective operations using the multiple‐endpoint MPI feature. The high‐level vector coding scheme applied to VASP's general gradient approximation routine gives up 9× performance gain on AVX512 platforms with the Intel compiler.

Wende, Florian↗