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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

3-regular three-XORSAT planted solutions benchmark of classical and quantum heuristic optimizers

With current semiconductor technology reaching its physical limits, special-purpose hardware has emerged as an option to tackle specific computing-intensive challenges. Optimization in the form of solving quadratic unconstrained binary optimization problems, or equivalently Ising spin glasses, has been the focus of several new dedicated hardware platforms. These platforms come in many different flavors, from highly-efficient hardware implementations on digital-logic of established algorithms to proposals of analog hardware implementing new algorithms. In this work, we use a mapping of a specific class of linear equations whose solutions can be found efficiently, to a hard constraint satisfaction problem (three-regular three-XORSAT, or an Ising spin glass) with a 'golf-course' shaped energy landscape, to benchmark several of these different approaches. We perform a scaling and prefactor analysis of the performance of Fujitsu's digital annealer unit (DAU), the D-Wave advantage quantum annealer, a virtual MemComputing machine, Toshiba's simulated bifurcation machine (SBM), the SATonGPU algorithm from Bernaschi et al, and our implementation of parallel tempering. We identify the SATonGPU and DAU as currently having the smallest scaling exponent for this benchmark, with SATonGPU having a small scaling advantage and in addition having by far the smallest prefactor thanks to its use of massive parallelism. Furthermore, our work provides an objective assessment and a snapshot of the promise and limitations of dedicated optimization hardware relative to a particular class of optimization problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Parthenon—a performance portable block-structured adaptive mesh refinement framework

On the path to exascale the landscape of computer device architectures and corresponding programming models has become much more diverse. While various low-level performance portable programming models are available, support at the application level lacks behind. To address this issue, we present the performance portable block-structured adaptive mesh refinement (AMR) framework Parthenon, derived from the well-tested and widely used Athena++ astrophysical magnetohydrodynamics code, but generalized to serve as the foundation for a variety of downstream multi-physics codes. Parthenon adopts the Kokkos programming model, and provides various levels of abstractions from multidimensional variables, to packages defining and separating components, to launching of parallel compute kernels. Parthenon allocates all data in device memory to reduce data movement, supports the logical packing of variables and mesh blocks to reduce kernel launch overhead, and employs one-sided, asynchronous MPI calls to reduce communication overhead in multi-node simulations. Using a hydrodynamics miniapp, we demonstrate weak and strong scaling on various architectures including AMD and NVIDIA GPUs, Intel and AMD x86 CPUs, IBM Power9 CPUs, as well as Fujitsu A64FX CPUs. At the largest scale on Frontier (the first TOP500 exascale machine), the miniapp reaches a total of 1.7 × 10 13 zone-cycles/s on 9216 nodes (73,728 logical GPUs) at [Formula: see text] weak scaling parallel efficiency (starting from a single node). In combination with being an open, collaborative project, this makes Parthenon an ideal framework to target exascale simulations in which the downstream developers can focus on their specific application rather than on the complexity of handling massively-parallel, device-accelerated AMR.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

A parallel, distributed memory implementation of the adaptive sampling configuration interaction method

The many-body simulation of quantum systems is an active field of research that involves several different methods targeting various computing platforms. Many methods commonly employed, particularly coupled cluster methods, have been adapted to leverage the latest advances in modern high-performance computing. Selected configuration interaction (sCI) methods have seen extensive usage and development in recent years. However, the development of sCI methods targeting massively parallel resources has been explored only in a few research works. Here, we present a parallel, distributed memory implementation of the adaptive sampling configuration interaction approach (ASCI) for sCI. In particular, we will address the key concerns pertaining to the parallelization of the determinant search and selection, Hamiltonian formation, and the variational eigenvalue calculation for the ASCI method. Load balancing in the search step is achieved through the application of memory-efficient determinant constraints originally developed for the ASCI-PT2 method. The presented benchmarks demonstrate near optimal speedup for ASCI calculations of Cr 2 (24e, 30o) with 10 6 , 10 7 , and 3 × 10 8 variational determinants on up to 16 384 CPUs. Importantly, to the best of the authors’ knowledge, this is the largest variational ASCI calculation to date.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Scaled ILU Smoothers for Navier-Stokes Pressure Projection

Incomplete LU (ILU) smoothers are effective in the algebraic multigrid (AMG) V-cycle for reducing high-frequency components of the error. However, the requisite direct triangular solves are comparatively slow on GPUs. Previous work has demonstrated the advantages of Jacobi iteration as an alternative to direct solution of these systems. Depending on the threshold and fill-level parameters chosen, the factors can be highly nonnormal and Jacobi is unlikely to converge in a low number of iterations. We demonstrate that row scaling can reduce the departure from normality, allowing us to replace the inherently sequential solve with a rapidly converging Richardson iteration. There are several advantages beyond the lower compute time. Scaling is performed locally for a diagonal block of the global matrix because it is applied directly to the factor. Further, an ILUT Schur complement smoother maintains a constant GMRES iteration count as the number of MPI ranks increases, and thus parallel strong-scaling is improved. Our algorithms have been incorporated into hypre, and we demonstrate improved time to solution for linear systems arising in the Nalu-Wind and PeleLM pressure solvers. For large problem sizes, GMRES+AMG executes at least five times faster when using iterative triangular solves compared with direct solves on massively parallel GPUs.

algebraic multigrid↗
DOE OSTI2021

DeepGRN: prediction of transcription factor binding site across cell-types using attention-based deep neural networks

Abstract Background Due to the complexity of the biological systems, the prediction of the potential DNA binding sites for transcription factors remains a difficult problem in computational biology. Genomic DNA sequences and experimental results from parallel sequencing provide available information about the affinity and accessibility of genome and are commonly used features in binding sites prediction. The attention mechanism in deep learning has shown its capability to learn long-range dependencies from sequential data, such as sentences and voices. Until now, no study has applied this approach in binding site inference from massively parallel sequencing data. The successful applications of attention mechanism in similar input contexts motivate us to build and test new methods that can accurately determine the binding sites of transcription factors. Results In this study, we propose a novel tool (named DeepGRN) for transcription factors binding site prediction based on the combination of two components: single attention module and pairwise attention module. The performance of our methods is evaluated on the ENCODE-DREAM in vivo Transcription Factor Binding Site Prediction Challenge datasets. The results show that DeepGRN achieves higher unified scores in 6 of 13 targets than any of the top four methods in the DREAM challenge. We also demonstrate that the attention weights learned by the model are correlated with potential informative inputs, such as DNase-Seq coverage and motifs, which provide possible explanations for the predictive improvements in DeepGRN. Conclusions DeepGRN can automatically and effectively predict transcription factor binding sites from DNA sequences and DNase-Seq coverage. Furthermore, the visualization techniques we developed for the attention modules help to interpret how critical patterns from different types of input features are recognized by our model.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

In situ Parallel Training of Analog Neural Network Using Electrochemical Random-Access Memory

In-memory computing based on non-volatile resistive memory can significantly improve the energy efficiency of artificial neural networks. However, accurate in situ training has been challenging due to the nonlinear and stochastic switching of the resistive memory elements. One promising analog memory is the electrochemical random-access memory (ECRAM), also known as the redox transistor. Its low write currents and linear switching properties across hundreds of analog states enable accurate and massively parallel updates of a full crossbar array, which yield rapid and energy-efficient training. While simulations predict that ECRAM based neural networks achieve high training accuracy at significantly higher energy efficiency than digital implementations, these predictions have not been experimentally achieved. In this work, we train a 3 × 3 array of ECRAM devices that learns to discriminate several elementary logic gates (AND, OR, NAND). We record the evolution of the network’s synaptic weights during parallel in situ (on-line) training, with outer product updates. Due to linear and reproducible device switching characteristics, our crossbar simulations not only accurately simulate the epochs to convergence, but also quantitatively capture the evolution of weights in individual devices. The implementation of the first in situ parallel training together with strong agreement with simulation results provides a significant advance toward developing ECRAM into larger crossbar arrays for artificial neural network accelerators, which could enable orders of magnitude improvements in energy efficiency of deep neural networks.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

The Kokkos Ecosystem [Brief]

In 2016/2017, the field of High-Performance Computing (HPC) entered a new era driven by fundamental physics challenges to produce ever more energy and cost-efficient processors. Since the convergence on the Message-Passing Interface (MPI) standard in the mid-1990s, application developers enjoyed a seemingly static view of the underlying machine — that of a distributed collection of homogeneous nodes executing in collaboration. However, after almost two decades of dominance, the sole use of MPI to derive parallelism acted as a limiter to improved future performance. While MPI is widely expected to continue to function as the basic mechanism for communication between compute nodes for the immediate future, additional parallelism is required on the computing node itself if high performance and efficiency goals are to be realized. When reviewing the architectures of the top HPC systems today, the change in paradigm is clear: the compute nodes of the leading machines in the world are either powered by many-core chips with a few dozen cores each, or use heterogeneous designs, where traditional CPUs marshal work to massively parallel compute accelerators which has as many as 200,000 processing threads in flight simultaneously. Complicating matters further for application developers, each processor vendor has its own preferred way of writing code for their architecture.The Kokkos EcoSystem was released by Sandia in 2017 to address this new era in HPC system design by providing a vendor independent performance portable programming system for scientific, engineering, and mathematical software applications written in the C++ programming language. Using Kokkos, application developers can be more productive because they will not have to create and maintain separate versions of their software for each architecture, nor will they have to be experts in each architecture's peculiar requirements. Instead, they will have a single method of programming for the diverse set of modern HPC architectures. While Kokkos started in 2011 as a programming model only, it soon became clear that complex applications needed more. It is also critical to have a portable mathematical functions and developers need tools to debug their applications, gain insight into the performance characteristics of their codes and tune algorithm performance parameters through automated processes. The Kokkos EcoSystem addresses those needs through its three main components: the Kokkos Core programming model, the Kokkos Kernels math library, and the Kokkos Tools project.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

The Effective Fragment Molecular Orbital Method: Achieving High Scalability and Accuracy for Large Systems

The effective fragment molecular orbital (EFMO) method has been developed to predict the total energy of a very large molecular system accurately (with respect to the underlying quantum mechanical method) and efficiently by taking advantage of the locality of strong chemical interactions and employing a two-level hierarchical parallelism. The accuracy of the EFMO method is partly attributed to the accurate and robust intermolecular interaction prediction between distant fragments, in particular, the many-body polarization and dispersion effects, which require the generation of static and dynamic polarizability tensors by solving the coupled perturbed Hartree–Fock (CPHF) and time-dependent HF (TDHF) equations, respectively. Solving the CPHF and TDHF equations is the main EFMO computational bottleneck due to the inefficient (serial) and I/O-intensive implementation of the CPHF and TDHF solvers. In this work, the efficiency and scalability of the EFMO method are significantly improved with a new CPU memory-based implementation for solving the CPHF and TDHF equations that are parallelized by either message passing interface (MPI) or hybrid MPI/OpenMP. Here, the accuracy of the EFMO method is demonstrated for both covalently bonded systems and noncovalently bound molecular clusters by systematically examining the effects of basis sets and a key distance-related cutoff parameter, R cut . R cut determines whether a fragment pair (dimer) is treated by the chosen ab initio method or calculated using the effective fragment potential (EFP) method (separated dimers). Decreasing the value of Rcut increases the number of separated (EFP) dimers, thereby decreasing the computational effort. It is demonstrated that excellent accuracy (<1 kcal/mol error per fragment) can be achieved when using a sufficiently large basis set with diffuse functions coupled with a small R cut value. With the new parallel implementation, the total EFMO wall time is substantially reduced, especially with a high number of MPI ranks. Given a sufficient workload, nearly ideal strong scaling is achieved for the CPHF and TDHF parts of the calculation. For the first time, EFMO calculations with the inclusion of long-range polarization and dispersion interactions on a hydrated mesoporous silica nanoparticle with explicit water solvent molecules (more than 15k atoms) are achieved on a massively parallel supercomputer using nearly 1000 physical nodes. In addition, EFMO calculations on the carbinolamine formation step of an amine-catalyzed aldol reaction at the nanoscale with explicit solvent effects are presented.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

From NWChem to NWChemEx: Evolving with the Computational Chemistry Landscape

Since the advent of the first computers, chemists have been at the forefront of using computers to understand and solve complex chemical problems. As the hardware and software have evolved, so have the theoretical and computational chemistry methods and algorithms. Parallel computers clearly changed the common computing paradigm in the late 1970s and 80s, and the field has again seen a paradigm shift with the advent of graphical processing units. This review explores the challenges and some of the solutions in transforming software from the terascale to the petascale and now to the upcoming exascale computers. While discussing the field in general, NWChem and its redesign, NWChemEx, will be highlighted as one of the early codesign projects to take advantage of massively parallel computers and emerging software standards to enable large scientific challenges to be tackled.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

A Cryogenic Readout IC with 100 KSPS in-Pixel ADC for Skipper CCD-in-CMOS Sensors

The Skipper CCD-in-CMOS Parallel Read-Out Circuit (SPROCKET) is a mixed-signal front-end design for the readout of Skipper CCD-in-CMOS image sensors. SPROCKET is fabricated in a 65 nm CMOS process and each pixel occupies a 50$\mu$m $\times$ 50$\mu$m footprint. SPROCKET is intended to be heterogeneously integrated with a Skipper-in-CMOS sensor array, such that one readout pixel is connected to a multiplexed array of nine Skipper-in-CMOS pixels to enable massively parallel readout. The front-end includes a variable gain preamplifier, a correlated double sampling circuit, and a 10-bit serial successive approximation register (SAR) ADC. The circuit achieves a sample rate of 100 ksps with 0.48 $\mathrm{e^-_{rms}}$ equivalent noise at the input to the ADC. SPROCKET achieves a maximum dynamic range of 9,000 $e^-$ at the lowest gain setting (or 900 $e^-$ at the lowest noise setting). The circuit operates at 100 Kelvin with a power consumption of 40 $\mu W$ per pixel. A SPROCKET test chip was submitted in September 2022, and test results will be presented at the conference.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2021

A parallel evolutionary multiple-try metropolis Markov chain Monte Carlo algorithm for sampling spatial partitions

We develop an Evolutionary Markov Chain Monte Carlo (EMCMC) algorithm for sampling spatial partitions that lie within a large, complex, and constrained spatial state space. Our algorithm combines the advantages of evolutionary algorithms (EAs) as optimization heuristics for state space traversal and the theoretical convergence properties of Markov Chain Monte Carlo algorithms for sampling from unknown distributions. Local optimality information that is identified via a directed search by our optimization heuristic is used to adaptively update a Markov chain in a promising direction within the framework of a Multiple-Try Metropolis Markov Chain model that incorporates a generalized Metropolis-Hastings ratio. We further expand the reach of our EMCMC algorithm by harnessing the computational power afforded by massively parallel computing architecture through the integration of a parallel EA framework that guides Markov chains running in parallel.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Scalable molecular dynamics on CPU and GPU architectures with NAMD

NAMD is a molecular dynamics program designed for high-performance simulations of very large biological objects on CPU- and GPU-based architectures. NAMD offers scalable performance on petascale parallel supercomputers consisting of hundreds of thousands of cores, as well as on inexpensive commodity clusters commonly found in academic environments. It is written in C++ and leans on Charm++ parallel objects for optimal performance on low-latency architectures. NAMD is a versatile, multipurpose code that gathers state-of-the-art algorithms to carry out simulations in apt thermodynamic ensembles, using the widely popular CHARMM, AMBER, OPLS, and GROMOS biomolecular force fields. Here, we review the main features of NAMD that allow both equilibrium and enhanced-sampling molecular dynamics simulations with numerical efficiency. We describe the underlying concepts utilized by NAMD and their implementation, most notably for handling long-range electrostatics; controlling the temperature, pressure, and pH; applying external potentials on tailored grids; leveraging massively parallel resources in multiple-copy simulations; and hybrid quantum-mechanical/molecular-mechanical descriptions. We detail the variety of options offered by NAMD for enhanced-sampling simulations aimed at determining free-energy differences of either alchemical or geometrical transformations and outline their applicability to specific problems. Last, we discuss the roadmap for the development of NAMD and our current efforts toward achieving optimal performance on GPU-based architectures, for pushing back the limitations that have prevented biologically realistic billion-atom objects to be fruitfully simulated, and for making large-scale simulations less expensive and easier to set up, run, and analyze. NAMD is distributed free of charge with its source code at www.ks.uiuc.edu.

high-performance computing↗
DOE OSTI2023

Parallel Simulation of Beam Dynamics in Particle Accelerators [Slides]

Particle accelerators are among the most versatile and important tools of scientific discovery. The Nation's accelerators are responsible for a wealth of advances in materials science, chemistry, the biosciences, particle physics, and nuclear physics. They also have important applications to national security, the environment, energy, medicine, and on the quality of people's lives. LANL has a long history of making pioneering contributions to Accelerator Science including key contributions to the field of Computational Accelerator Physics. These include the development of early beam dynamics codes with space charge (such as PARMILA and PARMELA), the development of rf cavity codes and magnet codes (including Poisson and Superfish), and the development and distribution of codes to the accelerator community through the Los Alamos Accelerator Code Group. LANL researchers also helped pioneer the development of massively parallel space-charge codes. In project t22_accelsim we have moved beyond electrostatic models of collective effects (i.e., solving the Poisson equation in the bunch frame) to fully electromagnetic models based on the Lienard-Wiechert formalism. This approach enables the large-scale simulation of radiation production and collective effects in high brightness electron beams. This is highly relevant to LANL given its future goal of developing an X-ray Free Electron Laser (XFEL). It also directly impacts a LANL LDRD project to develop an undulator-based non-invasive beam profile monitor for beams created in laser-plasma accelerator systems.

43 PARTICLE ACCELERATORS↗
DOE OSTI2025

Intelligently Partitioned Phasor-EMT Hybrid Simulations of Large-Scale, High-IBR Power Systems

As the penetration level of power electronics-interfaced renewables such as photovoltaics (PV) and wind has surged in modern electric grids, new operational risks caused by the dynamics of those inverter-based resources (IBRs) are emerging in parallel. Lessons learned from various grid events include that the impact of IBRs on system-level grid stability will become prominent along with the increase of renewables and that the short-timescale dynamic impacts of IBRs on grid stability are not fully captured by current commercial dynamic simulation tools [1] [2]. For example, IBRs can be controlled to mitigate those destabilizing interactions, but conventional phasor-domain tools (e.g. PSS/E, PSLF) often cannot capture that; likewise, the existing electromagnetic transient (EMT) simulation tools (e.g. PSCAD, EMTP) can simulate detailed IBR controls, but for large power systems with many IBRs, slow simulation speeds severely impede the ability to study dynamic events [3] [4]. Massively paralleling simulations using high-performance computing (HPC) can help address this, especially now that cloud-based HPC capability is widely available, but today s EMT tools are not HPC-compatible, and parallelization of dynamic simulation solvers is not trivial because each region can dynamically affect the others. Thus, dynamic simulation of grids with very large numbers of IBRs potentially poses a barrier to the ongoing energy transition.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

MEMS RF accelerators for nuclear energy and advanced manufacturing

Energetic ions are widely used to develop radiation hard structural materials and fuels for advanced nuclear energy. Ion beams are also used to generate neutrons for nuclear materials testing, as well as in a series of high impact, high value adding manufacturing processes (ranging from doping of semiconductors to hardening of materials against wear and to increase bio-compatibility of materials). But to date, high power beams of high energy ions are simply too expensive because they are delivered from large single beam accelerators. We have recently demonstrated that MEMS technology enables massively parallel, low cost batch fabrication of ion beams. We propose to scale intense ion accelerators based on MEMS (micro-electro mechanical systems) to high beam power (>10 kW). With our approach, hundreds to thousands of ion beamlets will be densely packed on silicon wafers. Ions are injected and accelerated across gaps formed in stacks of wafers, leading to uniquely high current densities for intense ion accelerators with variable kinetic energy (0.1 to 10 MeV) and variable ion species. Our team brings together experts in high power ion accelerators from Lawrence Berkeley National Laboratory and leading experts in MEMS technology from Cornell University. We will deliver a disruptive technology of low cost, flexible and massively scalable ion accelerators that will enable the rapid development of radiation hard nuclear materials for advanced nuclear energy and enable new applications in manufacturing.

43 PARTICLE ACCELERATORS↗
DOE OSTI2022

A parallel discrete dislocation dynamics/kinetic Monte Carlo method to study non-conservative plastic processes

Non-conservative processes play a fundamental role in plasticity and are behind important macroscopic phenomena such as creep, dynamic strain aging, loop raft formation, etc. In the most general case, vacancy-induced dislocation climb is the operating unit mechanism. While dislocation/vacancy interactions have been modeled in the literature using a variety of methods, the approaches developed rely on continuum descriptions of both the vacancy population and its fluxes. However, there are numerous situations in physics where point defect populations display heterogeneous concentrations and/or non-smooth kinetics. Here, a kinetic Monte Carlo (kMC) approach for modeling vacancy transport in response to arbitrary stress fields is used. Vacancies are treated as point particles and are coupled to the dislocation substructure representing a deformed material via an advection term defined by the local stress gradients. The stress fields and the dislocation substructure are evolved using a discrete dislocation dynamics (DDD) module. To extend the coupled model to the treatment of large systems, we have implemented it in the massively-parallel DDD code ParaDiS. To avoid numerical incompatibilities associated with merging deterministic (DDD) and stochastic (kMC) integration algorithms, we cast the entire elasto-plastic-diffusive problem within a single stochastic framework, taking advantage of a parallel kMC algorithm to evolve the system as a single event-driven process. The large-scale implementation enables the study of the evolution of a variety of dislocation-defect scenarios governed by non-conservative transport kinetics. After carrying out an exhaustive numerical and computational analysis of our parallel algorithm, we show results that emphasize situations where inhomogeneous vacancy dynamics are of relevance, and compare discrete kinetics to continuum solutions for several cases.

36 MATERIALS SCIENCE↗
DOE OSTI2021

The JOREK non-linear extended MHD code and applications to large-scale instabilities and their control in magnetically confined fusion plasmas

JOREK is a massively parallel fully implicit non-linear extended magneto-hydrodynamic (MHD) code for realistic tokamak X-point plasmas. It has become a widely used versatile simulation code for studying large-scale plasma instabilities and their control and is continuously developed in an international community with strong involvements in the European fusion research programme and ITER organization. This article gives a comprehensive overview of the physics models implemented, numerical methods applied for solving the equations and physics studies performed with the code. A dedicated section highlights some of the verification work done for the code. A hierarchy of different physics models is available including a free boundary and resistive wall extension and hybrid kinetic-fluid models. The code allows for flux-surface aligned iso-parametric finite element grids in single and double X-point plasmas which can be extended to the true physical walls and uses a robust fully implicit time stepping. Particular focus is laid on plasma edge and scrape-off layer (SOL) physics as well as disruption related phenomena. Among the key results obtained with JOREK regarding plasma edge and SOL, are deep insights into the dynamics of edge localized modes (ELMs), ELM cycles, and ELM control by resonant magnetic perturbations, pellet injection, as well as by vertical magnetic kicks. Also ELM free regimes, detachment physics, the generation and transport of impurities during an ELM, and electrostatic turbulence in the pedestal region are investigated. Regarding disruptions, the focus is on the dynamics of the thermal quench (TQ) and current quench triggered by massive gas injection and shattered pellet injection, runaway electron (RE) dynamics as well as the RE interaction with MHD modes, and vertical displacement events. Also the seeding and suppression of tearing modes (TMs), the dynamics of naturally occurring TQs triggered by locked modes, and radiative collapses are being studied.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Enhancing scalability of a matrix-free eigensolver for studying many-body localization

We propose several techniques to enhance the parallel scalability of a matrix-free eigensolver designed for studying many-body localization (MBL) of quantum spin chain models with nearest-neighbor interactions and on-site disorder. This type of problem is computationally challenging because the dimension of the associated Hamiltonian matrix grows exponentially with respect to the number of spins L, and we need to average over different realizations of the random disorder to obtain relevant statistical behavior. For each disorder realization, we need to compute eigenvalues from different regions of the spectrum and their corresponding eigenvectors. In previous work, the interior eigenstates for a single eigenvalue problem are computed via the shift-and-invert Lanczos algorithm. Due to the extremely high memory footprint of the LU factorizations, this technique is not well suited for large L’s. For example, we need thousands of compute nodes on modern high performance computing infrastructures to go beyond L = 24. The matrix-free approach does not suffer from this memory bottleneck, however, its scalability is limited by a computation and communication load imbalance. To reduce this imbalance and to significantly enhance the scalability of the matrix-free eigensolver, we reorder the matrix and leverage the consistent space runtime, CSPACER. We also show its efficiency in managing irregular communication patterns at scale compared to optimized MPI non-blocking two-sided and one-sided RMA implementation variants. This effort enables us to study MBL for spin chains with a larger number of spins. The efficiency and effectiveness of the proposed algorithm is demonstrated by computing eigenstates on a massively parallel many-core high performance computer.

METIS↗