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All sourcesNASA NTRSDOE OSTI
DOE OSTI2014

2HOT: An improved parallel hashed oct-tree N-body algorithm for cosmological simulation

Here we report on improvements made over the past two decades to our adaptive treecode N-body method (HOT). A mathematical and computational approach to the cosmological N-body problem is described, with performance and scalability measured up to 256k (218) processors. We present error analysis and scientific application results from a series of more than ten 69 billion (40963) particle cosmological simulations, accounting for 4×1020 floating point operations. These results include the first simulations using the new constraints on the standard model of cosmology from the Planck satellite. Our simulations set a new standard for accuracy and scientific throughput, while meeting or exceeding the computational efficiency of the latest generation of hybrid TreePM N-body methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2011

Applied & Computational MathematicsChallenges for the Design and Control of Dynamic Energy Systems

The Energy Independence and Security Act of 2007 (EISA) was passed with the goal 'to move the United States toward greater energy independence and security.' Energy security and independence cannot be achieved unless the United States addresses the issue of energy consumption in the building sector and significantly reduces energy consumption in buildings. Commercial and residential buildings account for approximately 40% of the U.S. energy consumption and emit 50% of CO{sub 2} emissions in the U.S. which is more than twice the total energy consumption of the entire U.S. automobile and light truck fleet. A 50%-80% improvement in building energy efficiency in both new construction and in retrofitting existing buildings could significantly reduce U.S. energy consumption and mitigate climate change. Reaching these aggressive building efficiency goals will not happen without significant Federal investments in areas of computational and mathematical sciences. Applied and computational mathematics are required to enable the development of algorithms and tools to design, control and optimize energy efficient buildings. The challenge has been issued by the U.S. Secretary of Energy, Dr. Steven Chu (emphasis added): 'We need to do more transformational research at DOE including computer design tools for commercial and residential buildings that enable reductions in energy consumption of up to 80 percent with investments that will pay for themselves in less than 10 years.' On July 8-9, 2010 a team of technical experts from industry, government and academia were assembled in Arlington, Virginia to identify the challenges associated with developing and deploying newcomputational methodologies and tools thatwill address building energy efficiency. These experts concluded that investments in fundamental applied and computational mathematics will be required to build enabling technology that can be used to realize the target of 80% reductions in energy consumption. In addition the finding was that there are tools and technologies that can be assembled and deployed in the short term - the next 3-5 years - that can be used to significantly reduce the cost and time effective delivery of moderate energy savings in the U.S. building stock. Simulation tools, which are a core strength of current DOE computational research programs, provide only a part of the answer by providing a basis for simulation enabled design. New investments will be required within a broad dynamics and control research agenda which must focus on dynamics, control, optimization and simulation of multi-scale energy systems during design and operation. U.S. investments in high performance and high productivity computing (HP2C) should be leveraged and coupled with advances in dynamics and control to impact both the existing building stock through retrofits and also new construction. The essential R&D areas requiring investment are: (1) Characterizing the Dynamics of Multi-scale Energy Systems; (2) Control and Optimization Methodologies of Multi-scale Energy Systems Under Uncertainty; and (3) Multiscale Modeling and Simulation Enabled Design and Operation. The concept of using design and control specific computational tools is a new idea for the building industry. The potential payoffs in terms of accelerated design cycle times, performance optimization and optimal supervisory control to obtain and maintain energy savings are huge. Recent advances in computational power, computer science, and mathematical algorithms offer the foundations to address the control problems presented by the complex dynamics of whole building systems. The key areas for focus and associated metrics with targets for establishing competitiveness in energy efficient building design and operation are: (1) Scalability - Current methodology and tools can provide design guidance for very low energy buildings in weeks to months; what is needed is hours to days. A 50X improvement is needed. (2) Installation and commissioning - Current methodology and tools can target a three month window for commissioning of building subsystems; what is needed is one week. A 10X improvement is needed. (3) Quality - Current design tools can achieve 30% accuracy; what is needed to make design decisions is 5% with quantification of uncertainty. A 5X improvement is needed. These challenges cannot be overcome by raw computational power alone and require the development of new algorithms. Here algorithms mean much more than simulating the building physics but need to be inclusive of a much better understanding of the building and the control systems associated with the building and to capture the entire set of dynamics. The algorithmsmust represent computationally new mathematical approaches to modeling, simulation, optimization and control of large multi-scale dynamic systems and bringing these elements to bear on industry in simulation enabled design approaches.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2018

Parallelizable adjoint stencil computations using transposed forward-mode algorithmic differentiation

Algorithmic differentiation (AD) is a tool for generating discrete adjoint solvers, which efficiently compute gradients of functions with many inputs, for example for use in gradient-based optimization. AD is often applied to large computations such as stencil operators, which are an important part of most structured-mesh PDE solvers. Stencil computations are often parallelized, for example by using OpenMP, and optimized by using techniques such as cache-blocking and tiling to fully utilize multicore CPUs and many-core accelerators and GPUs. Differentiating these codes with conventional reverse-mode AD results in adjoint codes that cannot be expressed as stencil operations and may not be easily parallelizable. They thus leave most of the compute power of modern architectures unused. We present a method that combines forward-mode AD and loop transformation to generate adjoint solvers that use the same memory access pattern as the original computation that they are derived from and can benefit from the same optimization techniques. The effectiveness of this method is demonstrated by generating a scalable adjoint CFD solver for multicore CPUs and Xeon Phi accelerators.

algorithmic differentiation↗
DOE OSTI2021

Data acquisition and slow control interface for the Mu2e experiment

The Mu2e experiment at the Fermilab Muon Campus will search for the coherent neutrinoless conversion of a muon into an electron in the field of an aluminum nucleus with a sensitivity improvement by a factor of 10000 over existing limits. The Mu2e Trigger and Data Acquisition System (TDAQ) uses otsdaq as the online Data Acquisition System (DAQ) solution. Developed at Fermilab, otsdaq integrates both the artdaq DAQ and the art analysis frameworks for event transfer, filtering, and processing. otsdaq is an online DAQ software suite with a focus on flexibility and scalability and provides a multi-user, web-based, interface accessible through a web browser. The data stream from the detector subsystems is read by a software filter algorithm that selects events which are combined with the data flux coming from a cosmic ray veto system. The Detector Control System (DCS) has been developed using the Experimental Physics and Industrial Control System (EPICS) open source platform for monitoring, controlling, alarming, and archiving. The DCS system has been integrated into otsdaq. A prototype of the TDAQ and the DCS systems has been built at Fermilab's Feynman Computing Center. In this study, we report on the progress of the integration of this prototype in the online otsdaq software.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2016

A Hartree-Fock Application Using UPC++ and the New DArray Library

The Hartree-Fock (HF) method is the fundamental first step for incorporating quantum mechanics into many-electron simulations of atoms and molecules, and it is an important component of computational chemistry toolkits like NWChem. The GTFock code is an HF implementation that, while it does not have all the features in NWChem, represents crucial algorithmic advances that reduce communication and improve load balance by doing an up-front static partitioning of tasks, followed by work stealing whenever necessary. To enable innovations in algorithms and exploit next generation exascale systems, it is crucial to support quantum chemistry codes using expressive and convenient programming models and runtime systems that are also efficient and scalable. Here, this paper presents an HF implementation similar to GTFock using UPC++, a partitioned global address space model that includes flexible communication, asynchronous remote computation, and a powerful multidimensional array library. UPC++ offers runtime features that are useful for HF such as active messages, a rich calculus for array operations, hardware-supported fetch-and-add, and functions for ensuring asynchronous runtime progress. We present a new distributed array abstraction, DArray, that is convenient for the kinds of random-access array updates and linear algebra operations on block-distributed arrays with irregular data ownership. Finally, we analyze the performance of atomic fetch-and-add operations (relevant for load balancing) and runtime attentiveness, then compare various techniques and optimizations for each. Our optimized implementation of HF using UPC++ and the DArrays library shows up to 20% improvement over GTFock with Global Arrays at scales up to 24,000 cores.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Real-Time Stochastic Optimization of Complex Energy Systems on High-Performance Computers

A scalable approach computes in operationally-compatible time the energy dispatch under uncertainty for electrical power grid systems of realistic size with thousands of scenarios. The authors propose several algorithmic and implementation advances in their parallel solver PIPS-IPM for stochastic optimization problems. New developments include a novel, incomplete, augmented, multicore, sparse factorization implemented within the PARDISO linear solver and new multicore- and GPU-based dense matrix implementations. They show improvement on the interprocess communication on Cray XK7 and XC30 systems. PIPS-IPM is used to solve 24-hour horizon power grid problems with up to 1.95 billion decision variables and 1.94 billion constraints on Cray XK7 and Cray XC30, with observed parallel efficiencies and solution times within an operationally defined time interval. To the authors' knowledge, "real-time"-compatible performance on a broad range of architectures for this class of problems hasn't been possible prior to this work

Computer Science↗
DOE OSTI2014

A Communication-Optimal Framework for Contracting Distributed Tensors

Tensor contractions are extremely compute intensive generalized matrix multiplication operations encountered in many computational science fields, such as quantum chemistry and nuclear physics. Unlike distributed matrix multiplication, which has been extensively studied, limited work has been done in understanding distributed tensor contractions. In this paper, we characterize distributed tensor contraction algorithms on torus networks. We develop a framework with three fundamental communication operators to generate communication-efficient contraction algorithms for arbitrary tensor contractions. We show that for a given amount of memory per processor, our framework is communication optimal for all tensor contractions. We demonstrate performance and scalability of our framework on up to 262,144 cores of BG/Q supercomputer using five tensor contraction examples.

communication efficiency↗
DOE OSTI2015

Diagnosis of Performance Faults in LargeScale MPI Applications via Probabilistic Progress-Dependence Inference

Debugging large-scale parallel applications is challenging. Most existing techniques provide little information about failure root causes. Further, most debuggers significantly slow down program execution, and run sluggishly with massively parallel applications. This paper presents a novel technique that scalably infers the tasks in a parallel program on which a failure occurred, as well as the code in which it originated. Our technique combines scalable runtime analysis with static analysis to determine the least-progressed task(s) and to identify the code lines at which the failure arose. We present a novel algorithm that infers probabilistically progress dependence among MPI tasks using a globally constructed Markov model that represents tasks' control-flow behavior. In comparison to previous work, our algorithm infers more precisely the least-progressed task. Further, we combine this technique with static backward slicing analysis, further isolating the code responsible for the current state. A blind study demonstrates that our technique isolates the root cause of a concurrency bug in a molecular dynamics simulation, which only manifests itself at 7,996 tasks or more. We extensively evaluate fault coverage of our technique via fault injections in 10 HPC benchmarks and show that our analysis takes less than a few seconds on thousands of parallel tasks.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Coupled cluster theory on modern heterogeneous supercomputers

This study examines the computational challenges in elucidating intricate chemical systems, particularly through ab-initio methodologies. This work highlights the Divide-Expand-Consolidate (DEC) approach for coupled cluster (CC) theory—a linear-scaling, massively parallel framework—as a viable solution. Detailed scrutiny of the DEC framework reveals its extensive applicability for large chemical systems, yet it also acknowledges inherent limitations. To mitigate these constraints, the cluster perturbation theory is presented as an effective remedy. Attention is then directed towards the CPS (D-3) model, explicitly derived from a CC singles parent and a doubles auxiliary excitation space, for computing excitation energies. The reviewed new algorithms for the CPS (D-3) method efficiently capitalize on multiple nodes and graphical processing units, expediting heavy tensor contractions. As a result, CPS (D-3) emerges as a scalable, rapid, and precise solution for computing molecular properties in large molecular systems, marking it an efficient contender to conventional CC models.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1996

Design and implementation of scalable tape archiver

In order to reduce costs, computer manufacturers try to use commodity parts as much as possible. Mainframes using proprietary processors are being replaced by high performance RISC microprocessor-based workstations, which are further being replaced by the commodity microprocessor used in personal computers. Highly reliable disks for mainframes are also being replaced by disk arrays, which are complexes of disk drives. In this paper we try to clarify the feasibility of a large scale tertiary storage system composed of 8-mm tape archivers utilizing robotics. In the near future, the 8-mm tape archiver will be widely used and become a commodity part, since recent rapid growth of multimedia applications requires much larger storage than disk drives can provide. We designed a scalable tape archiver which connects as many 8-mm tape archivers (element archivers) as possible. In the scalable archiver, robotics can exchange a cassette tape between two adjacent element archivers mechanically. Thus, we can build a large scalable archiver inexpensively. In addition, a sophisticated migration mechanism distributes frequently accessed tapes (hot tapes) evenly among all of the element archivers, which improves the throughput considerably. Even with the failures of some tape drives, the system dynamically redistributes hot tapes to the other element archivers which have live tape drives. Several kinds of specially tailored huge archivers are on the market, however, the 8-mm tape scalable archiver could replace them. To maintain high performance in spite of high access locality when a large number of archivers are attached to the scalable archiver, it is necessary to scatter frequently accessed cassettes among the element archivers and to use the tape drives efficiently. For this purpose, we introduce two cassette migration algorithms, foreground migration and background migration. Background migration transfers cassettes between element archivers to redistribute frequently accessed cassettes, thus balancing the load of each archiver. Background migration occurs the robotics are idle. Both migration algorithms are based on access frequency and space utility of each element archiver. To normalize these parameters according to the number of drives in each element archiver, it is possible to maintain high performance even if some tape drives fail. We found that the foreground migration is efficient at reducing access response time. Beside the foreground migration, the background migration makes it possible to track the transition of spatial access locality quickly.

Nemoto, Toshihiro↗
NASA NTRS1997

A Comparison of PETSC Library and HPF Implementations of an Archetypal PDE Computation

Two paradigms for distributed-memory parallel computation that free the application programmer from the details of message passing are compared for an archetypal structured scientific computation a nonlinear, structured-grid partial differential equation boundary value problem using the same algorithm on the same hardware. Both paradigms, parallel libraries represented by Argonne's PETSC, and parallel languages represented by the Portland Group's HPF, are found to be easy to use for this problem class, and both are reasonably effective in exploiting concurrency after a short learning curve. The level of involvement required by the application programmer under either paradigm includes specification of the data partitioning (corresponding to a geometrically simple decomposition of the domain of the PDE). Programming in SPAM style for the PETSC library requires writing the routines that discretize the PDE and its Jacobian, managing subdomain-to-processor mappings (affine global- to-local index mappings), and interfacing to library solver routines. Programming for HPF requires a complete sequential implementation of the same algorithm, introducing concurrency through subdomain blocking (an effort similar to the index mapping), and modest experimentation with rewriting loops to elucidate to the compiler the latent concurrency. Correctness and scalability are cross-validated on up to 32 nodes of an IBM SP2.

Hayder, M. Ehtesham↗
NASA NTRS2000

HTMT-class Latency Tolerant Parallel Architecture for Petaflops Scale Computation

Computational Aero Sciences and other numeric intensive computation disciplines demand computing throughputs substantially greater than the Teraflops scale systems only now becoming available. The related fields of fluids, structures, thermal, combustion, and dynamic controls are among the interdisciplinary areas that in combination with sufficient resolution and advanced adaptive techniques may force performance requirements towards Petaflops. This will be especially true for compute intensive models such as Navier-Stokes are or when such system models are only part of a larger design optimization computation involving many design points. Yet recent experience with conventional MPP configurations comprising commodity processing and memory components has shown that larger scale frequently results in higher programming difficulty and lower system efficiency. While important advances in system software and algorithms techniques have had some impact on efficiency and programmability for certain classes of problems, in general it is unlikely that software alone will resolve the challenges to higher scalability. As in the past, future generations of high-end computers may require a combination of hardware architecture and system software advances to enable efficient operation at a Petaflops level. The NASA led HTMT project has engaged the talents of a broad interdisciplinary team to develop a new strategy in high-end system architecture to deliver petaflops scale computing in the 2004/5 timeframe. The Hybrid-Technology, MultiThreaded parallel computer architecture incorporates several advanced technologies in combination with an innovative dynamic adaptive scheduling mechanism to provide unprecedented performance and efficiency within practical constraints of cost, complexity, and power consumption. The emerging superconductor Rapid Single Flux Quantum electronics can operate at 100 GHz (the record is 770 GHz) and one percent of the power required by convention semiconductor logic. Wave Division Multiplexing optical communications can approach a peak per fiber bandwidth of 1 Tbps and the new Data Vortex network topology employing this technology can connect tens of thousands of ports providing a bi-section bandwidth on the order of a Petabyte per second with latencies well below 100 nanoseconds, even under heavy loads. Processor-in-Memory (PIM) technology combines logic and memory on the same chip exposing the internal bandwidth of the memory row buffers at low latency. And holographic storage photorefractive storage technologies provide high-density memory with access a thousand times faster than conventional disk technologies. Together these technologies enable a new class of shared memory system architecture with a peak performance in the range of a Petaflops but size and power requirements comparable to today's largest Teraflops scale systems. To achieve high-sustained performance, HTMT combines an advanced multithreading processor architecture with a memory-driven coarse-grained latency management strategy called "percolation", yielding high efficiency while reducing the much of the parallel programming burden. This paper will present the basic system architecture characteristics made possible through this series of advanced technologies and then give a detailed description of the new percolation approach to runtime latency management.

Sterling, Thomas↗
DOE OSTI2021

Nonlinear Matrix Approximation with Radial Basis Function Components

We introduce and investigate matrix approximation by decomposition into a sum of radial basis function (RBF) components. An RBF component is a generalization of the outer product between a pair of vectors, where an RBF function replaces the scalar multiplication between individual vector elements. Even though the RBF functions are positive definite, the summation across components is not restricted to convex combinations and allows us to compute the decomposition for any real matrix that is not necessarily symmetric or positive definite. We formulate the problem of seeking such a decomposition as an optimization problem with a nonlinear and non-convex loss function. Several modern versions of the gradient descent method, including their scalable stochastic counterparts, are used to solve this problem. We provide extensive empirical evidence of the effectiveness of the RBF decomposition and that of the gradient-based fitting algorithm. While being conceptually motivated by singular value decomposition (SVD), our proposed nonlinear counterpart outperforms SVD by drastically reducing the memory required to approximate a data matrix with the same L2 error for a wide range of matrix types. For example, it leads to 2 to 6 times memory save for Gaussian noise, graph adjacency matrices, and kernel matrices. Moreover, this proximity-based decomposition can offer additional interpretability in applications that involve, e.g., capturing the inner low-dimensional structure of the data, retaining graph connectivity structure, and preserving the acutance of images.

Rebrova, Elizaveta↗
DOE OSTI2023

Distributed approximate minimal Steiner trees with millions of seed vertices on billion-edge graphs

In this report, we present a parallel 2-approximation Steiner minimal tree algorithm and its MPI-based distributed implementation. In place of expensive distance computations between all pairs of seed vertices, the solution we employ exploits a cheaper Voronoi cell computation. Our design leverages asynchronous processing and message prioritization to accelerate convergence of distance computations, and harnesses vertex and edge centric processing to offer fast time-to-solution. We demonstrate scalability and performance using real-world graphs with up to 128 billion edges and 512 compute nodes, and show the ability to find Steiner trees with up to one million seed vertices. Using 12 data instances, we present comparison with the state-of-the-art exact solver, SCIP-Jack, and two sequential 2-approximate algorithms. We empirically show that, on average, the total distance of the Steiner tree identified by our solution is 1.1290 times greater than the Steiner minimal tree – well within the theoretical approximation bound of 2.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Performance analysis of distributed symmetric sparse matrix vector multiplication algorithm for multi-core architectures

In this article, sparse matrix vector multiply (SpMVM) is an important kernel that frequently arises in high performance computing applications. Due to its low arithmetic intensity, several approaches have been proposed in literature to improve its scalability and efficiency in large scale computations. In this paper, our target systems are high end multi-core architectures and we use messaging passing interface + open multiprocessing hybrid programming model for parallelism. We analyze the performance of recently proposed implementation of the distributed symmetric SpMVM, originally developed for large sparse symmetric matrices arising in ab initio nuclear structure calculations. We also study important features of this implementation and compare with previously reported implementations that do not exploit underlying symmetry. Our SpMVM implementations leverage the hybrid paradigm to efficiently overlap expensive communications with computations. Our main comparison criterion is the "CPU core hours" metric, which is the main measure of resource usage on supercomputers. We analyze the effects of topology-aware mapping heuristic using simplified network load model. Furthermore, we have tested the different SpMVM implementations on two large clusters with 3D Torus and Dragonfly topology. Our results show that the distributed SpMVM implementation that exploits matrix symmetry and hides communication yields the best value for the "CPU core hours" metric and significantly reduces data movement overheads.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Using Graph Partitioning for Scalable Distributed Quantum Molecular Dynamics

The simulation of the physical movement of multi-body systems at an atomistic level, with forces calculated from a quantum mechanical description of the electrons, motivates a graph partitioning problem studied in this article. Several advanced algorithms relying on evaluations of matrix polynomials have been published in the literature for such simulations. We aim to use a special type of graph partitioning to efficiently parallelize these computations. For this, we create a graph representing the zero–nonzero structure of a thresholded density matrix, and partition that graph into several components. Each separate submatrix (corresponding to each subgraph) is then substituted into the matrix polynomial, and the result for the full matrix polynomial is reassembled at the end from the individual polynomials. This paper starts by introducing a rigorous definition as well as a mathematical justification of this partitioning problem. We assess the performance of several methods to compute graph partitions with respect to both the quality of the partitioning and their runtime.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2011

NWChem: scalable parallel computational chemistry

NWChem is a general purpose computational chemistry code specifically designed to run on distributed memory parallel computers. The core functionality of the code focuses on molecular dynamics, Hartree-Fock and density functional theory methods for both plane-wave basis sets as well as Gaussian basis sets, tensor contraction engine based coupled cluster capabilities and combined quantum mechanics/molecular mechanics descriptions. It was realized from the beginning that scalable implementations of these methods required a programming paradigm inherently different from what message passing approaches could offer. In response a global address space library, the Global Array Toolkit, was developed. The programming model it offers is based on using predominantly one-sided communication. This model underpins most of the functionality in NWChem and the power of it is exemplified by the fact that the code scales to tens of thousands of processors. In this paper the core capabilities of NWChem are described as well as their implementation to achieve an efficient computational chemistry code with high parallel scalability. NWChem is a modern, open source, computational chemistry code1 specifically designed for large scale parallel applications2. To meet the challenges of developing efficient, scalable and portable programs of this nature a particular code design was adopted. This code design involved two main features. First of all, the code is build up in a modular fashion so that a large variety of functionality can be integrated easily. Secondly, to facilitate writing complex parallel algorithms the Global Array toolkit was developed. This toolkit allows one to write parallel applications in a shared memory like approach, but offers additional mechanisms to exploit data locality to lower communication overheads. This framework has proven to be very successful in computational chemistry but is applicable to any engineering domain. Within the context created by the features above NWChem has grown into a general purpose computational chemistry code that supports a wide variety of energy expressions and capabilities to calculate properties based there upon. The main energy expressions are classical mechanics force fields, Hartree-Fock and DFT both for finite systems and condensed phase systems, coupled cluster, as well as QM/MM. For most energy expressions single point calculations, geometry optimizations, excited states, and other properties are available. Below we briefly discuss each of the main energy expressions and the critical points involved in scalable implementations thereof.

99 GENERAL AND MISCELLANEOUS↗
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↗