19 research outputs found
A Hybrid Quantum–Classical Spectral Solver for Nonlinear Differential Equations
No full textWe investigate hybrid quantum–classical solvers for nonlinear boundary value problems using Chebyshev spectral collocation. Unlike prior methods such as H–DES, which repeatedly recompile circuits and encode the entire spectral basis on the quantum processor, our framework offloads only the residual minimisation to a quantum backend while retaining classical enforcement of boundary conditions. Two paradigms are considered: (i) gate-based residual minimisation on CUDA-Q using variational circuits to evaluate a Cubic Unconstrained Binary Optimisation (CUBO) cost, which naturally arises from the discretisation, and (ii) a Quadratic Unconstrained Binary Optimisation (QUBO) reformulation, which is required for execution on a quantum annealer, executed via a classical–quantum mapping. We further explore a CUBO extension on CUDA-Q and direct residual-to-energy mapping on annealers. Benchmarks confirm that the classical solver reproduces the analytic solution with spectral accuracy; among quantum-enhanced methods, the annealer-based QUBO yields the closest approximation. The gate-based CUBO solver improves upon a legacy variational baseline but exhibits a small interior bias due to limited circuit depth and precision. These findings underscore the complementary roles of annealers and gate-based devices in hybrid scientific computing and demonstrate a feasible workflow for the NISQ era rather than a speedup over classical methods. Recent progress in quantum algorithms for differential equations signals a rapidly maturing field with significant potential for practical quantum advantage.The author wish to thank Aditya Yadav, CEO of Automatski, for providing special access to the Automatski annealer simulators used in this work. His support and assistance were invaluable. The author would also like to thank Monica Van Dieren of NVIDIA for her guidance on using CUDA-Q
Distributed Memory Fast Fourier Transforms in the Exascale Era
No full textA summary of performance and software engineering concerns for the fast Fourier transform on distributed memory parallel computers is given. Index Terms—Fast Fourier Transform, Parallel software libraries, Computer performanc
Domain Decomposition Strategies for Communication-Intensive Workloads on Fugaku Supercomputer: Insights from a Comparative Study
No full textThe Fugaku supercomputer has a novel high-bandwidth and low-latency interconnect that enables good performance for communication-intensive workloads. This study focuses on the overhead of performance tool measurements when profiling Fast Fourier Transform (FFT)-based solvers for the Klein Gordon equation using the 2Decomp&FFT and FFTE libraries. The study compares the performance of the libraries using TAU and Extrae profiling and tracing tools, and examines the impact of domain decomposition strategies on strong scaling behavior and collective communications on Fugaku. The findings highlight the importance of auto-tuning and scalability in optimizing domain decomposition methods for efficient MPI communication, particularly in the context of strong scaling behavior and collective communications on high-performance computing architectures. Understanding the trade-offs between collective communications, profiling overheads, and strong scaling behavior is essential for developing and implementing effective domain decomposition strategies for communication-intensive workloads, ultimately contributing to improved performance and efficiency in scientific computing applications
Benchmarking Solvers for the One Dimensional Cubic Nonlinear Klein Gordon Equation on a Single Core
No full textTo determine the best method for solving a numerical problem modeled by a partial differential equation, one should consider the discretization of the problem, the computational hardware used and the implementation of the software solution. In solving a scientific computing problem, the level of accuracy can also be important, with some numerical methods being efficient for low accuracy simulations, but others more efficient for high accuracy simulations. Very few high performance benchmarking efforts allow the computational scientist to easily measure such tradeoffs in order to obtain an accurate enough numerical solution at a low computational cost. These tradeoffs are examined in the numerical solution of the one dimensional Klein Gordon equation on single cores of an ARM CPU, an AMD x86-64 CPU, two Intel x86-64 CPUs and a NEC SX-ACE vector processor. The work focuses on comparing the speed and accuracy of several high order finite difference spatial discretizations using a conjugate gradient linear solver and a fast Fourier transform based spatial discretization. In addition implementations using second and fourth order timestepping are also included in the comparison. The work uses accuracy-efficiency frontiers to compare the effectiveness of five hardware platformsBKM was partially supported by HPC Europa 3 (INFRAIA-2016-1-730897). Compute time on Isamabard was partially supported by ESPRC grant EP/P020224/1.. Acknowledgements. We thank Holger Berger, José Gracia, John Linford and Simon McIntosh-Smith for helpful conversations. We thank Höchstleistungsrechenzentrum Stuttgart (HLRS), the KAUST Supercomputing Laboratory, the University of Tartu High Performance Computing Center and the GW4 Isamabard project for access to supercomputing resources used in development and testing
Fundamental problems for a weakened infinite plate by a curvilinear hole in a half-plane
No full textComplex variable method (Cauchy integral method) has been applied to derive exact and closed expressions of Goursat functions for the first and second fundamental problems for an infinite plate weakened by a curvilinear hole. The area outside the hole with the hole itself is conformally mapped on the right half-plane by the use of a rational mapping function. This rational mapping consists of complex constants, in order to make the hole take different famous shapes, which can be found throughout the nature
Challenges in fluid flow simulations using Exascale computing
No full textIn this paper, I discuss the challenges in porting hydrodynamic codes to futuristic exascale HPC systems. In particular, we describe the computational complexities of finite difference method, pseudo-spectral method, and Fast Fourier Transform (FFT). We show how global data communication among the processors brings down the efficiency of pseudo-spectral codes and FFT. It is argued that FFT scaling may saturate at 1/2 million processors. However, finite difference and finite volume codes scale well beyond million processors, hence they are likely candidates to be tried on exascale systems. The codes based on spectral-element and Fourier continuation, that are more accurate than finite difference, could also scale well on such systems.The author thanks all the co-developers of FFTK, TARANG, and finite difference code of our group. Some of the key contributors to the codes are Anando Chatterjee, Rosan Samuel, Shaswat Bhattacharya, Ravi Samtaney, Fahad Anwer, Gaurav Gautam, Abhishek Kumar, Mani Chandra, Akash Anand, Awanish Tiwari, and Soumyadeep Chatterjee. In addition, author is grateful to Akash Anand, Samar Aseeri, Rooh Khurram, Bilel Hadri, V. Balaji, and Preeti Malakar for discussion and ideas; and to Ritu Arora, Venkatesh Shenoy, and Amitava Majumdar for organzing wonderful conference “Software Challenges to Exascale Computing (SCEC)”. Funding: This study was funded by research grants INT/RUS/RSF/P-03 by the Department of Science and Technology India. Our numerical simulations were performed on Cray XC40 (Shaheen II) and Blue Gene/P (Shaheen I) at KAUST supercomputing laboratory, Saudi Arabia, through project k105
A Comparison of Parallel Profiling Tools for Programs utilizing the FFT
No full textPrograms and datasets for a study of performance profiling for fast Fourier transform based solvers for the three dimensional Klein Gordon equation utilizing FFTE and 2decomp&FFT
mpi4py.futures: MPI-based asynchronous task execution for Python
No full textWe present mpi4py.futures, a lightweight, asynchronous task execution framework targeting the Python programming language and using the Message Passing Interface (MPI) for interprocess communication. mpi4py.futures follows the interface of the concurrent.futures package from the Python standard library and can be used as its drop-in replacement, while allowing applications to scale over multiple compute nodes. We discuss the design, implementation, and feature set of mpi4py.futures and compare its performance to other solutions on both shared and distributed memory architectures. On a shared-memory system, we show mpi4py.futures to consistently outperform Python's concurrent.futures with speedup ratios between 1.4X and 3.7X in throughput (tasks per second) and between 1.9X and 2.9X in bandwidth. On a Cray XC40 system, we compare mpi4py.futures to Dask – a well-known Python parallel computing package. Although we note more varied results, we show mpi4py.futures to outperform Dask in most scenarios.The research reported in this paper was funded by King Abdullah University of Science and Technology (KAUST). We are thankful to the KAUST Supercomputing Laboratory for their computing resources. We would like to thank the Dask developer community, and especially John Kirkham, for their feedback. Some discussions in this work were inspired by a series of blog posts by Matthew Rocklin, the initial author of Dask
Reproducibility in Benchmarking Parallel Fast Fourier Transform based Applications
No full textAn overview of concerns observed in allowing for reproducibility in parallel applications that heavily depend on the three dimensional distributed memory fast Fourier transform are summarized. Suggestions for reproducibility categories for benchmark results are given.We thank all the authors of [2] and those who have given a presentation on their use of the FFT in the ongoing discussion at www.fft.report. We also thank Robert Henschel for an overview of the SPEC benchmarking process at the benchmarking in the data center workshop at HPC Asia 2019. We thank RIKEN for the use of the K computer, HLRS for the use of Kabuki and Hazelhen, and the KAUST Supercomputing Laboratory for the use of Shaheen II. B.K.M. was partially supported by HPC Europa 3 (INFRAIA-2016-1-730897). B.K.M. thanks H. Berger, A. Chepstov, J. Gracia and A. Jocksch for helpful hints and discussions
