Harnessing the power of modern multi-GPU architectures, we present a massively parallel simulation system based on the Material Point Method (MPM) for simulating physical behaviors of materials ...undergoing complex topological changes, self-collision, and large deformations. Our system makes three critical contributions. First, we introduce a new particle data structure that promotes coalesced memory access patterns on the GPU and eliminates the need for complex atomic operations on the memory hierarchy when writing particle data to the grid. Second, we propose a kernel fusion approach using a new Grid-to-Particles-to-Grid (G2P2G) scheme, which efficiently reduces GPU kernel launches, improves latency, and significantly reduces the amount of global memory needed to store particle data. Finally, we introduce optimized algorithmic designs that allow for efficient sparse grids in a shared memory context, enabling us to best utilize modern multi-GPU computational platforms for hybrid Lagrangian-Eulerian computational patterns. We demonstrate the effectiveness of our method with extensive benchmarks, evaluations, and dynamic simulations with elastoplasticity, granular media, and fluid dynamics. In comparisons against an open-source and heavily optimized CPU-based MPM codebase Fang et al. 2019 on an elastic sphere colliding scene with particle counts ranging from 5 to 40 million, our GPU MPM achieves over 100x per-time-step speedup on a workstation with an Intel 8086K CPU and a single Quadro P6000 GPU, exposing exciting possibilities for future MPM simulations in computer graphics and computational science. Moreover, compared to the state-of-the-art GPU MPM method Hu et al. 2019a, we not only achieve 2x acceleration on a single GPU but our kernel fusion strategy and Array-of-Structs-of-Array (AoSoA) data structure design also generalizes to multi-GPU systems. Our multi-GPU MPM exhibits near-perfect weak and strong scaling with 4 GPUs, enabling performant and large-scale simulations on a 10243 grid with close to 100 million particles with less than 4 minutes per frame on a single 4-GPU workstation and 134 million particles with less than 1 minute per frame on an 8-GPU workstation.
The rapid increase in the performance of graphics hardware, coupled with recent improvements in its programmability, have made graphics hardware a compelling platform for computationally demanding ...tasks in a wide variety of application domains. In this report, we describe, summarize, and analyze the latest research in mapping general‐purpose computation to graphics hardware.
We begin with the technical motivations that underlie general‐purpose computation on graphics processors (GPGPU) and describe the hardware and software developments that have led to the recent interest in this field. We then aim the main body of this report at two separate audiences. First, we describe the techniques used in mapping general‐purpose computation to graphics hardware. We believe these techniques will be generally useful for researchers who plan to develop the next generation of GPGPU algorithms and techniques. Second, we survey and categorize the latest developments in general‐purpose application development on graphics hardware.
Neural graphics primitives, parameterized by fully connected neural networks, can be costly to train and evaluate. We reduce this cost with a versatile new input encoding that permits the use of a ...smaller network without sacrificing quality, thus significantly reducing the number of floating point and memory access operations: a small neural network is augmented by a multiresolution hash table of trainable feature vectors whose values are optimized through stochastic gradient descent. The multiresolution structure allows the network to disambiguate hash collisions, making for a simple architecture that is trivial to parallelize on modern GPUs. We leverage this parallelism by implementing the whole system using fully-fused CUDA kernels with a focus on minimizing wasted bandwidth and compute operations. We achieve a combined speedup of several orders of magnitude, enabling training of high-quality neural graphics primitives in a matter of seconds, and rendering in tens of milliseconds at a resolution of 1920×1080.
We propose a matrix-free parallel two-level deflation method combined with the Complex Shifted Laplacian Preconditioner (CSLP) for two-dimensional heterogeneous Helmholtz problems encountered in ...seismic exploration, antennas, and medical imaging. These problems pose challenges in terms of accuracy and convergence due to scalability issues with numerical solvers. Motivated by the limitations imposed by excessive computational time and memory constraints when employing a sequential solver with constructed matrices, we parallelize the two-level deflation method without constructing any matrices. Our approach utilizes preconditioned Krylov subspace methods and approximates the CSLP preconditioner with a parallel geometric multigrid V-cycle. For the two-level deflation, standard inter-grid deflation vectors and further high-order deflation vectors are considered. As another main contribution, the matrix-free Galerkin coarsening approach and a novel re-discretization scheme as well as high-order finite-difference schemes on the coarse grid are studied to obtain wavenumber-independent convergence. The optimal settings for an efficient coarse-grid problem solver are investigated. Numerical experiments of model problems show that the wavenumber independence has been obtained for medium wavenumbers. The matrix-free parallel framework shows satisfactory weak and strong parallel scalability.
•We introduce a parallel iterative solver for 2D heterogeneous Helmholtz problems with strong and weak scalability.•A matrix-free parallelization of the two-level deflation method is presented, reducing memory requirements.•We propose a novel re-discretization scheme for coarse grid operators, yielding wavenumber-independent convergence.•Optimization of coarse grid solver tolerance settings significantly enhances overall efficiency.
We have developed a parallel implementation of an Elasto-Viscoplastic Fast Fourier Transform-based (EVPFFT) micromechanical solver to enable computationally efficient crystal plasticity modeling for ...polycrystalline materials. Our primary focus lies in achieving performance portability, allowing a single EVPFFT implementation to run optimally on various homogeneous architectures, including multi-core Central Processing Units (CPUs), as well as on heterogeneous computer architectures comprising multi-core CPUs and Graphics Processing Units (GPUs) from different vendors. To accomplish this goal, we have leveraged MATAR, a C++ software library that simplifies the creation and utilization of multidimensional dense or sparse matrix and array data structures. These data structures are designed to be portable across diverse architectures through the use of Kokkos, a performance-portable library. Additionally, we have employed the Message Passing Interface (MPI) to efficiently distribute the computational workload among processors. The heFFTe (Highly Efficient FFT for Exascale) library is used to facilitate the performance portability of the fast Fourier transforms (FFTs) computation. The computational performance of EVPFFT is evaluated and presented in terms of parallel scalability and simulation runtime on different high-performance computing (HPC) architectures. The utility of the developed framework to efficiently simulate the micro-mechanical fields in polycrystalline microstructures in engineering applications is discussed.
Program Title: EVPFFT
CPC Library link to program files:https://doi.org/10.17632/2k8579fyyv.1
Developer's repository link:https://github.com/lanl/Fierro
Licensing provisions: BSD 3-Clause License
Programming language: C++
External routines/libraries: MPI, Kokkos, MATAR, HeFFTe, HDF5
Nature of problem: EVPFFT is a crystal plasticity code designed to compute micro-mechanical fields within a polycrystalline representative volume element (RVE) and predict the macroscale response of the RVE.
Solution method: EVPFFT uses the periodic Green's function method in Fourier space to solve the field equations of static stress equilibrium in a periodic spatial domain.
•MPI+X (where X can be CUDA, HIP, SYCL, OpenMP, or Pthreads) implementation of the EVPFFT model is developed.•Achieved performance portability on diverse computing architectures, including CPUs and GPUs.•Demonstrated parallel scalability across different representative volume element sizes using both multi-CPUs and multi-GPUs.•Future-proofed the EVPFFT program for evolving high-performance computing platforms.
This paper is concerned with computational issues related to penalized quantile regression (PQR) with ultrahigh dimensional predictors. Various algorithms have been developed for PQR, but they become ...ineffective and/or infeasible in the presence of ultrahigh dimensional predictors due to the storage and scalability limitations. The variable updating schema of the feature-splitting algorithm that directly applies the ordinary alternating direction method of multiplier (ADMM) to ultrahigh dimensional PQR may make the algorithm fail to converge. To tackle this hurdle, we propose an efficient and parallelizable algorithm for ultrahigh dimensional PQR based on the three-block ADMM. The compatibility of the proposed algorithm with parallel computing alleviates the storage and scalability limitations of a single machine in the large-scale data processing. We establish the rate of convergence of the newly proposed algorithm. In addition, Monte Carlo simulations are conducted to compare the finite sample performance of the proposed algorithm with that of other existing algorithms. The numerical comparison implies that the proposed algorithm significantly outperforms the existing ones. We further illustrate the proposed algorithm via an empirical analysis of a real-world data set.
The coupled-wave equations (CWEs) in nonlinear optics are the fundamental starting point in the study, analysis, and understanding of various frequency conversion processes in dielectric media ...subjected to intense laser radiation. In this work, a useful package for the modeling of optical parametric oscillators (OPOs) based on the Split-Step Fourier Method algorithm is presented. The algorithm is scripted in the CUDA programming language in order to speed up the calculations and obtain results in a relatively short time frame by using a graphics processing unit (GPU). Our results show a speedup higher than 50X for vector size of 214 in comparison with the analogous code scripted for running only in CPU. The package implements the CWEs to model the propagation of light in second-order nonlinear crystals widely used in optical frequency conversion experiments. In addition, the code allows the user to adapt the cavity configuration by selecting the resonant electric fields and/or incorporating intracavity elements. The package is useful for modeling OPOs or other mathematically similar problems.
Program Title:cuOPO
CPC Library link to program files:https://doi.org/10.17632/5djxwg4fbp.1
Developer's repository link:https://github.com/alfredos84/cuOPO
Licensing provisions: MIT
Programming language: CUDA
Nature of problem: The problem that is solved in this work is that of two or three coupled differential equations that describe the propagation of light in a second order nonlinear medium, allowing the three-wave mixing process. By placing the medium in an optical cavity, an optical parametric oscillator is formed. The optical cavity is modeled by including the appropriate boundary conditions for the differential equations. As a result we obtain the electric fields of the interacting waves in the time and frequency domains.
Solution method: The coupled differential equations are solved using the well-known fixed-step Split-Step Fourier method. Due to the eventual computational demand that some problems may have, we chose to implement the coupled equations in the CUDA programming language. This allows us to significantly speed up simulations, thanks to the computing power provided by a graphics processing unit (GPU) card. The output files obtained are the interacting electric fields, which have to be analyzed during post-processing.
In this paper, a Pearson’s correlation coefficient based decision tree (PCC-Tree) is established and its parallel implementation is developed in the framework of Map-Reduce (MR-PCC-Tree). The ...proposed methods employ Pearson’s correlation coefficient as a new measure of feature quality to confirm the optimal splitting attributes and splitting points in the growth of decision trees. Besides, the proposed MR-PCC-Tree adopts Map-Reduce technology to every component during the decision trees learning process for parallel computing, which mainly consists of a parallel Pearson’s correlation coefficient based splitting rule and a parallel splitting data method. The experimental analysis is conducted on a series of UCI benchmark data sets with different scales. In contrast to several traditional decision tree classifiers including BFT, C4.5, LAD, SC and NBT on 17 data sets, the proposed PCC-Tree is no worse than the traditional models as a whole. Furthermore, the experimental results on other 8 data sets show the feasibility of the proposed MR-PCC-Tree and its good parallel performance on reducing computational time for large-scale data classification problems.
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