Parallel Graphics Processing Units Research Articles

Force Field X: A computational microscope to study genetic variation and organic crystals using theory and experiment.

Force Field X (FFX) is an open-source software package for atomic resolution modeling of genetic variants and organic crystals that leverages advanced potential energy functions and experimental data. FFX currently consists of nine modular packages with novel algorithms that include global optimization via a many-body expansion, acid-base chemistry using polarizable constant-pH molecular dynamics, estimation of free energy differences, generalized Kirkwood implicit solvent models, and many more. Applications of FFX focus on the use and development of a crystal structure prediction pipeline, biomolecular structure refinement against experimental datasets, and estimation of the thermodynamic effects of genetic variants on both proteins and nucleic acids. The use of Parallel Java and OpenMM combines to offer shared memory, message passing, and graphics processing unit parallelization for high performance simulations. Overall, the FFX platform serves as a computational microscope to study systems ranging from organic crystals to solvated biomolecular systems.

Incorporation of adaptive compression into a GPU parallel computing framework for analyzing large-scale vessel trajectories

Automatic Identification System (AIS) offers a wealth of vessel navigation data, which underpins research in maritime data mining, situational awareness, and knowledge discovery within the realm of intelligent transportation systems. The flourishing marine industry has prompted AIS satellites and base stations to generate massive amounts of vessel trajectory data, escalating both data storage and calculation costs. The conventional Douglas-Peucker (DP) algorithm used for trajectory compression sets a uniform threshold, which hampers effective compression. Additionally, compressing and accelerating the computation of large datasets poses a significant challenge in real-world applications. To address these limitations, this paper aims to develop a new Graphics Processing Unit (GPU) parallel computing and compression framework that enables the acceleration of the optimal threshold calculation for each trajectory automatically in maritime big data mining. It achieves this by incorporating a new Adaptive DP with Speed and Course (ADPSC) algorithm, which utilizes the dynamic navigation characteristics of different vessels. It can effectively solve the associated computational time cost concern when using the ADPSC algorithm to compress vast trajectory datasets in the real world. Additionally, this paper proposes a novel evaluation metric for assessing compression efficacy based on the Dynamic Time Warping (DTW) method. Comprehensive experiments encompass vessel trajectory datasets from three representative research areas: Tianjin Port, Chengshan Jiao Promontory, and Caofeidian Port. The experimental results demonstrate that 1) the newly developed ADPSC method outperforms in terms of compression, and 2) the designed GPU parallel computing framework can significantly shorten the compression time for extensive datasets. The GPU-accelerated compression methodology not only minimizes storage and transmission costs for data from both manned and unmanned vessels but also enhances data processing speed, supporting real-time decision-making. From a theoretical perspective, it provides the key to the puzzle of realizing the real-time anti-collision of manned and unmanned ships, particularly in complex waters. It hence makes significant contributions to maritime safety in the autonomous shipping era.

A GPU-accelerated adaptation of the PSO algorithm for multi-objective optimization applied to artificial neural networks to predict energy consumption

Optimization research often confronts the challenge of developing time consuming processes. This article introduces an innovative approach that leverages the computational power of Graphics Processing Units (GPUs) to speed up that optimization process. We present an innovative adaptation of Particle Swarm Optimisation (PSO) to meet the requirements of multiobjective optimization problems. This approach aims to leverage the strengths of a multi-objective approach to perform energy consumption prediction using neural networks. By employing GPU parallel techniques, our method not only speeds up the optimization process but also enhances the efficiency of neural network training execution. The main advantage of our approach lies in its dual ability to simultaneously optimizing neural network architectures by determining the minimum number of hidden neurons and fitting the weights of the networks in order to achieve the lowest error. Preliminary results suggest a notable enhancement in prediction accuracy of forecasting electric energy consumption, as a result of optimizing the architecture and parameters of the neural network using the proposed method. This PSO adaptation stands out for its ability to address complex problems, increase efficiency and produce accurate predictions, making it a novel solution in Machine Learning heuristic methods for application in the solution of advanced prediction problems with time constraints from time series.

Numerical simulation of supersonic combustion chemical reactions based on multi-GPUs

To achieve a large-scale and efficient numerical solution to supersonic combustion chemical reaction problems, a numerical simulation algorithm for combustion chemical reactions was established on a graphics processing unit (GPU). Numerical simulation of the combustion chemical reaction of a hydrocarbon fuel/air mixture in a supersonic combustor was conducted to verify the accuracy of GPU parallel calculation results and analyze its parallel performance. Numerical results show that GPU parallel computing can accurately simulate the complex flowfield in the combustor. The distribution law of wall pressure is basically consistent with the experimental values, and the numerical agreement is good, indicating that the numerical simulation algorithm for the multi-GPU supersonic combustion chemical reaction established in this paper is correct and reliable. On the Tesla V100 GPU parallel computing platform, the speedup of GPU parallel computing can reach over 100 times, greatly improving computational efficiency. When the grid size is 18.64 million, the parallel efficiency of single and double precision floating-point operations on four GPUs is 66.2% and 69.1%, respectively, which demonstrates that the multi-GPU parallel algorithm has good scalability.

Electromagnetic scattering and imaging simulation of extremely large-scale sea-ship scene based on GPU parallel technology

Aiming to solve the bottleneck problem of electromagnetic scattering simulation in the scenes of extremely large-scale seas and ships, a high-frequency method by using graphics processing unit (GPU) parallel acceleration technique is proposed. For the implementation of different electromagnetic methods of physical optics (PO), shooting and bouncing ray (SBR) and physical theory of diffraction (PTD), a parallel computing scheme based on the central processing unit (CPU)-GPU parallel computing scheme is realized to balance computing tasks. Finally, a multi-GPU framework is further proposed to solve the computational difficulty caused by the massive number of ray tubes in the ray tracing process. By using the established simulation platform, signals of ships at different seas are simulated and their images are achieved as well. It is shown that the higher sea states degrade the averaged peak signal-to-noise ratio (PSNR) of radar image.

Volumetric lattice Boltzmann method for pore-scale mass diffusion-advection process in geopolymer porous structures

Porous materials present significant advantages for absorbing radioactive isotopes in nuclear waste streams. To improve absorption efficiency in nuclear waste treatment, a thorough understanding of the diffusion-advection process within porous structures is essential for material design. In this study, we present advancements in the volumetric lattice Boltzmann method (VLBM) for modeling and simulating pore-scale diffusion-advection of radioactive isotopes within geopolymer porous structures. These structures are created using the phase field method (PFM) to precisely control pore architectures. In our VLBM approach, we introduce a concentration field of an isotope seamlessly coupled with the velocity field and solve it by the time evolution of its particle population function. To address the computational intensity inherent in the coupled lattice Boltzmann equations for velocity and concentration fields, we implement graphics processing unit (GPU) parallelization. Validation of the developed model involves examining the flow and diffusion fields in porous structures. Remarkably, good agreement is observed for both the velocity field from VLBM and multiphysics object-oriented simulation environment (MOOSE), and the concentration field from VLBM and the finite difference method (FDM). Furthermore, we investigate the effects of background flow, species diffusivity, and porosity on the diffusion-advection behavior by varying the background flow velocity, diffusion coefficient, and pore volume fraction, respectively. Notably, all three parameters exert an influence on the diffusion-advection process. Increased background flow and diffusivity markedly accelerate the process due to increased advection intensity and enhanced diffusion capability, respectively. Conversely, increasing the porosity has a less significant effect, causing a slight slowdown of the diffusion-advection process due to the expanded pore volume. This comprehensive parametric study provides valuable insights into the kinetics of isotope uptake in porous structures, facilitating the development of porous materials for nuclear waste treatment applications.

ACCELERATING ORE SINTERING MATHEMATICAL MODEL USING GPU

The study aims to enhance the efficiency and computational speed of the ore sintering model through the utilization of graphics processing units (GPUs). The purpose of this research is to address the growing demand for faster and more scalable simulations in the field of ore sintering, a crucial process in the production of iron and steel. Methodology involves the integration of parallel computing capabilities offered by GPUs into the existing ore sintering model. By leveraging the parallel processing power of GPUs, the computational workload is distributed across multiple cores, significantly reducing the simulation time. Results demonstrate a substantial acceleration in the ore sintering simulation process. Comparative analyses between CPU and GPU implementations reveal a remarkable reduction in computation time, thereby enabling real-time or near-real-time simulations. The achieved speedup not only enhances the efficiency of ore sintering modeling but also opens avenues for exploring larger and more complex scenarios. This is the successful integration of GPU parallel computing into the ore sintering model, showcasing the adaptability of advanced computational technologies to traditional industrial processes. The study contributes to the field by bridging the gap between computational power and metallurgical simulations, demonstrating the potential for GPU acceleration in other areas of metallurgical processes. Practical significance of this research is underscored by its potential to revolutionize the ore sintering industry. Faster simulations facilitate quicker decision-making in process optimization, leading to improved energy efficiency and reduced environmental impact. This research sets the stage for the broader adoption of GPU acceleration in metallurgical modeling, signaling a paradigm shift towards more efficient and sustainable industrial practices

Comparative analysis of soft-error sensitivity in LU decomposition algorithms on diverse GPUs

Graphics processing units (GPUs) have become integral to embedded systems and supercomputing centres due to their large memory, cutting-edge technology and high performance per watt. However, their susceptibility to transient errors requires a comprehensive analysis of error sensitivity, as well as the development of error mitigation techniques and fault-tolerant algorithms. This study focuses on evaluating the soft-error sensitivity of two distinct versions of LU decomposition algorithms implemented on two very different GPUs—a low-power SoC embedded GPU and a high-performance massively parallel GPU. Through extensive fault injection campaigns on both GPUs, we examine the vulnerability of the algorithms, identify error causes, and determine critical code components requiring enhanced protection. The experiments reveal that most single bit flip fault injections in the instruction results lead to erroneous outcomes or unrecoverable errors. Notably, efficient GPU resource utilisation can increase the number of masked errors, thereby enhancing error resilience. Additionally, while different parts of the code exhibit similar error occurrence types and rates, the propagation of errors to elements within the result matrix differs significantly.

Study on the flooding characteristics of a deep-water submarine based on δ plus-smoothed particle hydrodynamics method and graphic processing units acceleration

The process of a damaged ship flooding is a complicated free surface flow problem. There is a complex coupling effect between the ship cabin and the flow inside and outside of the cabin. In this paper, a GPU (graphic processing unit)-δ+-SPH (smoothed particle hydrodynamics) numerical model for the cabin flooding in deep-water environments is developed based on GPU parallel acceleration technology and Nvidia's CUDA (compute unified device architecture). First, the computational accuracy and efficiency of this numerical model are verified by experiments results on the water flooding of a simple damaged cabin model. Furthermore, the flooding characteristics of a submarine cabin are analyzed, considering different numbers of damaged cabins, depths, and opening positions. Finally, the progressive flooding and the dynamic response characteristics of a full-scale submarine model are investigated. The results show that the process of progressive flooding in a submarine cabin is characterized by its rapidity and intensity. Different factors, for example, damaged cabin numbers, cabin depths, and opening positions, have great influences on the process of flooding and the motion of the submarine cabin. This study can offer valuable technical assistance in the post-damage remediation process.

High-efficiency computation for electromagnetic forming process: An explicit-implicit GPU approach

Low computational efficiency is one of the crucial challenges in electromagnetic forming process simulation. However, the huge gap in switching from the electromagnetic field to mechanics hinders the development of high-efficiency parallel coupling. A graphics processing unit (GPU)-based explicit-implicit coupling method is proposed to address the high-computational cost in simulations of the electromagnetic forming process, in which the large deformation (explicit) and electromagnetic field (implicit) are intimately coupled. The electromagnetic-mechanical coupling is achieved by constructing five parallel algorithms, which include the parallel operations of vector-vector, matrix-matrix, matrix-vector, vector assembly, and matrix-free assembly parallel preconditioned conjugate gradient algorithm. The high-efficiency GPU parallel computing is realized through the special data storage structure and parallel strategies. The explicit-implicit GPU method is validated against the experimental results, and several examples are presented for simulations of the electromagnetic forming process to illustrate both the accuracy and high-efficiency parallel acceleration performance of the present program.

A parallel strategy to accelerate neighborhood operation for raster data coordinating CPU and GPU

ABSTRACT This study presents an asynchronous parallel strategy coordinating central processing unit (CPU) and graphic processing unit (GPU) to accelerate neighborhood operation (NO). Specifically, we propose a data partitioning method called multi-anchor task queuing and a task scheduling method called bi-direction task scheduling, which can support CPU and GPU to find the responsible data blocks rapidly and concurrently handle their tasks via a bi-direction merge. Moreover, we optimize the organization of threads distributed among the CPU and GPU. Experimental results show that when a 1.7 GB raster dataset is processed, the speedup ratio achieved by the proposed parallel algorithm reaches 29.63, which is 19% and 18% higher than those of the GPU and standard asynchronous parallel algorithm, respectively. Additionally, the load balance index is below 0.085, which is significantly better than the value achieved by a conventional algorithm. Thus, the strategy achieves a higher speedup ratio and more adaptable load balance, thereby accelerating the NO more efficiently. Further, the impacts of the data volume, computational intensity, organization mode of the GPU threads, and granularity of the GPU stream on the parallel efficiency are evaluated and discussed. We also test the efficiency of four other common NOs with our strategy.

A novel travel route planning method based on an ant colony optimization algorithm

Abstract As people’s living standards improve, tourism has become an important way for people to spend their time on leisure and entertainment. The growing number of tourists in recent years has given rise to the creation of tourism-related ancillary services. Travelers need to choose a travel route that suits their needs and expectations and do it in a way that does not cause a waste of time, whether it is an emerging self-driving tour or a traditional tour group. Therefore, the optimization of tourist routes is of great significance to the majority of tourists. Given the planning requirements of tourist attractions in the post-epidemic era, an ant colony-based optimization algorithm is proposed to resolve the planning problem of optimal tourist routes. An optimized pheromone update strategy is also proposed based on the basic ant colony optimization algorithm. The optimized ant colony algorithm tries to balance two conflicting concepts, namely, flows into tourist attractions and the carrying capacity of destinations. To analyze the performance of the proposed optimization algorithm, the effects of different optimization algorithms on the route planning of tourist attractions were compared in the experiment, and the acceleration ratio of the optimized ant colony algorithm was tested using the graphics processing unit parallel computing program. The results show that the proposed algorithm provides certain advantages and has certain potential in parallel computing. To sum up, this study provides a better scientific basis for optimal tourist route planning and has a good reference value.

DEM–SPH Coupling Method for Landslide Surge Based on a GPU Parallel Acceleration Technique

A high-performance DEM–SPH coupling method for landslide surge is proposed based on a graphics processing unit (GPU) parallel acceleration technique. A GPU-based simulation program, namely, G-DeSp, is developed using C++ and Compute Unified Device Architecture language, which can simulate 3D landslide surge with millions of particles precisely and efficiently. A two-phase flow dam-break test is adopted to validate the accuracy and efficiency of G-DeSp. Three-dimensional landslide surge simulations are conducted with the different diameter of solid particles and the maximum climb height of the surge by granular slide and rigid slide is analyzed. Results show that G-DeSp accurately simulates landslide surge, such as the movement and deformation of the landslide, the generation and propagation of surge waves, and the violent interaction of the fluid–solid. The velocity and displacement of the granular slides and surge decrease with the increase in the diameter of solid particles. The maximum climbing height of surge by the rigid slide is 6.5 times that of surge by the granular slide with the same volume, which indicates that the surge hazard induced by the rigid slide is much more serious than that induced by the granular slide.

GPU accelerated volumetric lattice Boltzmann model for image-based hemodynamics in portal hypertension

We are developing a new technique for monitoring portal hypertension by the pressure gradient between the portal vein and the inferior vena cava (PPG) based on non-invasive measurements (MRI images). Massive parametrization and classification are required to investigate the underlying relationship between the porosity and the stages of liver cirrhosis numerically, and the hepatic-portal venous system is a multi-scale system. Both of them need high computational costs. The suitability of the lattice Boltzmann method for GPU (Graphics Processing Unit) parallel computation provides an opportunity to overcome it. In this paper, we perform GPU parallelization and optimization for the volumetric lattice Boltzmann method with arbitrary geometry based on images. Three application cases, including pipe flow, hemodynamics in the portal venous system, and hemodynamics in a simple hepatic-portal venous system, are employed to prove the method can be applied in the hepatic-portal venous system based on accuracy and efficiency. The reliability of the model is qualitatively validated by the analytical solution of velocity and pressure difference distribution of pipe flow and quantitatively confirmed by the pulsatility of velocity and pressure difference that can be neglected in the portal venous system. The performance of the application cases is examined with Intel Broadwell E5-2683 v3@ 2.30 GHz (CPU) and NVIDIA Tesla V100 16GB (GPU). It shows the GPU algorithm for sparse geometry (SPARSE) has a similar speed to the regular GPU algorithm for dense geometry (DENSE) when the fluid volume fraction (q) is close to 1. And SPARSE speeds up to 2.2 times compared with DENSE when q is in the range of 0.19∼0.27. Meanwhile, the saving ratio of memory cost depends on q. For a numerical case in the hepatic-portal venous system, i.e., a large-scale system, parallel execution can be converged around half an hour with SPARSE, while the memory spills the limitation with DENSE with a single GPU. Hence, multi-GPU implementation is applied to release the limitation, and it can improve performance by increasing the number of GPU cards. In summary, the method presented in the paper is feasibility applied in the hepatic-portal venous system, laying the foundation of the new technique development.

Biomedical-named entity recognition using CUDA accelerated KNN algorithm

Biomedical named entity recognition (Bio-NER) is a highly complex and time-consuming research domain using natural language processing (NLP). It’s widely used in information retrieval, knowledge summarization, biomolecular event extraction, and discovery applications. This paper proposes a method for the recognition and classification of named entities in the biomedical domain using machine learning (ML) techniques. Support vector machine (SVM), decision trees (DT), K-nearest neighbor (KNN), and its kernel versions are used. However, recent advancements in programmable, massively parallel graphics processing units (GPU) hold promise in terms of increased computational capacity at a lower cost to address multi-dimensional data and time complexity. We implement a novel parallel version of KNN by porting the distance computation step on GPU using the compute unified device architecture (CUDA) and compare the performance of all the algorithms using the BioNLP/NLPBA 2004 corpus. Results demonstrate that CUDA-KNN takes full advantage of the GPU’s computational capacity and multi-leveled memory architecture, resulting in a 35× performance enhancement over the central processing unit (CPU). In a comparative study with existing research, the proposed model provides an option for a faster NER system for higher dimensionality and larger datasets as it offers balanced performance in terms of accuracy and speed-up, thus providing critical design insights into developing a robust BioNLP system.

GPU-HADVPPM V1.0: a high-efficiency parallel GPU design of the piecewise parabolic method (PPM) for horizontal advection in an air quality model (CAMx V6.10)

Abstract. With semiconductor technology gradually approaching its physical and thermal limits, graphics processing units (GPUs) are becoming an attractive solution for many scientific applications due to their high performance. This paper presents an application of GPU accelerators in an air quality model. We demonstrate an approach that runs a piecewise parabolic method (PPM) solver of horizontal advection (HADVPPM) for the air quality model CAMx on GPU clusters. Specifically, we first convert the HADVPPM to a new Compute Unified Device Architecture C (CUDA C) code to make it computable on the GPU (GPU-HADVPPM). Then, a series of optimization measures are taken, including reducing the CPU–GPU communication frequency, increasing the data size computation on the GPU, optimizing the GPU memory access, and using thread and block indices to improve the overall computing performance of the CAMx model coupled with GPU-HADVPPM (named the CAMx-CUDA model). Finally, a heterogeneous, hybrid programming paradigm is presented and utilized with GPU-HADVPPM on the GPU clusters with a message passing interface (MPI) and CUDA. The offline experimental results show that running GPU-HADVPPM on one NVIDIA Tesla K40m and an NVIDIA Tesla V100 GPU can achieve up to a 845.4× and 1113.6× acceleration. By implementing a series of optimization schemes, the CAMx-CUDA model results in a 29.0× and 128.4× improvement in computational efficiency by using a GPU accelerator card on a K40m and V100 cluster, respectively. In terms of the single-module computational efficiency of GPU-HADVPPM, it can achieve 1.3× and 18.8× speedup on an NVIDIA Tesla K40m GPU and NVIDIA Tesla V100 GPU, respectively. The multi-GPU acceleration algorithm enables a 4.5× speedup with eight CPU cores and eight GPU accelerators on a V100 cluster.

Smoothed particle hydrodynamics with κ-ε closure for simulating wall-bounded turbulent flows at medium and high Reynolds numbers

In this study, an improved SPH (smoothed particle hydrodynamics) method coupling the κ-ε turbulence model and the wall function is proposed to simulate wall-bounded turbulent flows at medium and high Reynolds numbers. The second-order partial derivative term of the composite function containing the turbulent viscosity coefficient is decomposed into the sum of two terms, which helps SPH to avoid numerical errors and difficulties in dealing with boundary conditions in the nested approximation of first-order partial derivatives. Particle shifting technique, δ-SPH method, and graphics processing unit parallel technology are used in the simulations to ensure uniform particles, smooth pressure field, and high computational efficiency, respectively. The SPH method with the κ-ε turbulence model and the wall function is tested and validated by simulating four classical wall-bounded turbulent flows at medium and high Reynolds numbers, which are the turbulent flat plate boundary layer at Re = 4.2 × 106 and Re = 107, backward step separation flow at ReH = 3025, the flow around the airfoil at Re = 3 × 106, and the flow around the pitching airfoil at Re = 1.35 × 105, respectively. The simulation results are consistent with the references, validating the suitability of the current SPH method for simulating wall-bounded turbulent flows at medium and high Reynolds numbers. Finally, the airfoil motion combining the pitching and deforming at Re = 3 × 106 is investigated by the current SPH method. The results show that the deformation of the airfoil's relative thickness affects the lift coefficients of the pitching airfoil. Furthermore, the increase in the relative thickness increment reduces the amplitude of the lift coefficient, while the increase in the deformation period has little effect on the amplitude of the lift coefficient.

High-Performance Evaluation of the Interpolations and Anterpolations in the GPU-Accelerated Massively Parallel MLFMA

This communication investigates high-performance computation schemes for local Lagrange interpolation and anterpolation operations in the parallel graphics processing unit (GPU)-accelerated distributed-memory multilevel fast multipole algorithm (MLFMA). Two ELLPACK format-based schemes, namely, block ELLPACK (ELL-B) and hybrid compressed sparse column (CSC)-block ELLPACK (CSC-ELL-B), are proposed for the evaluation of interpolation and anterpolation operations, respectively, which ensure high computational throughput for GPU calculation. Optimization using the GPU hierarchical memory architecture, the mechanism of the stream and the CPU/GPU asynchronous computation pattern are employed to further improve the overall performance. The proposed schemes are proven to be an order of magnitude faster than the conventional schemes for aggregation/disaggregation operations. For an aircraft model involving over 10 billion unknowns, the iteration time is reduced by over half, which is remarkable progress in the development of GPU-accelerated parallelization of MLFMA.

Efficiency and accuracy of GPU-parallelized Fourier spectral methods for solving phase-field models

Phase-field models are widely employed to simulate microstructure evolution during processes such as solidification or heat treatment. The resulting partial differential equations, often strongly coupled together, may be solved by a broad range of numerical methods, but this often results in a high computational cost, which calls for advanced numerical methods to accelerate their resolution. Here, we quantitatively test the efficiency and accuracy of semi-implicit Fourier spectral-based methods, implemented in Python programming language and parallelized on a graphics processing unit (GPU), for solving a phase-field model coupling Cahn–Hilliard and Allen–Cahn equations. We compare computational performance and accuracy with a standard explicit finite difference (FD) implementation with similar GPU parallelization on the same hardware. For a similar spatial discretization, the semi-implicit Fourier spectral (FS) solvers outperform the FD resolution as soon as the time step can be taken 5 to 6 times higher than afforded for the stability of the FD scheme. The accuracy of the FS methods also remains excellent even for coarse grids, while that of FD deteriorates significantly. Therefore, for an equivalent level of accuracy, semi-implicit FS methods severely outperform explicit FD, by up to 4 orders of magnitude, as they allow much coarser spatial and temporal discretization.

Non-stationary wave relaxation methods for general linear systems of Volterra equations: convergence and parallel GPU implementation

In the present paper, a parallel-in-time discretization of linear systems of Volterra equations of type u¯(t)=u¯0+∫0tK(t-s)u¯(s)ds+f¯(t),0<t≤T,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\begin{aligned} \\bar{u}(t) = \\bar{u}_0 + \\int _0^t \ extbf{K}(t-s) \\bar{u}(s)\\,\ ext{ d }s + \\bar{f}(t),\\qquad 0<t\\le T, \\end{aligned}$$\\end{document}is addressed. Related to the analytical solution, a general enough functional setting is firstly stated. Related to the numerical solution, a parallel numerical scheme based on the Non-Stationary Wave Relaxation (NSWR) method for the time discretization is proposed, and its convergence is studied as well. A CUDA parallel implementation of the method is carried out in order to exploit Graphics Processing Units (GPUs), which are nowadays widely employed for reducing the computational time of several general purpose applications. The performance of these methods is compared to some sequential implementation. It is revealed throughout several experiments of special interest in practical applications the good performance of the parallel approach.