Speed up big integer multiplication in the Block Wiedemann on graphics processing unit

2017 ◽  
Author(s):  
Peng-Bo Wu ◽  
Jing-Fei Jiang ◽  
Yang Zhao
Keyword(s):  
Graphics Processing Unit ◽  
Processing Unit ◽  
Speed Up ◽  
Integer Multiplication ◽  
Graphics Processing

scholarly journals Finite element method completely implemented for graphic processor units using parallel algorithm libraries

2017 ◽  
Vol 33 (1) ◽  
pp. 53-66 ◽  
Author(s):  
Franz Pichler ◽  
Gundolf Haase
Keyword(s):  
Finite Element ◽  
Graphics Processing Unit ◽  
Computational Cost ◽  
Processing Unit ◽  
Time Step ◽  
Device Architecture ◽  
Transient Problems ◽  
Speed Up ◽  
Automotive Batteries ◽  
Graphics Processing

A finite element code is developed in which all of the computationally expensive steps are performed on a graphics processing unit via the THRUST and the PARALUTION libraries. The code focuses on the simulation of transient problems where the repeated computations per time-step create the computational cost. It is used to solve partial and ordinary differential equations as they arise in thermal-runaway simulations of automotive batteries. The speed-up obtained by utilizing the graphics processing unit for every critical step is compared against the single core and the multi-threading solutions which are also supported by the chosen libraries. This way a high total speed-up on the graphics processing unit is achieved without the need for programming a single classical Compute Unified Device Architecture kernel.

Implementation of a Semi-Implicit Pressure-Based Multigrid Fluid Flow Algorithm on a Graphics Processing Unit

2009 ◽  
Author(s):  
Aaron F. Shinn ◽  
S. P. Vanka
Keyword(s):  
Stokes Equations ◽  
Graphics Processing Unit ◽  
Navier Stokes ◽  
Processing Unit ◽  
Navier Stokes Equations ◽  
Driven Cavity ◽  
Multigrid Algorithm ◽  
Computational Speed ◽  
Speed Up ◽  
Graphics Processing

A semi-implicit pressure based multigrid algorithm for solving the incompressible Navier-Stokes equations was implemented on a Graphics Processing Unit (GPU) using CUDA (Compute Unified Device Architecture). The multigrid method employed was the Full Approximation Scheme (FAS), which is used for solving nonlinear equations. This algorithm is applied to the 2D driven cavity problem and compared to the CPU version of the code (written in Fortran) to assess computational speed-up.

Parallel computations of the step response of a floor heater with the use of a graphics processing unit. Part 2: results and their evaluation

2013 ◽  
Vol 61 (4) ◽  
pp. 949-954 ◽  
Author(s):  
J. Gołębiowski ◽  
J. Forenc
Keyword(s):  
Graphics Processing Unit ◽  
Sparse Matrix ◽  
Temporal Distribution ◽  
Step Response ◽  
Processing Unit ◽  
Commercial Program ◽  
Speed Up ◽  
Spatio Temporal ◽  
Graphics Processing ◽  
Linear Systems Of Equations

Abstract Using models and algorithms presented in the first part of the article, a spatio-temporal distribution of the step response of a floor heater was determined. The results have been presented in the form of heating curves and temperature profiles of the heater in the selected time moments. The computations results were verified through comparing them with the solution obtained with the use of a commercial program - NISA. Additionally, the distribution of the average time constant of thermal processes occurring in the heater was determined. The analysis of the use of a graphics processing unit in numerical computations based on the conjugate gradient method was done. It was proved that the use of a graphics processing unit is profitable in the case of solving linear systems of equations with dense coefficient matrices. In the case of a sparse matrix, the speed-up depends on the number of its non-zero elements.

Ultrasonic pulse propagation simulation using OpenCL for environment mapping and discovery

2019 ◽  
Vol 33 (5) ◽  
pp. 1019-1029
Author(s):  
Mohammad Y Al-Shorman ◽  
Majd M Al-Kofahi
Keyword(s):  
Experimental Data ◽  
Pulse Propagation ◽  
Graphics Processing Unit ◽  
Ultrasonic Pulse ◽  
Processing Unit ◽  
Time Profiles ◽  
Simulation Process ◽  
Front End ◽  
Speed Up ◽  
Graphics Processing

A fast, highly parallelized, simulation of unidirectional ultrasonic pulse propagating in a two-dimensional environment is presented. The pulse intensity versus time is recorded using an array of unidirectional ultrasonic receivers located at known locations and arranged in a small circle around the transmitter. To speed up the simulation process, OpenCL 2.0 heterogeneous compute language on a graphics processing unit is used. The simulation result is then compared with experimental data to validate its accuracy. By comparing both simulated and experimental data, the collected intensity–time profiles can be used to map an environment. Environments can be mapped using not only direct reflections but also higher order reflections from objects that are not directly seen by the transmitter. With the help of this simulation, subtle characteristics in an environment, such as a slight tilt or curvature, can be measured. The front end of the simulation is written using C#, while the back end is written using C\C++ and OpenCL.

scholarly journals Construction of an optoacoustic image of biological tissues based on an algorithm for a graphics processor

2021 ◽  
pp. 106-109
Author(s):  
Denis Kravchuk
Keyword(s):  
Gpu Computing ◽  
Graphics Processing Unit ◽  
Biological Tissues ◽  
Ultrasonic Field ◽  
Processing Unit ◽  
Optoacoustic Imaging ◽  
Optoacoustic Interaction ◽  
Speed Up ◽  
Migration Method ◽  
Graphics Processing

The use of optical contrast between different blood particles allows the use of optoacoustic imaging to visualize the distribution of blood particles (erythrocytes, taking into account oxygen saturation), the delivery of drugs to organs through blood vessels. An algorithm for calculating the ultrasonic field obtained as a result of optoacoustic interaction has been developed to speed up calculations on the GPU board. An architecture for fast restoration of an optoacoustic signal based on graphics processing unit (GPU) programming is proposed. The algorithm used in combination with the pre-migration method provides an improvement in the resolution and sharpness of the optoacoustic image of the simulated biological tissues. Thanks to the advanced graphics processing unit (GPU) computing architecture, time-consuming main processing unit (CPU) computing is accelerated with great computational efficiency.

HIGH PRECISION INTEGER ADDITION, SUBTRACTION AND MULTIPLICATION WITH A GRAPHICS PROCESSING UNIT

2010 ◽  
Vol 20 (04) ◽  
pp. 293-306 ◽  
Author(s):  
NIALL EMMART ◽  
CHARLES WEEMS
Keyword(s):  
High Precision ◽  
Graphics Processing Unit ◽  
Divide And Conquer ◽  
Processing Unit ◽  
Good Potential ◽  
Addition And Subtraction ◽  
Integer Multiplication ◽  
On Chip ◽  
Graphics Processing ◽  
Gpu Architecture

In this paper we evaluate the potential for using an NVIDIA graphics processing unit (GPU) to accelerate high precision integer multiplication, addition, and subtraction. The reported peak vector performance for a typical GPU appears to offer good potential for accelerating such a computation. Because of limitations in the on-chip memory, the high cost of kernel launches, and the nature of the architecture's support for parallelism, we used a hybrid algorithmic approach to obtain good performance on multiplication. On the GPU itself we adapt the Strassen FFT algorithm to multiply 32KB chunks, while on the CPU we adapt the Karatsuba divide-and-conquer approach to optimize application of the GPU's partial multiplies, which are viewed as "digits" by our implementation of Karatsuba. Even with this approach, the result is at best a factor of three increase in performance, compared with using the GMP package on a 64-bit CPU at a comparable technology node. Our implementations of addition and subtraction achieve up to a factor of eight improvement. We identify the issues that limit performance and discuss the likely impact of planned advances in GPU architecture.

scholarly journals Analysis of GPU Computation of Parabolic, Bessel, Wright and Riemann Zeta Functions

2021 ◽  
Vol 40 ◽  
pp. 02005
Author(s):  
Ashish A. Jadhav ◽  
Abhijeet D. Kalamkar ◽  
Pritish A. Gaikwad ◽  
Vishwesh Vyawahare ◽  
Navin Singhaniya
Keyword(s):  
Fractional Calculus ◽  
Gpu Computing ◽  
Graphics Processing Unit ◽  
Zeta Functions ◽  
Computation Time ◽  
Processing Unit ◽  
Mathematical Functions ◽  
Speed Up ◽  
Sequential Code ◽  
Graphics Processing

This paper deals with GPU computing of special mathematical functions that are used in Fractional Calculus. The graphics processing unit (GPU) has grown to be an integral part of nowadays’s mainstream computing structures. The special mathematical functions are an integral part of Fractional Calculus. This paper deals with a novel parallel approach for computing special mathematical functions used in Fractional Calculus. NVIDIA’s GPU hardware is used to speed up the parallel algorithm. A comparison of the sequential code, vectorized code and GPU code is performed. We have successfully reduced the computation time of special mathematical functions using the parallel computing capabilities of GPU.

scholarly journals AMIDE v2: High-Throughput Screening Based on AutoDock-GPU and Improved Workflow Leading to Better Performance and Reliability

2021 ◽  
Vol 22 (14) ◽  
pp. 7489
Author(s):  
Pierre Darme ◽  
Manuel Dauchez ◽  
Arnaud Renard ◽  
Laurence Voutquenne-Nazabadioko ◽  
Dominique Aubert ◽  
...  
Keyword(s):  
High Throughput ◽  
High Throughput Screening ◽  
High Performance ◽  
Graphics Processing Unit ◽  
Target Identification ◽  
Computation Time ◽  
Processing Unit ◽  
Biological Target ◽  
Speed Up ◽  
Graphics Processing

Molecular docking is widely used in computed drug discovery and biological target identification, but getting fast results can be tedious and often requires supercomputing solutions. AMIDE stands for AutoMated Inverse Docking Engine. It was initially developed in 2014 to perform inverse docking on High Performance Computing. AMIDE version 2 brings substantial speed-up improvement by using AutoDock-GPU and by pulling a total revision of programming workflow, leading to better performances, easier use, bug corrections, parallelization improvements and PC/HPC compatibility. In addition to inverse docking, AMIDE is now an optimized tool capable of high throughput inverse screening. For instance, AMIDE version 2 allows acceleration of the docking up to 12.4 times for 100 runs of AutoDock compared to version 1, without significant changes in docking poses. The reverse docking of a ligand on 87 proteins takes only 23 min on 1 GPU (Graphics Processing Unit), while version 1 required 300 cores to reach the same execution time. Moreover, we have shown an exponential acceleration of the computation time as a function of the number of GPUs used, allowing a significant reduction of the duration of the inverse docking process on large datasets.

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