Bjorn Nutti, Dragan Marinkovic
The paper presents a highly efficient way of simulating the dynamic behavior of deformable objects by means of the finite element method (FEM) with computations performed on Graphics Processing Units (GPU). The presented implementation reduces bottlenecks related to memory accesses by grouping the necessary data per node pairs, in contrast to the classical way done […]
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A. F. P. Camargos, V. C. Silva
We present a performance analysis of a parallel implementation of both conjugate gradient and preconditioned conjugate gradient solvers using graphic processing units with CUDA parallel programming model. The solvers were optimized for a fast solution of sparse systems of equations arising from Finite Element Analysis (FEA) of electromagnetic phenomena. The preconditioners were Incomplete Cholesky factorization […]
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Amani AlOnazi
The progress of high performance computing platforms is dramatic, and most of the simulations carried out on these platforms, result in improvements on one level, yet exposes shortcomings of the current CFD packages capabilities. Therefore, hardware-aware design and optimizations are crucial towards exploiting the modern computing resources. This thesis proposes optimizations aimed at acceleration numerical […]
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Xiangge Li
Matrix solvers play a crucial role in solving real world physics problem. In engineering practice, transition analysis is most often used, which requires a series of similar matrices to be solved. However, any specific solver with/without preconditioner cannot achieve high performance gain for all matrices. This paper recommends Conjugate Gradient iterative solver with SSOR approximate […]
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Jianfei Zhang, Lei Zhang
Graphics Processing Unit (GPU) has obtained great success in scientific computations for its tremendous computational horsepower and very high memory bandwidth. This paper discusses the efficient way to implement polynomial preconditioned conjugate gradient solver for the finite element computation of elasticity on NVIDIA GPUs using Compute Unified Device Architecture (CUDA). Sliced Block ELLPACK (SBELL) format […]
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Shi-Lun Huang
The purpose of this work is to study the performance of parallel computation of Finite Element Method using the NVIDIA’s CUDA. The numerical experiments are performed only on the stiffness matrix using the conjugate gradient method. In addition, the generalized minimal residual method is considered to solve the Stokes problem using both PETSc and CUDA. […]
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Eike Mueller, Xu Guo, Robert Scheichl, Sinan Shi
Many problems in geophysical and atmospheric modelling require the fast solution of elliptic partial differential equations (PDEs) in "flat" three dimensional geometries. In particular, an anisotropic elliptic PDE for the pressure correction has to be solved at every time step in the dynamical core of many numerical weather prediction models, and equations of a very […]
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Sinan Shi
Numerical weather predicting models often require solving a 3-D Helmholtz problem which derived from the governing equation of dynamical core in Met Office Unified Model, by preconditioned iterative solvers. In this dissertation, a GPU implementation of preconditioned conjugate gradient (CG) iterative method will be focused on. A given serial code has been ported on GPU. […]
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Emmanuel Agullo, Luc Giraud, Abdou Guermouche, Stojce Nakov, Jean Roman
Whereas most today parallel High Performance Computing (HPC) software is written as highly tuned code taking care of low-level details, the advent of the manycore area forces the community to consider modular programming paradigms and delegate part of the work to a third party software. That latter approach has been shown to be very productive […]
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Mickeal Verschoor, Andrei C. Jalba
The Conjugate Gradient (CG) method is a widely-used iterative method for solving linear systems described by a (sparse) matrix. The method requires a large amount of Sparse-Matrix Vector (SpMV) multiplications, vector reductions and other vector operations to be performed. We present a number of mappings for the SpMV operation on modern programmable GPUs using the […]
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Stephen J. Tarsa, Tsung-han Lin, H.T. Kung
Conjugate gradient is an important iterative method used for solving least squares problems. It is compute-bound and generally involves only simple matrix computations. One would expect that we could fully parallelize such computation on the GPU architecture with multiple Stream Multiprocessors (SMs), each consisting of many SIMD processing units. While implementing a conjugate gradient method […]
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Ruipeng Li, Yousef Saad
This work is an overview of our preliminary experience in developing high-performance iterative linear solver accelerated by GPU co-processors. Our goal is to illustrate the advantages and difficulties encountered when deploying GPU technology to perform sparse linear algebra computations. Techniques for speeding up sparse matrix-vector product (SpMV) kernels and finding suitable preconditioning methods are discussed. […]
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