An efficient sparse matrix-vector multiplication on CUDA-enabled graphic processing units for finite element method simulations

2016 ◽  
Vol 110 (1) ◽  
pp. 57-78 ◽  
Author(s):  
Atakan Altinkaynak
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Sparse Matrix ◽  
Graphic Processing Units ◽  
Matrix Vector Multiplication ◽  
Matrix Vector ◽  
Element Method ◽  
Graphic Processing

scholarly journals FPGA architecture and implementation of sparse matrix–vector multiplication for the finite element method

2008 ◽  
Vol 178 (8) ◽  
pp. 558-570 ◽  
Author(s):  
Yousef Elkurdi ◽  
David Fernández ◽  
Evgueni Souleimanov ◽  
Dennis Giannacopoulos ◽  
Warren J. Gross
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Sparse Matrix ◽  
The Finite Element Method ◽  
Matrix Vector Multiplication ◽  
Fpga Architecture ◽  
Matrix Vector ◽  
Element Method

scholarly journals Finite-Element Sparse Matrix Vector Multiplication on Graphic Processing Units

2010 ◽  
Vol 46 (8) ◽  
pp. 2982-2985 ◽  
Author(s):  
Maryam Mehri Dehnavi ◽  
David M. Fernandez ◽  
Dennis Giannacopoulos
Keyword(s):  
Finite Element ◽  
Sparse Matrix ◽  
Graphic Processing Units ◽  
Matrix Vector Multiplication ◽  
Matrix Vector ◽  
Graphic Processing

GPU-Friendly Preconditioners for Efficient 3-D Finite Element Analysis of Thin Structures

2011 ◽  
Author(s):  
Vikalp Mishra ◽  
Krishnan Suresh
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Sparse Matrix ◽  
Grid Method ◽  
Double Precision ◽  
Thin Structures ◽  
Element Analysis ◽  
Dual Representation ◽  
Matrix Vector Multiplication ◽  
Matrix Vector

A serious computational bottle-neck in finite element analysis today is the solution of the underlying system of equations. To alleviate this problem, researchers have proposed the use of graphics programmable units (GPU) for fast iterative solution of such equations. Indeed, researchers have shown that a GPU-implementation of a double-precision sparse-matrix-vector multiplication (that underlies all iterative methods) is approximately an order of magnitude faster than that of an optimized CPU implementation. Unfortunately, fast matrix-vector multiplication alone is insufficient… a good preconditioner is necessary for rapid convergence. Furthermore, most modern preconditioners, such as incomplete Cholesky, are expensive to compute, and cannot be easily ported to the GPU. In this paper, we propose a special class of preconditioners for the analysis of thin structures, such as beams and plates. The proposed preconditioners are developed by combining the multi-grid method, with recently developed dual-representation method for thin structures. It is shown, that these preconditioners are computationally inexpensive, perform better than standard pre-conditioners, and can be easily ported to the GPU.

scholarly journals A Novel CSR-Based Sparse Matrix-Vector Multiplication on GPUs

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Guixia He ◽  
Jiaquan Gao
Keyword(s):  
Sparse Matrix ◽  
Sparse Matrices ◽  
Poor Performance ◽  
Test Results ◽  
Graphic Processing Units ◽  
Multiple Gpus ◽  
Matrix Vector Multiplication ◽  
Compressed Sparse Row ◽  
Access Patterns ◽  
Matrix Vector

Sparse matrix-vector multiplication (SpMV) is an important operation in scientific computations. Compressed sparse row (CSR) is the most frequently used format to store sparse matrices. However, CSR-based SpMVs on graphic processing units (GPUs), for example, CSR-scalar and CSR-vector, usually have poor performance due to irregular memory access patterns. This motivates us to propose a perfect CSR-based SpMV on the GPU that is called PCSR. PCSR involves two kernels and accesses CSR arrays in a fully coalesced manner by introducing a middle array, which greatly alleviates the deficiencies of CSR-scalar (rare coalescing) and CSR-vector (partial coalescing). Test results on a single C2050 GPU show that PCSR fully outperforms CSR-scalar, CSR-vector, and CSRMV and HYBMV in the vendor-tuned CUSPARSE library and is comparable with a most recently proposed CSR-based algorithm, CSR-Adaptive. Furthermore, we extend PCSR on a single GPU to multiple GPUs. Experimental results on four C2050 GPUs show that no matter whether the communication between GPUs is considered or not PCSR on multiple GPUs achieves good performance and has high parallel efficiency.

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