Sparse Matrix-Vector Multiplication for Finite Element Method Matrices on FPGAs

2006 ◽  
Author(s):  
Yousef El-Kurdi ◽  
Warren Gross ◽  
Dennis Giannacopoulos
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Sparse Matrix ◽  
Matrix Vector Multiplication ◽  
Matrix Vector ◽  
Element Method

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

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.

The application of simultaneous elimination and back-substitution method (SEBSM) in finite element method

2016 ◽  
Vol 33 (8) ◽  
pp. 2339-2355 ◽  
Author(s):  
Yunfei Liu ◽  
Jun Lv ◽  
Xiaowei Gao
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Sparse Matrix ◽  
Direct Method ◽  
Computational Time ◽  
Substitution Method ◽  
Content Type ◽  
Memory Space ◽  
Simultaneous Elimination ◽  
Element Method

Purpose The purpose of this paper is to introduce a new method called simultaneous elimination and back-substitution method (SEBSM) to solve a system of linear equations as a new finite element method (FEM) solver. Design/methodology/approach In this paper, a new technique assembling the global stiffness matrix will be proposed and meanwhile the direct method SEBSM will be applied to solve the equations formed in FEM. Findings The SEBSM solver for FEM with the present assembling technique has distinct advantages in both computational time and memory space occupation over the conventional methods, such as the Gauss elimination and LU decomposition methods. Originality/value The developed solver requires less memory space no matter the coefficient matrix is a typical sparse matrix or not, and it is applicable to both symmetric and unsymmetrical linear systems of equations. The processes of assembling matrix and dealing with constraints are straightforward, so it is convenient for coding. Compared to the previous solvers, the proposed solver has favorable universality and good performances.

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