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.

GPU Accelerated Reconstruction in Compton Scattering Tomography Using Matrix Compression

2014 ◽  
Vol 519-520 ◽  
pp. 102-107
Author(s):  
Yu Fei Yu ◽  
Bin Yan ◽  
Biao Wang ◽  
Lei Li ◽  
Yu Han ◽  
...  
Keyword(s):  
Compton Scattering ◽  
Graphics Processing Unit ◽  
Sparse Matrix ◽  
Reconstruction Algorithm ◽  
Processing Unit ◽  
Matrix Vector Multiplication ◽  
Speedup Ratio ◽  
Parallel Features ◽  
Graphics Processing ◽  
Matrix Vector

An acceleration strategy for TV-ADM reconstruction algorithm in Compton scattering tomography (CST) is proposed. By analyzing the sparse characteristic of CST projection matrixes, firstly, the sparse matrix vector CSR format and ELL format are used to store them, which greatly reduce the memory consumption. Then, a Sparse Matrix Vector multiplication (SpMV) method is utilized to accelerate the projector and back projector process. Finally, based on the parallel features, the TV-ADM is computed with Graphics Processing Unit (GPU). Numerical experiments show that the TV-ADM with the presented acceleration strategy could achieve a 96 times speedup ratio and 224 times memory compression ratio without precision loss.

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.

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