這篇論文提出了BiCGstab和BiCGstab($l$)演算法的GPU平行化。並使用兩個易於使用的CUDA函示庫cuBLAS和cuSPARSE來協助撰寫程式碼，這兩個函式庫最常被用來在執行線性代數運算,利用Poisson-Fermi模型構建的TRPV通道矩陣和佛羅里達大學稀疏矩陣集合中選取的矩陣來檢驗這兩種方法的性能。數值結果表明BiCGstab($l$)在有幾乎純虛根特徵值的矩陣中優於BiCGstab。

This thesis presents the GPU parallelizations of the BiCGstab and BiCGstab($l$) algorithms. Two easy-to-use CUDA libraries, cuBLAS and cuSPARSE, are em- ployed to perform the linear algebra operations in the methods. The matrices constructed by Poisson-Fermi model for TRPV channel and selected from the university of florida sparse matrix collection are used to test the performance of these two methods. The numerical results show that BiCGstab($l$) outperforms BiCGstab in some matrices which have almost pure imaginary eigenvalues.

Contents

Abstract i
Acknowledgement iii
1 Introduction 1
2 GPU computing 3
2.1 GPUVSCPU 3
2.2 CUDA 4
2.2.1 cuBLAS(CUDA Basic Linear Algebra Subroutines library) 5
2.2.2 cuSPARSE(CUDA Sparse Matrix library) 5
3 Algorithm 6
3.1 BiCGstab method. 6
3.2 BiCGstab(l) method 7
4 Parallelization 9
4.1 Compressed Sparse matrix(CSR) 9
4.2 Subroutine of Library 10
4.2.1 Subroutine of cuBLAS 11
4.2.2 Subroutine of cuSPARSE 12
4.3 Parallelization of BiCGstab and BiCGstab(l) 14
4.4 Computational cost of BiCGstab and BiCGstab(l) 20
5 Result 21
5.1 Example1. TRPV 22
5.2 Example2. ORSIRR1 24
5.3 Example3. fs1834 26
6 Conclusion 30
Reference 31

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