Title :
Iterative Solver for Linear System Obtained by Edge Element: Variable Preconditioned Method With Mixed Precision on GPU
Author :
Ikuno, Soichiro ; Kawaguchi, Yuki ; Fujita, Norihisa ; Itoh, Taku ; Nakata, Susumu ; Watanabe, Kota
Author_Institution :
Sch. of Comput. Sci., Tokyo Univ. of Technol., Tokyo, Japan
Abstract :
The variable preconditioned (VP) Krylov subspace method with mixed precision is implemented on graphics processing unit (GPU) using compute unified device architecture (CUDA), and the linear system obtained from the edge element is solved by means of the method. The VPGCR method has the sufficient condition for the convergence. This sufficient condition leads us that the residual equation for the preconditioned procedure of VPGCR can be solved in the range of single precision. To stretch the sufficient condition, we propose the hybrid scheme of VP Krylov subspace method that uses single and double precision operations. The results of computations show that VPCG with mixed precision on GPU demonstrated significant achievement than that of CPU. Especially, VPCG-JOR on GPU with mixed precision is 41.853 times faster than that of VPCG-CG on CPU.
Keywords :
computer graphic equipment; coprocessors; iterative methods; linear systems; mathematics computing; parallel architectures; GPU; compute unified device architecture; convergence sufficient condition; edge element; graphics processing unit; iterative solver; linear system; variable preconditioned Krylov subspace method; Educational institutions; Graphics processing unit; Linear systems; Mathematical model; Peer to peer computing; Symmetric matrices; Vectors; Compute unified device architecture (CUDA); edge element; graphics processing unit (GPU); variable preconditioned Krylov subspace method;
Journal_Title :
Magnetics, IEEE Transactions on
DOI :
10.1109/TMAG.2011.2175375
