Parallel Solution to Block-Tridiagonal Linear Equations by Two-layer Mixed-block Algorithm
Abstract
A novel scalable parallel algorithm, PTHB, is proposed to solve block-tridiagonal equations with strict block diagonal dominant based on the idea of Sun's about PTH method. By precision analysis, divide-conquer strategy is obtained ensuring the accuracy and optimal efficiency. PTHB provides an approximate solution that is equivalent to the exact solution within machine accuracy. The method has been implemented on the "ZiQiang 3000" supercomputer of Shanghai University.The numerical results are the same with the theoretical analysis. With the given the accuracy, the linear speedup rate is obtained, and parallel efficiency over 90% is reached.
- Publication:
-
Numerical Analysis and Applied Mathematics ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics
- Pub Date:
- September 2011
- DOI:
- 10.1063/1.3637805
- Bibcode:
- 2011AIPC.1389.1102Z
- Keywords:
-
- computer science;
- supercomputers;
- subroutines;
- matrix algebra;
- 89.20.Ff;
- 07.05.Bx;
- 02.60.Gf;
- 02.10.Yn;
- Computer science and technology;
- Computer systems: hardware operating systems computer languages and utilities;
- Algorithms for functional approximation;
- Matrix theory