多核环境下非线性特征值问题残量反迭代法并行计算

Parallel Algorithm for Inverse Residual of Nonlinear Eigenvalue Problems Based on Multi-core Computing System Environment

非线性特征值问题不满足Schur类分解的结论,因此线性特征值问题的很多数值方法不能直接推广到非线性问题.基于多核并行环境的非线性特征值问题数值解法的并行计算,给出了适合于多核并行环境的并行Newton类残量反迭代算法,在多核计算环境上使用Intel Fortran+OpenMP进行了数值试验.数值试验结果表明算法具有较高的加速比和并行效率.

For the reason that nonlinear eigenvalue problems do not meet the requirements of Schur faetorization（algorithm）, a lot of the existing numerical methods for linear eigenvalue problems cannot be directly extended to nonlinear cases. The numerical methods for nonlinear ei- genvalue problems using parallel computation are studied under the multi-core computing system environment in this paper. The Newton-type parallel inverse residual iteration method （NPIM） is proposed, which agrees with the multi-core parallel system environment. Numerical experiments are performed with Intel Fortran and OpenMP in the multi-core platform. The results show that NPIM has reasonable speedup and parallel efficiency.