The prolongation structure technique of Wahlquist and Estanbrook is improved and applied to a newequation proposed by Z.J.Qiao [J.Math.Phys.48 (2007) 082701].Two potentials and two pseudopotentials areobtained,from wh...The prolongation structure technique of Wahlquist and Estanbrook is improved and applied to a newequation proposed by Z.J.Qiao [J.Math.Phys.48 (2007) 082701].Two potentials and two pseudopotentials areobtained,from which a new type of inverse scattering problem,Lax equations,and infinite number of conservation lawsare obtained.展开更多
As one of the most important mathematics-physics equations, heat equation has been widely used in engineering area and computing science research. Large-scale heat problems are difficult to solve due to computational ...As one of the most important mathematics-physics equations, heat equation has been widely used in engineering area and computing science research. Large-scale heat problems are difficult to solve due to computational intractability. The parallelization of heat equation is available to improve the simulation model efficiency. In order to solve the three-dimensional heat problems more rapidly, the OpenMP was adopted to parallelize the preconditioned conjugate gradient （PCG） algorithm in this paper. A numerical experiment on the three-dimensional heat equation model was carried out on a computer with four cores. Based on the test results, it is found that the execution time of the original serial PCG program is about 1.71 to 2.81 times of the parallel PCG program executed with different number of threads. The experiment results also demonstrate the available performance of the parallel PCG algorithm based on OpenMP in terms of solution quality and computational performance.展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos. 11075055, 61021004, 10735030the Shanghai Leading Academic Discipline Project, China under Grant No. B412the Program for Changjiang Scholars and the Innovative Research Team in University of Ministry of Education of China under Grant No. IRT 0734
文摘The prolongation structure technique of Wahlquist and Estanbrook is improved and applied to a newequation proposed by Z.J.Qiao [J.Math.Phys.48 (2007) 082701].Two potentials and two pseudopotentials areobtained,from which a new type of inverse scattering problem,Lax equations,and infinite number of conservation lawsare obtained.
文摘As one of the most important mathematics-physics equations, heat equation has been widely used in engineering area and computing science research. Large-scale heat problems are difficult to solve due to computational intractability. The parallelization of heat equation is available to improve the simulation model efficiency. In order to solve the three-dimensional heat problems more rapidly, the OpenMP was adopted to parallelize the preconditioned conjugate gradient （PCG） algorithm in this paper. A numerical experiment on the three-dimensional heat equation model was carried out on a computer with four cores. Based on the test results, it is found that the execution time of the original serial PCG program is about 1.71 to 2.81 times of the parallel PCG program executed with different number of threads. The experiment results also demonstrate the available performance of the parallel PCG algorithm based on OpenMP in terms of solution quality and computational performance.
