介绍了求解抛物型波动方程的分步傅里叶变换(split step Fouriertransform,SSFT)算法计算过程,分析了算法的并行性,并基于西方快速傅里叶变换(fastest Fourier transform in the West,FFTW)函数库研究了2种分步傅里叶变换算法并行方案...介绍了求解抛物型波动方程的分步傅里叶变换(split step Fouriertransform,SSFT)算法计算过程,分析了算法的并行性,并基于西方快速傅里叶变换(fastest Fourier transform in the West,FFTW)函数库研究了2种分步傅里叶变换算法并行方案。所做测试结果表明,文中所提方案尤其是分布式模式方案,对于实现波动方程的快速求解是有效的,且所做工作对于以波动方程为基础的电波传播、电磁环境数据生成等问题的研究具有一定的指导意义。展开更多
In this paper we develop explicit fast exponential Runge-Kutta methods for the numerical solutions of a class of parabolic equations.By incorporating the linear splitting technique into the explicit exponential Runge-...In this paper we develop explicit fast exponential Runge-Kutta methods for the numerical solutions of a class of parabolic equations.By incorporating the linear splitting technique into the explicit exponential Runge-Kutta schemes,we are able to greatly improve the numerical stability.The proposed numerical methods could be fast implemented through use of decompositions of compact spatial difference operators on a regular mesh together with discrete fast Fourier transform techniques.The exponential Runge-Kutta schemes are easy to be adopted in adaptive temporal approximations with variable time step sizes,as well as applied to stiff nonlinearity and boundary conditions of different types.Linear stabilities of the proposed schemes and their comparison with other schemes are presented.We also numerically demonstrate accuracy,stability and robustness of the proposed method through some typical model problems.展开更多
文摘介绍了求解抛物型波动方程的分步傅里叶变换(split step Fouriertransform,SSFT)算法计算过程,分析了算法的并行性,并基于西方快速傅里叶变换(fastest Fourier transform in the West,FFTW)函数库研究了2种分步傅里叶变换算法并行方案。所做测试结果表明,文中所提方案尤其是分布式模式方案,对于实现波动方程的快速求解是有效的,且所做工作对于以波动方程为基础的电波传播、电磁环境数据生成等问题的研究具有一定的指导意义。
基金The work is supported in part by China Fundamental Research of Civil Aircraft under grant number MJ-F-2012-04the Fundamental Research Funds for the Central Universities(YWF-15-SXXY-017).
文摘In this paper we develop explicit fast exponential Runge-Kutta methods for the numerical solutions of a class of parabolic equations.By incorporating the linear splitting technique into the explicit exponential Runge-Kutta schemes,we are able to greatly improve the numerical stability.The proposed numerical methods could be fast implemented through use of decompositions of compact spatial difference operators on a regular mesh together with discrete fast Fourier transform techniques.The exponential Runge-Kutta schemes are easy to be adopted in adaptive temporal approximations with variable time step sizes,as well as applied to stiff nonlinearity and boundary conditions of different types.Linear stabilities of the proposed schemes and their comparison with other schemes are presented.We also numerically demonstrate accuracy,stability and robustness of the proposed method through some typical model problems.
