Simulation And Calculation Of Fiber Nonlinear Schrodinger Equation Based On GPU

Simulation of signal propagation in optical fibers plays an important role in the research and development of optical transmission systems.The transmission characteristics of the research signal in the fiber are mainly transformed into a mathematical model to numerically solve the fiber nonlinear Schrodinger equation.The performance of the numerical method mainly considers the error precision and the computational efficiency.At present,the numerical method for solving the single-mode nonlinear transmission equation is perfect.The fixed-step method has the Runge-Kuta interactive picture method with global error fourth-order accurate,in order to further optimize the performance of the method,a large number of variable step size calculation criteria are derived,and the local error method is widely used.The calculation of multi-mode nonlinear transmission equations is more complicated than single-mode.At present,only the fixed-step method with lower precision is used.Therefore,it is necessary to optimize the multi-mode variable step size numerical method.In addition,in long-distance multimode fiber-optic communication,especially when nonlinear effects dominate,the simulation time is often as long as several days,and improving computational efficiency has become a top priority.The optimization of the numerical method is more to improve the numerical precision.To accelerate the calculation on a large scale,it is necessary to use GPU parallel computing to speed up the solution process.The main results of this research work are as follows:(1)Three error estimation criteria for solving nonlinear transmission equation of multimode fiber—max,sum and ave criterion are proposed.The multimode error vector is converted to the error scalar,and the adaptive step size uniform change of multi-mode is realized based on the local error method of symmetric split-step Fourier.By simulating the transmission of Gaussian pulse in the graded-index multimode fiber,the performance of local error and global error of the fixed-step and variable-step method in different criteria are verified.The experimental results show that all the variable step size algorithms of the three criteria are convergent,besides,using the sum criterion calculate local error to control step size change can obtain higher numerical precision under the same calculation amount,and in the case of the same global error,the calculation amount is relatively less.The study is of significance for further improving the computational effciency of multimode nonlinear transmission equations.(2)The GPU-based parallel comuting multi-mode nonlinear transmission equation achieves significant acceleration.When the GPU utilization is close to the maximum,the acceleration effect is most obvious.Experiments simulate that multiple Gaussian pulses are incident on the multimode fiber,and the GPU utilization rate is 90%by adjusting the number of transmission pulses.The research shows that under the single precision condition,15 modes and 100 pulses are transmitted,compared with the CPU calculation time,the GPUs acceleration ratio is up to 100 times,which can significantly improve computing efficiency.In addition,under the condition of single and double precision,the relationship between the error precision of the multi-mode multi-pulse numerical algorithm and the number of transmission steps and the number of modes is simulated.The results show that under different mode numbers,as the number of transmission steps increases,the error accuracy under double precision conditions will be higher.