Research On Parallel Numerical Simulation Technology For Solving Ocean Acoustic Helmholtz Equation Based On Spectral Method

Acoustic waves are an important means of underwater communication,detection,and seabed surveying and mapping.Due to the influence of factors such as the sea surface,the seabed and the water body,the sound wave propagation is more complicated,but it satisfies the most basic underwater acoustic wave equation mathematically.For the steady-state sound field,the common methods for solving are divided into solving the Helmholtz equation in the frequency domain or solving its approximate model.It is difficult to solve partial differential equations such as Helmholtz equation or its approximate model by theoretical methods,so numerical discrete methods are often used to solve them.The spectral method is a numerical discrete method with high accuracy and fast convergence speed.It has been applied to solve the normal wave model of acoustic wave propagation.However,the spectral method has a large amount of calculation and is difficult to meet the requirements of real-time performance.Therefore,it is necessary to use a high-performance computing platform to accelerate the algorithm in parallel.In addition,the current approximate model solved by the spectral method only contains one sound velocity profile,and the approximate model has limitations in application conditions,which will greatly reduce the actual application range.In order to meet the needs of practical acoustic applications,the spectral method is used to directly calculate the two-dimensional underwater acoustic Helmholtz equation,which has a wide range of applications,higher accuracy,and can overcome the problems of limited application range of simplified models and model errors.Therefore,the main work of this paper is:1.To solve the long running time problem of one-dimensional spectral method program,the serial program tuning methods such as compiler option opti- mization,optimized memory access,simplified calculation,invocation of Intel Math Kernel Library(MKL)are used.Then the platform Tianhe-2 carries out multi-threaded parallel acceleration processing,and the test results show that the optimized speed increased by 23.98 times.2.Aiming at the problem that the one-dimensional spectral method solves the simplified model has a small practical application range and introduces model errors,a calculation method based on the spectral method to directly solve the two-dimensional underwater acoustic propagation Helmholtz equation is developed.Firstly,the Chebyshev-Galerkin spectral method and the Chebyshevcollocation spectral method are used to discretize the two-dimensional Helmholtz model equations,and the correctness of the two methods are verified by examples.Since the collocation spectral method does not require harsh boundary conditions as Galerkin method,the Chebyshev-collocation spectral method is used to solve the two-dimensional underwater acoustic propagation Helmholtz equation,and the result is more accurate than the finite difference method.Aiming at the problem of slow calculation speed,a variety of serial optimization and parallel calculation schemes are used to accelerate the program.The test results show that the optimization speed is increased by 14.88 times.