| Inertial Confinement Fusion?ICF?can generate huge clean energy and is considered to be one of the important ways to solve the future energy crisis.Good capsule driving symmetry is an important condition for realizing the successful ignition of the laser-indirect-driven ICF.The radiation symmetry analysis involves solving the nonlinear view factor radiation flux equation model.In order to achieve the specified accuracy,the size of the discrete surface element is usually small,so that the number of equations is very large,and the solution process requires a lot of intensive calculations,resulting in low solve efficiency.In this paper,the radiation symmetry of the cylindrical cavity-spherical capsule model in ICF is taken as the research object.In order to improve its evaluation efficiency,the following research work is carried out:1)Influenced by the geometrical shape of the radiation surface on the inner wall of a cylindrical hohlraum,the radiation flux on different radiation surfaces usually presents different distribution laws.This radiation flux with multiple distribution characteristics is difficult to show good sparsity in a single orthogonal basis.In order to solve this problem,a method of using multiple orthogonal bases to represent the radiation flux with different distribution characteristics is proposed,that is,using Spherical Harmonic polynomials to represent the radiation flux on the surface of the capsule,constructing Annular Zernike polynomials to represent the radiation flux on the end surface of the cylindrical cavity,and constructing Legendre-Fourier polynomials to represent the radiation flux on the side of the cylindrical cavity.This method requires only a small number of polynomial low-order expansion terms to accurately represent the radiation flux,eliminating a large amount of redundant information and achieving a reduction in the scale of the equation.According to the sparse prior information of the radiation flux on the three orthogonal groups,the energy balance equation corresponding to each radiating surface is coupled to construct a sparse representation model of the radiation flux with respect to the sparse coefficients,and a small amount of uncorrelated sampling is performed on the model.A nonlinear radiation energy compressed observation model is established to achieve compression of the model.2)Because the radiation energy compressed observation model is non-linear,the existing compressed sensing reconstruction algorithm has many problems,such as many iterations,long solving time and poor robustness.Aiming at this problem,a Conjugate Gradient Hard Threshold Pursuit?CGHTP?algorithm is proposed to efficiently solve the radiation energy balance equation.The algorithm uses the hard threshold function and the least squares method to update the sparse coefficients,and optimizes the support set selection strategy.The gradient and conjugate gradient alternate optimization methods are used to accelerate the convergence of the algorithm and greatly reduce the number of iterations.In order to reduce the total solution time,an inner-outer loop iterative solution framework is designed to solve the nonlinear compressed observation model.The outer loop makes a linear approximation to the nonlinear system.The inner loop uses the reconstruction algorithm to solve the linear problem of the outer loop with a small number of iterations.The method can reduce the number of updates of the Jacobian matrix and the sensing matrix with large computational complexity in the iterative process as much as possible,and improve the efficiency of solving the model.The simulation results show that the first 400 terms Spherical Harmonic polynomial,the first 325 terms Annular Zernike polynomial and the first 1225 terms Legendre-Fourier polynomial can accurately represent the radiation energy(the representation error is less than 3×10-4);when the sparsity is 200,the reconstruction error of radiation flux is less than 1×10-3,which verifies the good sparsity of radiation flux on three orthogonal bases.Compared with the traditional method?Preconditioned Conjugate Gradient method?,the CGHTP algorithm has 10-80 times higher overall efficiency in obtaining radiation flux,and this advantage becomes more obvious with the increase of equation size.Compared with the similar Compressed Sensing reconstruction algorithm,its iteration time is greatly reduced,and the solution results are more accurate and stable,which verifies the superior performance of CGHTP algorithm.Finally,the method is integrated into the ICF simulation software IRad3D.Two cylindrical cavity capsule models in Shenguang-II and Shenguang-III are taken as examples to analyze the radiation symmetry.The effectiveness of the proposed method is verified. |
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