# Sparse Representation Based Efficient Radiation Symmetry Analysis Method for Cylindrical Model of Inertial Confinement Fusion

## TL;DR

This paper introduces a sparse representation method for efficient radiation symmetry analysis in inertial confinement fusion models, significantly reducing computation time while maintaining accuracy.

## Contribution

The paper proposes a novel sparse representation approach using specific polynomial bases and a new algorithm to efficiently solve nonlinear radiation flux equations in ICF models.

## Key findings

- Achieves tenfold reduction in computation time for radiation flux calculation.
- Maintains high accuracy with significantly fewer equations.
- Efficiency increases as mesh element size decreases.

## Abstract

Radiation symmetry evaluation is critical to the laser driven Inertial Confinement Fusion (ICF), which is usually done by solving a view-factor equation model. The model is nonlinear, and the number of equations can be very large when the size of discrete mesh element is very small to achieve a prescribed accuracy, which may lead to an intensive equation solving process. In this paper, an efficient radiation symmetry analysis approach based on sparse representation is presented, in which, 1) the Spherical harmonics, annular Zernike polynomials and Legendre-Fourier polynomials are employed to sparsely represent the radiation flux on the capsule and cylindrical cavity, and the nonlinear energy equilibrium equations are transformed into the equations with sparse coefficients, which means there are many redundant equations, 2) only a few equations are selected to recover such sparse coefficients with Latin hypercube sampling, 3) a Conjugate Gradient Subspace Thresholding Pursuit (CGSTP) algorithm is then given to rapidly obtain such sparse coefficients equation with as few iterations as possible. Finally, the proposed method is validated with two experiment targets for Shenguang II and Shenguang III laser facility in China. The results show that only one tenth of computation time is required to solve one tenth of equations to achieve the radiation flux with comparable accuracy. Further more, the solution is much more efficient as the size of discrete mesh element decreases, in which, only 1.2\% computation time is required to obtain the accurate result.