Variance reduction method for particle transport equation in spherical geometry

TL;DR

This paper presents an importance sampling method for particle transport equations in spherical geometry, significantly reducing variance in Monte Carlo simulations of inertial confinement fusion with moderate additional computational cost.

Contribution

It introduces a variance reduction technique based on importance sampling using the stationary adjoint problem in a spherical model, tailored for inertial confinement fusion simulations.

Findings

Variance reduced by a factor of 50 to 100

Computational cost increased by a factor of 2 to 8

Effective for spherical symmetry in fusion simulations

Abstract

This article is devoted to the design of importance sampling method for the Monte Carlo simulation of a linear transport equation. This model is of great importance in the simulation of inertial confinement fusion experiments. Our method is restricted to a spherically symmetric idealized design : an outer sphere emitting radiation towards an inner sphere, which in practice should be thought of as the hohlraum and the fusion capsule, respectively. We compute the importance function as the solution of the corresponding stationary adjoint problem. Doing so, we have an important reduction of the variance (by a factor 50 to 100), with a moderate increase of computational cost (by a factor 2 to 8).