An Accurate Quadrature Rule on the Sphere for Fast Computation of the Radiative Transport Equation

TL;DR

This paper introduces a new quadrature rule on the sphere that enables fast and accurate numerical solutions of the three-dimensional radiative transport equation, significantly reducing computational costs.

Contribution

The paper proposes a novel quadrature formula on the sphere with fewer localized points, improving efficiency in solving the 3D RTE.

Findings

Achieves high accuracy with fewer quadrature points.

Reduces computational resources required for 3D RTE.

Enables faster numerical computation of radiative transfer in three dimensions.

Abstract

We present an accurate quadrature formula on the sphere with less localized quadrature points for efficient numerical computation of the radiative transport equation (RTE) in the three dimensions. High accuracy of the present method dramatically reduces computational resources and fast computation of 3D RTE is achieved.