Accurate Reduced Floating-Point Precision Implicit Monte Carlo

TL;DR

This paper presents methods for implementing the Implicit Monte Carlo scheme for thermal radiative transfer using reduced-precision floating-point arithmetic, achieving comparable accuracy to double-precision implementations.

Contribution

It introduces scaling and floating-point manipulation techniques that enable accurate reduced-precision IMC computations for complex radiative transfer problems.

Findings

Reduced-precision IMC solutions match high-precision results.

Scaling and manipulation techniques effectively minimize numerical errors.

Half-precision implementations are feasible for complex radiative transfer simulations.

Abstract

This work describes methodologies to successfully implement the Implicit Monte Carlo (IMC) scheme for thermal radiative transfer in reduced-precision floating-point arithmetic. The methods used can be broadly categorized into scaling approaches and floating-point arithmetic manipulations. Scaling approaches entail re-scaling values to ensure computations stay within a representable range. Floating-point arithmetic manipulations involve changes to order of operations and alternative summation algorithms to minimize errors in calculations. The Implicit Monte Carlo method has nonlinear dependencies, quantities spanning many orders of magnitude, and a sensitive coupling between radiation and material energy that provide significant difficulties to accurate reduced-precision implementations. Results from reduced and higher-precision implementations of IMC solving the Su & Olson volume source benchmark problem are compared to demonstrate the accuracy of a correctly implemented reduced-precision IMC code. We show that the scaling approaches and floating-point manipulations used in this work can produce solutions with similar accuracy using half-precision data types as compared to a standard double-precision implementation.