3-Dimensional Adaptive Unstructured Tessellated Look-up Tables for the Approximation of Compton Form Factors

TL;DR

This paper introduces a 3D adaptive unstructured tessellation method for approximating functions, significantly reducing computation time in nuclear physics simulations involving Compton Form Factors.

Contribution

It presents a novel iterative algorithm for creating unstructured tetrahedral tessellations to efficiently approximate functions with high precision.

Findings

Achieves 1% mean interpolation error

Reduces Monte Carlo simulation time by ~23 times for 10^7 events

Extrapolated reduction of ~955 times for 10^10 events

Abstract

We describe an iterative algorithm to construct an unstructured tessellation of simplices (irregular tetrahedra in 3-dimensions) to approximate an arbitrary function to a desired precision by interpolation. The method is applied to the generation of Compton Form Factors for simulation and analysis of nuclear femtography, as enabled by high energy exclusive processes such as electron-proton scattering producing just an electron, proton, and gamma-ray in the final state. While producing tessellations with only a 1% mean interpolation error, our results show that the use of such tessellations can significantly decrease the computation time for Monte Carlo event generation by $\sim23$ times for $10^{7}$ events (and using extrapolation, by $\sim955$ times for $10^{10}$ events).