Functional programming framework for GRworkbench

TL;DR

This paper introduces a functional programming framework for GRworkbench, enhancing numerical differential geometry computations in General Relativity with more accurate derivatives and improved performance.

Contribution

The paper presents a novel functional programming approach in C++ for GRworkbench, enabling direct function representation and automatic differentiation for better accuracy and efficiency.

Findings

Automatic differentiation improves derivative accuracy

Performance of geometric operations increased tenfold

Framework closely mirrors mathematical formalism of Differential Geometry

Abstract

The software tool GRworkbench is an ongoing project in visual, numerical General Relativity at The Australian National University. Recently, the numerical differential geometric engine of GRworkbench has been rewritten using functional programming techniques. By allowing functions to be directly represented as program variables in C++ code, the functional framework enables the mathematical formalism of Differential Geometry to be more closely reflected in GRworkbench . The powerful technique of `automatic differentiation' has replaced numerical differentiation of the metric components, resulting in more accurate derivatives and an order-of-magnitude performance increase for operations relying on differentiation.