Numerical Methods in Gravitational Lensing

TL;DR

This paper reviews numerical methods essential for solving complex problems in gravitational lensing, including image finding, light ray propagation, and mass reconstruction, emphasizing adaptive-grid techniques and statistical reliability.

Contribution

It introduces and discusses advanced numerical approaches tailored for gravitational lensing challenges, focusing on adaptive-grid methods and shear-inversion techniques.

Findings

Adaptive-grid methods improve image detection accuracy.

Spatial resolution impacts weak lensing statistics.

Shear-inversion techniques are crucial for mass reconstruction.

Abstract

Most problems in gravitational lensing require numerical solutions. The most frequent types of problems are (1) finding multiple images of a single source and classifying the images according to their properties like magnification or distortion; (2) propagating light rays through large cosmological simulations; and (3) reconstructing mass distributions from their tidal field. This lecture describes methods for solving such problems. Emphasis is put on using adaptive-grid methods for finding images, issues of spatial resolution and reliability of statistics for weak lensing by large-scale structures, and methodical questions related to shear-inversion techniques.