Kadath: a spectral solver for theoretical physics

TL;DR

Kadath is a modular spectral solver library designed for solving complex, non-linear partial differential equations in theoretical physics, validated through applications in gauge field theory and general relativity.

Contribution

It introduces a flexible, modular spectral method library capable of handling various geometries and strongly non-linear problems in theoretical physics.

Findings

Successfully applied to four physics problems

Handles strongly non-linear equations

Supports multiple coordinate systems

Abstract

Kadath is a library that implements spectral methods in a very modular manner. It is designed to solve a wide class of problems that arise in the context of theoretical physics. Several types of coordinates are implemented and additional geometries can be easily encoded. Partial differential equations of various types are discretized by means of spectral methods. The resulting system is solved using a Newton-Raphson iteration. Doing so, Kadath is able to deal with strongly non-linear situations. The algorithms are validated by applying the library to four different problems of contemporary physics, in the fields of gauge field theory and general relativity