Education
Last updated: September 14, 2026.
The educational work connects numerical relativity with applied mathematics through freely available explanations, an online book, and executable examples. These resources support independent study and student training in the geometry and computation of wave propagation.
Online book
With Markus Wess, I have written Hyperboloidal Compactification in NGSolve, an online book introducing the implementation of hyperboloidal compactification in the finite element library NGSolve. It develops the scattering problem, compactification of the far field, and the weak formulation, with executable examples in both the frequency and time domains.
The book is intended for readers already familiar with finite element methods for Helmholtz or wave equations. Its source code and examples are publicly available. For the accompanying derivation and numerical analysis, see our preprint Finite Elements for Helmholtz Scattering with Infinity as a Computational Boundary.
Tutorials and notebooks
- How to solve wave equations on unbounded domains introduces hyperboloidal compactification through the one-dimensional wave equation. Its Google Colab notebook lets readers run and modify the examples in a browser.
- Banging a black hole (2026) extends this approach to gravitational waves from a perturbed Schwarzschild black hole, with an accompanying Google Colab notebook.
Further blog posts on hyperboloidal methods explain the underlying geometry at a level intended for beginning graduate students. Together, these materials provide a route from simple wave equations to black-hole perturbations and finite element scattering calculations.
Student training
The grant has supported two students: Ekrem Demirboğa and Govind Arun Kumar. Student training connects numerical relativity with applied mathematics and scientific computing.