The Bondi problem revisited: a spectral domain decomposition code

Understand

We present a simple domain decomposition code based on the Galerkin-Collocation method to integrate the field equations of the Bondi problem.

• The algorithm is stable, exhibits exponential convergence when considering the Bondi formula as an error measure, and is computationally economical.
• We have incorporated features of both Galerkin and Collocation methods along with the establishment of two non-overlapping subdomains.
• We have further applied the code to show the decay of the Bondi mass in the nonlinear regime and its power-law late time decay.