Towards Faster Supernovae Simulations: Enhancing Convergence in TARDIS with Adaptive Damping

This thesis investigates numerical techniques to improve the iterative convergence of TARDIS, an open-source one-dimensional Monte Carlo radiative transfer code for simulating supernova spectra. During each TARDIS simulation, a fixed-point iteration adjusts the ejecta’s plasma state (e.g., radiative temperature and dilution factor) to satisfy radiative equilibrium, but naive full updates can lead to slow or oscillatory convergence due to Monte Carlo noise and the nonlinear plasma–radiation coupling. We implement and evaluate two convergence enhancement strategies within TARDIS’s iterative framework: static damping (constant under-relaxation of state updates) and an adaptive damping technique that dynamically tunes the relaxation factor based on convergence history. Detailed benchmarks are conducted on multiple supernova ejecta models (SN Ia, SN Ibc, and SN Iax) to assess the performance of these methods. Convergence behavior is quantified using key metrics including shell-by-shell radiative temperature (𝑇→rad), dilution factor (𝑊→ ), and the inner boundary temperature (𝑇inner) that governs luminosity. The adaptive damping scheme modulates the update step to prevent overshoot and oscillations caused by estimator noise, while accelerating convergence when changes become small. We find that both damping strategies substantially improve the stability of the fixed-point iteration and reduce the number of iterations needed to reach a converged solution (compared to the default undamped approach), with the adaptive scheme achieving the fastest convergence and greater robustness against noise-induced fluctuations. We also analyze noise sensitivity, confirming that the adaptive method maintains reliable convergence even with varying Monte Carlo sampling. This study enhances the convergence methodology of TARDIS, contributing to more efficient and robust supernova spectral synthesis.