USING NUMERICAL METHODS AND PARALLEL PROGRAMMING FOR SIMULATING PHOTON TRAJECTORIES IN ASTROPHYSICAL ENVIRONMENTS
Zabelin, Timofey (2024)
Julkaisun pysyvä osoite on
https://urn.fi/URN:NBN:fi:amk-2024053018630
https://urn.fi/URN:NBN:fi:amk-2024053018630
Tiivistelmä
The objective of this thesis was to evaluate the efficiency of various numerical
methods in simulating photon trajectories in astrophysical environments,
specifically near a Kerr black hole. This study employed numerical methods
integrated with NVIDIA CUDA technology to compute the solutions to a system
of ordinary differential equations (ODEs) that model these photon movements.
Initially, previous analyses of damping systems suggested that higher-order
Runge-Kutta methods could offer computational time performance comparable
to the fourth order Runge-Kutta (RK4). Motivated by these findings, this
research aimed to determine whether similar efficiency could be achieved in
more complex astrophysical simulations.
Quantitative methods were utilized to implement and compare the second,
third, fourth, and eighth Order Runge-Kutta methods, along with the
Adams-Bashforth second-order method. The implementation was carried out
on a parallel programming architecture to leverage the computational power of
GPUs. Contrary to initial assumptions, the results indicated that higher-order
methods such as the Eighth Order Runge-Kutta (RK8) incurred longer
computational times compared to RK4. Surprisingly, the Adams-Bashforth
method exhibited the longest computation time, even exceeding that of RK8.
The study concluded that while higher-order numerical methods increased
accuracy, they did not improve computational efficiency within the context of
this specific astrophysical simulation. The findings suggest that lower-order
methods might be more suitable for large-scale simulations where both
accuracy and computational speed are critical. This research contributes to the
field by clarifying the computational trade-offs involved in using advanced
numerical methods for simulating complex astrophysical phenomena
methods in simulating photon trajectories in astrophysical environments,
specifically near a Kerr black hole. This study employed numerical methods
integrated with NVIDIA CUDA technology to compute the solutions to a system
of ordinary differential equations (ODEs) that model these photon movements.
Initially, previous analyses of damping systems suggested that higher-order
Runge-Kutta methods could offer computational time performance comparable
to the fourth order Runge-Kutta (RK4). Motivated by these findings, this
research aimed to determine whether similar efficiency could be achieved in
more complex astrophysical simulations.
Quantitative methods were utilized to implement and compare the second,
third, fourth, and eighth Order Runge-Kutta methods, along with the
Adams-Bashforth second-order method. The implementation was carried out
on a parallel programming architecture to leverage the computational power of
GPUs. Contrary to initial assumptions, the results indicated that higher-order
methods such as the Eighth Order Runge-Kutta (RK8) incurred longer
computational times compared to RK4. Surprisingly, the Adams-Bashforth
method exhibited the longest computation time, even exceeding that of RK8.
The study concluded that while higher-order numerical methods increased
accuracy, they did not improve computational efficiency within the context of
this specific astrophysical simulation. The findings suggest that lower-order
methods might be more suitable for large-scale simulations where both
accuracy and computational speed are critical. This research contributes to the
field by clarifying the computational trade-offs involved in using advanced
numerical methods for simulating complex astrophysical phenomena