International Journal of Mathematics and Physics

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Comparing the efficiency of GPU and CPU in gravitational lensing simulation
(Al-Farabi Kazakh National University, 2024-06-20)
Nurzada Beissen
;
Daniya Utepova
;
Vladimir N. Kossov
;
Saken Toktarbay
;
Manas Khassanov
In this study, we investigate the computational advancements in simulating gravitational lensing, particularly focusing on the Schwarzschild black hole model. The traditional approach of back ray tracing, where photons are traced back from the observer to the source, is computationally intensive, especially when aiming to achieve high-resolution images of lensing effects around black holes. By employing a numerical method that integrates the Schwarzschild metric with initial conditions derived from the observer's plane, we map the deflection of light around a black hole to generate simulated images of gravitational lensing.The core of our study is the comparison between traditional CPU-based computations and GPU-accelerated processes using the Numba library. Our findings reveal that GPU acceleration, with its parallel processing capabilities, significantly reduces computation time, particularly as the complexity of the simulation increases with larger grid sizes. This computational efficiency is crucial for simulations of gravitational lensing, where the number of independent calculations grows exponentially with the resolution and accuracy of the desired image.Our research underscores the importance of leveraging GPU technology for astrophysical simulations, offering a substantial improvement in performance over CPU-based methods. Keywords: Gravitational Lensing, GPU Parallelization, Schwarzschild Black Hole, Ray Tracing Methods, Numba Library.
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A novel numerical implementation for solving problem for loaded DEPCAG
(Al-Farabi Kazakh National University, 2023-01-10)
Zh. М. Каdirbayeva
;
Roza E. Uteshova
;
G. Marat
;
B. B. Мinglibayeva
In this work, we propose a new computational approach is implemented to solve a two-point BVP for a loaded differential equation with piecewise constant argument of generalized type (DEPCAG) based on the Dzhumabaev parameterization method. In this method, as parameters, we take the values of the desired solution at the partition points which are chosen taking into account the specifics of the equation. The problem under consideration reduces to an equivalent parametric problem for ordinary differential equations. A solution to this problem, which in turn are found from a system of linear algebraic equations. The found values of the parameters are used to determine the values of the unknown function at the remaining points of the interval by solving auxiliary initial-value problems. We develop a novel numerical implementation for solving the considered a two-point BVP for loaded DEPCAG and provide two examples illustrating its application, where Mathcad software will be used for the calculation.
Цитирования (OpenAlex) 8Цитирования (OpenCitations) 7
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A shadows from the static black hole mimickers
(Al-Farabi Kazakh National University, 2023-01-10)
Aray Muratkhan
;
Ayazhan Orazymbet
;
Madina Zhakipova
;
M. Assylbek
;
Saken Toktarbay
In this work, we study shadows from the naked singularity spacetime. The most analytical solutions of black hole shadows only investigated the case that the geodesic equations for photons can separate variables. We review the spherical null naked singularity metric and this spherically symmetric naked singularity spacetime metric is the solution of Einstein equations with an anisotropic fluid source which has no photon sphere. We also review a static, axially-symmetric singular solution of the vacuum Einstein’s equations without an event horizon which is can be used to describe the exterior gravitational field of a mass distribution with quadrupole moment. Moreover, the corresponding spacetime is characterized by the presence of naked singularities. It is theoretically known that not only a black hole can cast shadow, but other compact objects such as naked singularities, gravastar or boson stars can also cast shadows. We present the analytical calculation of shadows for both naked singularities spacetime and compare with the shadow of Schwarzschild static black hole, we show that this can serve as a black hole mimicker. Keywords: compact object, naked singularity, shadow.
Цитирования (OpenAlex) 5

International Journal of Mathematics and Physics

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