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A standard approach to solving the S$_N$ transport equations is to use source iteration with diffusion synthetic acceleration (DSA). Although this approach is widely used and effective on many problems, there remain some practical issues…
Numerical solution of reaction-diffusion equations in three dimensions is one of the most challenging applied mathematical problems. Since these simulations are very time consuming, any ideas and strategies aiming at the reduction of CPU…
The method of discrete ordinates ($S_N$) is a popular choice for the solution of the neutron transport equation. It is however well known that it suffers from slow convergence of the scattering source in optically thick and diffusive media,…
The multigroup neutron transport criticality calculations using modern supercomputers have been widely employed in a nuclear reactor analysis for studying whether or not a system is self-sustaining. However, the design and development of…
A collision-based hybrid method for the discrete ordinates approximation of the multigroup neutron transport equation is developed for two-dimensional time-dependent problems. At each time step, this algorithm splits the neutron transport…
We develop a numerical code to calculate the neutrino transfer with multi-energy and multi-angle in three dimensions (3D) for the study of core-collapse supernovae. The numerical code solves the Boltzmann equations for neutrino…
In this paper we present a parallelization strategy on distributed memory systems for the Fast Kinetic Scheme --- a semi-Lagrangian scheme developed in [J. Comput. Phys., Vol. 255, 2013, pp 680-698] for solving kinetic equations. The…
A high-performance gas kinetic solver using multi-level parallelization is developed to enable pore-scale simulations of rarefied flows in porous media. The Boltzmann model equation is solved by the discrete velocity method with an…
Tensor network techniques, known for their low-rank approximation ability that breaks the curse of dimensionality, are emerging as a foundation of new mathematical methods for ultra-fast numerical solutions of high-dimensional Partial…
In this paper we solve the Boltzmann transport equation using AI libraries. The reason why this is attractive is because it enables one to use the highly optimised software within AI libraries, enabling one to run on different computer…
The impressive progress of the kinetic schemes in the solution of gas dynamics problems and the development of effective parallel algorithms for modern high performance parallel computing systems led to the development of advanced methods…
We develop a multi-dimensional, parallelized domain decomposition strategy (DDC) for mass-transfer particle tracking (MTPT) methods. These methods are a type of Lagrangian algorithm for simulating reactive transport and are able to be…
In this paper we give an introduction to the Boltzmann equation for neutrino transport used in core collapse supernova models as well as a detailed mathematical description of the \emph{Isotropic Diffusion Source Approximation} (IDSA).…
Paper presents a new solver for numerical solution of the Boltzmann kinetic equation with Shakhov model collision integral (S-model) for arbitrary spatial domains. Numerical method utilizes Tensor-Train decomposition, which allows to reduce…
This research addresses the numerical simulation of the Boltzmann transport equation for semiconductor devices by proposing a multidimensional self-adaptive numerical simulation framework. This framework is applied to two important…
This paper presents an efficient parallel radiative transfer-based inverse-problem solver for time-domain optical tomography. The radiative transfer equation provides a physically accurate model for the transport of photons in biological…
We consider flux-corrected finite element discretizations of 3D convection-dominated transport problems and assess the computational efficiency of algorithms based on such approximations. The methods under investigation include…
In this paper we deal with the extension of the Fast Kinetic Scheme (FKS) [J. Comput. Phys., Vol. 255, 2013, pp 680-698] originally constructed for solving the BGK equation, to the more challenging case of the Boltzmann equation. The scheme…
We present a new deterministic approach for the solution of the Boltzmann kinetic equation based on nodal discontinuous Galerkin (DG) discretizations in velocity space. In the new approach the collision operator has the form of a bilinear…
The multigroup neutron transport equations have been widely used to study the motion of neutrons and their interactions with the background materials. Numerical simulation of the multigroup neutron transport equations is computationally…