Related papers: Fast Kinetic Scheme : efficient MPI parallelizatio…
A fast multilevel algorithm based on directionally scaled tensor-product Gaussian kernels on structured sparse grids is proposed for interpolation of high-dimensional functions and for the numerical integration of high-dimensional…
This paper presents a Graphics Processing Units (GPUs) acceleration method of an iterative scheme for gas-kinetic model equations. Unlike the previous GPU parallelization of explicit kinetic schemes, this work features a fast converging…
In recent years, there has been renewed interest in closing the performance gap between state-of-the-art planning solvers and generalized planning (GP), a research area of AI that studies the automated synthesis of algorithmic-like…
The numerical approximation of the Boltzmann collision operator presents significant challenges arising from its high dimensionality, nonlinear structure, and nonlocal integral form. In this work, we propose a Fourier Neural Operator (FNO)…
Most numerical schemes proposed for solving BGK models for rarefied gas dynamics are based on the discrete velocity approximation. Since such approach uses fixed velocity grids, one must secure a sufficiently large domain with fine velocity…
To prepare images for better segmentation, we need preprocessing applications, such as smoothing, to reduce noise. In this paper, we present an enhanced computation method for smoothing 2D object in binary case. Unlike existing approaches,…
In this paper, we propose a general framework to design asymptotic preserving schemes for the Boltzmann kinetic kinetic and related equations. Numerically solving these equations are challenging due to the nonlinear stiff collision (source)…
A scalable algorithm for solving compact banded linear systems on distributed memory architectures is presented. The proposed method factorizes the original system into two levels of memory hierarchies, and solves it using parallel cyclic…
An algorithm for the systematic analytical approximation of multi-scale Feynman integrals is presented. The algorithm produces algebraic expressions as functions of the kinematical parameters and mass scales appearing in the Feynman…
This paper introduces a parallel directional fast multipole method (FMM) for solving N-body problems with highly oscillatory kernels, with a focus on the Helmholtz kernel in three dimensions. This class of oscillatory kernels requires a…
Boltzmann equation requires some alternative simpler kinetic model like BGK to replace the collision term. Such a kinetic model which replaces the Boltzmann collision integral should preserve the basic properties and characteristics of the…
The ellipsoidal BGK model is a generalized version of the original BGK model designed to reproduce the physical Prandtl number in the Navier-Stokes limit. In this paper, we propose a new implicit semi-Lagrangian scheme for the ellipsoidal…
We design an asymptotic-preserving scheme for the semiconductor Boltzmann equation which leads to an energy-transport system for electron mass and internal energy as mean free path goes to zero. To overcome the stiffness induced by the…
Numerical studies of shock waves in large scale systems via kinetic simulations with millions of particles are too computationally demanding to be processed in serial. In this work we focus on optimizing the parallel performance of a…
In this paper a spectral-Lagrangian method for the Boltzmann equation for a multi-energy level gas is proposed. Internal energy levels are treated as separate species and inelastic collisions (leading to internal energy excitation and…
The numerical method of dynamical low-rank approximation (DLRA) has recently been applied to various kinetic equations showing a significant reduction of the computational effort. In this paper, we apply this concept to the linear…
Cell nuclei segmentation is one of the most important tasks in the analysis of biomedical images. With ever-growing sizes and amounts of three-dimensional images to be processed, there is a need for better and faster segmentation methods.…
We discuss two topics that we have encountered in our lattice-Boltzmann simulations of complex fluids: the sizes of droplets in particle-stabilised emulsions and deformable particles in fluid flow. The common factor in these seemingly…
We reduce the eight-dimensional weak form of the bilinear Boltzmann collision operator to a five-dimensional kinematic core by rigidly rotating the laboratory frame to align with the colliding pair and integrating over the $\mathrm{SO}(3)$…
This work introduces a kernel-independent, multilevel, adaptive algorithm for efficiently evaluating a discrete convolution kernel with a given source distribution. The method is based on linear algebraic tools such as low rank…