相关论文: Fast Numerical Simulation of Allen-Cahn Equation
The parabolic Allen-Cahn equation is a semilinear partial differential equation linked to the mean curvature flow by a singular perturbation. We show an improved convergence property of the parabolic Allen-Cahn equation to the mean…
We investigate the numerical approximation of the stochastic Allen--Cahn equation with multiplicative noise on a periodic domain. The considered scheme uses a recently proposed augmented variant of scalar auxiliary variable method for the…
In this work, we propose a bi-grid scheme framework for the Allen-Cahn equation in Finite Element Method. The new methods are based on the use of two FEM spaces, a coarse one and a fine one, and on a decomposition of the solution into mean…
In this note, we present the stability as well as performance analysis of asynchronous parallel computing algorithm implemented in 1D heat equation with CUDA. The primary objective of this note lies in dissemination of asynchronous parallel…
Simulations of systems with quenched disorder are extremely demanding, suffering from the combined effect of slow relaxation and the need of performing the disorder average. As a consequence, new algorithms, improved implementations, and…
Recent advances in deep learning have allowed neural networks (NNs) to successfully replace traditional numerical solvers in many applications, thus enabling impressive computing gains. One such application is time domain simulation, which…
Current trends in the computer graphics community propose leveraging the massive parallel computational power of GPUs to accelerate physically based simulations. Collision detection and solving is a fundamental part of this process. It is…
Quantum algorithms for simulating electronic ground states are slower than popular classical mean-field algorithms such as Hartree-Fock and density functional theory, but offer higher accuracy. Accordingly, quantum computers have been…
Asynchronous algorithms have attracted much attention recently due to the crucial demands on solving large-scale optimization problems. However, the accelerated versions of asynchronous algorithms are rarely studied. In this paper, we…
The paper deals with the developing of the methodological backgrounds for the modeling and simulation of complex dynamical objects. Such backgrounds allow us to perform coordinate transformation and formulate the algorithm of its usage for…
The Allen-Cahn equation is solved numerically by operator splitting Fourier spectral methods. The basic idea of the operator splitting method is to decompose the original problem into sub-equations and compose the approximate solution of…
Handling clustering problems are important in data statistics, pattern recognition and image processing. The mean-shift algorithm, a common unsupervised algorithms, is widely used to solve clustering problems. However, the mean-shift…
Hybrid computational architectures based on the joint power of Central Processing Units and Graphic Processing Units (GPUs) are becoming popular and powerful hardware tools for a wide range of simulations in biology, chemistry, engineering,…
In this paper, we study numerical methods for solving the coupled Allen-Cahn/Cahn-Hilliard system associated with a free energy functional of logarithmic type. To tackle the challenge posed by the special free energy functional, we propose…
We present error estimates for four unconditionally energy stable numerical schemes developed for solving Allen-Cahn equations with nonlocal constraints. The schemes are linear and second order in time and space, designed based on the…
We show how to accelerate the direct solution of the Boltzmann equation using Graphics Processing Units (GPUs). In order to fully exploit the computational power of the GPU, we choose a method of solution which combines a finite difference…
In this work, we present a second-order nonuniform time-stepping scheme for the time-fractional Allen-Cahn equation. We show that the proposed scheme preserves the discrete maximum principle, and by using the convolution structure of…
With the advent of high-performance computing techniques, the data for analysis has grown significantly. Here, graphic processing unit (GPU) based program kernels are discussed to exploit parallelism in the analysis codes specific to…
In this paper, we present high-performance computing for the BGK model of the Boltzmann equation with a mesh-free method. For the numerical simulation of the BGK equation we use an Arbitrary-Lagrangian-Eulerian (ALE) method developed in…
Molecular dynamics simulates the~movements of atoms. Due to its high cost, many methods have been developed to "push the~simulation forward". One of them, metadynamics, can hasten the~molecular dynamics with the~help of variables describing…