相关论文: Computing Nearly Singular Solutions Using Pseudo-S…

The single-step explicit time integration methods have long been valuable for solving large-scale nonlinear structural dynamic problems, classified into single-solve and multi-sub-step approaches. However, no existing explicit single-solve…

A novel semi-Lagrangian method is introduced to solve numerically the Euler equation for ideal incompressible flow in arbitrary space dimension. It exploits the time-analyticity of fluid particle trajectories and requires, in principle,…

This paper aims to investigate the numerical approximation of a general second order parabolic stochastic partial differential equation(SPDE) driven by multiplicative and additive noise under more relaxed conditions. The SPDE is discretized…

In this paper, we study the problem of computing the effective diffusivity for particles moving in chaotic flows. Instead of solving a convection-diffusion type cell problem in the Eulerian formulation (arising from homogenization theory…

The spectral deferred correction method is a variant of the deferred correction method for solving ordinary differential equations. A benefit of this method is that is uses low order schemes iteratively to produce a high order…

This paper presents a new resolution strategy for multi-scale streamer discharge simulations based on a second order time adaptive integration and space adaptive multiresolution. A classical fluid model is used to describe plasma…

The quasi-2D electrostatic systems, characterized by periodicity in two dimensions with a free third dimension, have garnered significant interest in many fields. We apply the sum-of-Gaussians (SOG) approximation to the Laplace kernel,…

Pseudospectral approximation provides a means to approximate the dynamics of delay differential equations (DDE) by ordinary differential equations (ODE). This article develops a computer-aided algorithm to determine the distance between the…

We develop Second Order Asymptotical Regularization (SOAR) methods for solving inverse source problems in elliptic partial differential equations with both Dirichlet and Neumann boundary data. We show the convergence results of SOAR with…

We present a unified algorithmic framework for quantum simulation of non-unitary dynamics and matrix functions, governed by the principle of spectral aliasing derived from the Poisson Summation Formula (PSF). By reinterpreting…

The present paper is devoted to implementation of the immersed boundary technique into the Fourier pseudo-spectral solution of the vorticity-velocity formulation of the two-dimensional incompressible Navier--Stokes equations. The immersed…

Semi-Lagrangian schemes with various splitting methods, and with different reconstruction/interpolation strategies have been applied to kinetic simulations. For example, the order of spatial accuracy of the algorithms proposed in {[Qiu and…

In this study, we introduce a refined method for ascertaining error estimations in numerical simulations of dynamical systems via an innovative application of composition techniques. Our approach involves a dual application of a basic…

In this paper we consider fully discrete approximations with inf-sup stable mixed finite element methods in space to approximate the Navier-Stokes equations. A continuous downscaling data assimilation algorithm is analyzed in which…

In this paper, we study a hierarchical SSOR (HSSOR) method which could be used as a standalone method or as a smoother for a two-grid method. It is found that the method leads to faster convergence compared to more costly incomplete LU…

In this article, we study the regularity theory for two linear equations that are important in fluid dynamics: the passive scalar equation for (time-varying) shear flows close to Couette in $\mathbb T \times [-1,1]$ with vanishing…

The numerical simulation of the 3D incompressible Euler equation is analyzed with respect to different integration methods. The numerical schemes we considered include spectral methods with different strategies for dealiasing and two…

We present an efficient and highly scalable geometric method for two-dimensional ideal fluid dynamics on the sphere. The starting point is Zeitlin's finite-dimensional model of hydrodynamics. The efficiency stems from exploiting a…

In this paper, we introduce an algorithm that provides approximate solutions to semi-linear ordinary differential equations with highly oscillatory solutions, which, after an appropriate change of variables, can be rewritten as…

We introduce an accurate and efficient method for a class of nonlocal potential evaluations with free boundary condition, including the 3D/2D Coulomb, 2D Poisson and 3D dipolar potentials. Our method is based on a Gaussian-sum approximation…