相关论文: Projective and Coarse Projective Integration for P…

A general high-order fully explicit scheme based on projective integration methods is here presented to solve systems of degenerate parabolic equations in general dimensions. The method is based on a BGK approximation of the…

In "equation-free" multiscale computation a dynamic model is given at a fine, microscopic level; yet we believe that its coarse-grained, macroscopic dynamics can be described by closed equations involving only coarse variables. These…

We propose a computer-assisted approach to studying the effective continuum behavior of spatially discrete evolution equations. The advantage of the approach is that the "coarse model" (the continuum, effective equation) need not be…

In this study, a new coupled Partial Differential Equation (CPDE) based image denoising model incorporating space-time regularization into non-linear diffusion is proposed. This proposed model is fitted with additive Gaussian noise which…

We develop a general framework for numerically solving differential equations while preserving invariants. As in standard projection methods, we project an arbitrary base integrator onto an invariant-preserving manifold, however, our method…

Equation-free approaches have been proposed in recent years for the computational study of multiscale phenomena in engineering problems where evolution equations for the coarse-grained, system-level behavior are not explicitly available. In…

Solving multiscale diffusion problems is often computationally expensive due to the spatial and temporal discretization challenges arising from high-contrast coefficients. To address this issue, a partially explicit temporal splitting…

The movement of many organisms can be described as a random walk at either or both the individual and population level. The rules for this random walk are based on complex biological processes and it may be difficult to develop a tractable,…

We have developed a new, very efficient numerical scheme to solve the CR diffusion convection equation that can be applied to the study of the nonlinear time evolution of CR modified shocks for arbitrary spatial diffusion properties. The…

We present a unified framework for solving partial differential equations (PDEs) using video-inpainting diffusion transformer models. Unlike existing methods that devise specialized strategies for either forward or inverse problems under…

Usually, the systems of partial differential equations (PDEs) are discovered from observational data in the single vector equation form. However, this approach restricts the application to the real cases, where, for example, the form of the…

We study a general, high-order, fully explicit numerical method for simulating kinetic equations with a BGK-type collision model with multiple relaxation times. In that case, the problem is stiff and its spectrum consists of multiple…

We have developed and implemented a numerical evolution scheme for a class of stochastic problems in which the temporal evolution occurs on widely-separated time scales, and for which the slow evolution can be described in terms of a small…

General relativity uses curved space-time to describe accelerating frames. The movement of particles in different curved space-times can be regarded as equivalent physical processes based on the covariant transformation between different…

Microscopic processes on surfaces such as adsorption, desorption, diffusion and reaction of interacting particles can be simulated using kinetic Monte Carlo (kMC) algorithms. Even though kMC methods are accurate, they are computationally…

Discrete translational symmetry plays a fundamental role in condensed matter physics and lattice gauge theories, enabling the analysis of systems that would otherwise be intractable. Despite this, many open problems remain. Quantum…

The simulation of problems in kinetic plasma physics are often challenging due to strongly coupled phenomena across multiple scales. In this work, we propose a wavelet-based coarse-grained numerical scheme, based on the framework of…

We describe a reverse integration approach for the exploration of low-dimensional effective potential landscapes. Coarse reverse integration initialized on a ring of coarse states enables efficient "navigation" on the landscape terrain:…

We follow up an earlier work (briefly reviewed below) to investigate the temporal stability of an exact travelling front solution, constructed in the form of an integral expression, for a one-dimensional discrete Nagumo-like model without…

Many man-made objects are characterised by a shape that is symmetric along one or more planar directions. Estimating the location and orientation of such symmetry planes can aid many tasks such as estimating the overall orientation of an…