相关论文: High-order fundamental and general solutions of co…

This paper is concerned with the two new boundary-type radial basis function collocation schemes, boundary knot method (BKM) and boundary particle method (BPM). The BKM is developed based on the dual reciprocity theorem, while the BPM…

A high-order finite element method is proposed to solve the nonlinear convection-diffusion equation on a time-varying domain whose boundary is implicitly driven by the solution of the equation. The method is semi-implicit in the sense that…

In this paper, we propose high order numerical methods to solve a 2D advection diffusion equation, in the highly oscillatory regime. We use an integrator strategy that allows the construction of arbitrary high-order schemes {leading} to an…

In theory, diffusion curves promise complex color gradations for infinite-resolution vector graphics. In practice, existing realizations suffer from poor scaling, discretization artifacts, or insufficient support for rich boundary…

The Cellular Potts Model (CPM) is a robust, cell-level methodology for simulation of biological tissues and morphogenesis. Both tissue physiology and morphogenesis depend on diffusion of chemical morphogens in the extra-cellular fluid or…

In this paper, we solve explicitly and analyze rigorously inhomogeneous initial-boundary-value problems (IBVP) for several fourth-order variations of the traditional diffusion equation and the associated linearized Cahn-Hilliard (C-H) model…

In our recent work [H. Zhang, F.X. Trias, A. Oliva, D. Yang, Y. Tan, Y. Sheng. PIBM: Particulate immersed boundary method for fluid-particle interaction problems. Powder Technology. 272(2015), 1-13.], a particulate immersed boundary method…

We describe an exact and highly efficient numerical algorithm for solving a special but important class of convection-diffusion equations. These equations occur in many problems in physics, chemistry, or biology, and they are usually hard…

In this paper, we employ an finite volume method (FVM) based on the heterogenous multiscale method (HMM), for the multiscale convection-diffusion-reaction problem. The optimal order convergence rate in H^1-norm is given for periodic medias.

The paper develops a hybrid method for solving a system of advection--diffusion equations in a bulk domain coupled to advection--diffusion equations on an embedded surface. A monotone nonlinear finite volume method for equations posed in…

A finite difference method is constructed to solve singularly perturbed convection-diffusion problems posed on smooth domains. Constraints are imposed on the data so that only regular exponential boundary layers appear in the solution. A…

In this paper we present a high-order kernel method for numerically solving diffusion and reaction-diffusion partial differential equations (PDEs) on smooth, closed surfaces embedded in $\mathbb{R}^d$. For two-dimensional surfaces embedded…

The Immersed Boundary Method (IBM) is a popular numerical approach to impose boundary conditions without relying on body-fitted grids, thus reducing the costly effort of mesh generation. To obtain enhanced accuracy, IBM can be combined with…

The boundary knot method (BKM) [1] is a meshless boundary-type radial basis function (RBF) collocation scheme, where the nonsingular general solution is used instead of fundamental solution to evaluate the homogeneous solution, while the…

In this paper, we derive two bound-preserving and mass-conserving schemes based on the fractional-step method and high-order compact (HOC) finite difference method for nonlinear convection-dominated diffusion equations. We split the…

In this paper, we present a meshless hybrid method combining the Generalized Finite Difference (GFD) and Finite Difference based Radial Basis Function (RBF-FD) approaches to solve non-homogeneous partial differential equations (PDEs)…

We propose an open-boundary molecular dynamics method in which an atomistic system is in contact with an infinite particle reservoir at constant temperature, volume and chemical potential. In practice, following the Hamiltonian adaptive…

Solutions of boundary value problems for a diffusion equation of fractional and variable order in differential and difference settings are studied. It is shown that the method of energy inequalities is applicable to obtaining a priori…

In this paper, using the approximate particular solutions of Helmholtz equations, we solve the boundary value problems of Helmholtz equations by combining the methods of fundamental solutions (MFS) with the methods of particular solutions…

We formulate a finite-particle method of mass transport that accounts for general mixed boundary conditions. The particle method couples a geometrically-exact treatment of advection; Wasserstein gradient-flow dynamics; and a…