Related papers: Deterministic particle method approximation of a c…
In this work we study the one-dimensional contact process with diffusion using two different approaches to research the critical properties of this model: the supercritical series expansions and finite-size exact solutions. With special…
We consider a parameter dependent family of damped hyperbolic equations with interesting limit behavior: the system approaches steady states exponentially fast and for parameter to zero the solutions converge to that of a parabolic limit…
Convection-diffusion-reaction equations model the conservation of scalar quantities. From the analytic point of view, solution of these equations satisfy under certain conditions maximum principles, which represent physical bounds of the…
In this paper we study a system of advection-diffusion equations in a bulk domain coupled to an advection-diffusion equation on an embedded surface. Such systems of coupled partial differential equations arise in, for example, the modeling…
We consider the initial/boundary value problem for a diffusion equation involving multiple time-fractional derivatives on a bounded convex polyhedral domain. We analyze a space semidiscrete scheme based on the standard Galerkin finite…
We consider a two-species simple exclusion process on a periodic lattice. We use the method of matched asymptotics to derive evolution equations for the two population densities in the dilute regime, namely a cross-diffusion system of…
Motivated by problems where the response is needed at select localized regions in a large computational domain, we devise a novel finite element discretization that results in exponential convergence at pre-selected points. The two key…
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…
Feedback particle filter (FPF) is a numerical algorithm to approximate the solution of the nonlinear filtering problem in continuous-time settings. In any numerical implementation of the FPF algorithm, the main challenge is to numerically…
As a counterpoint to classical stochastic particle methods for linear diffusion equations, we develop a deterministic particle method for the weighted porous medium equation (WPME) and prove its convergence on bounded time intervals. This…
In this paper, we develop a multiphysics finite element method for solving the quasi-static thermo-poroelasticity model with nonlinear permeability. The model involves multiple physical processes such as deformation, pressure, diffusion and…
The transition from a microscopic model for the movement of many particles to a macroscopic continuum model for a density flow is studied. The microscopic model for the free flow is completely deterministic, described by an interaction…
In this paper, we focus on the numerical analysis of quantitative photoacoustic tomography. Our goal is to reconstruct the optical coefficients, i.e., the diffusion and absorption coefficients, using multiple internal observational data.…
The numerical solution of a nonlinear and space-fractional anti-diffusive equation used to model dune morphodynamics is considered. Spatial discretization is effected using a finite element method whereas the Crank-Nicolson scheme is used…
We revise the encounter-based approach to imperfect diffusion-controlled reactions, which employs the statistics of encounters between a diffusing particle and the reactive region to implement surface reactions. We extend this approach to…
We present a high order parameter-robust numerical method for a system of (M>=2) coupled singularly perturbed parabolic reaction-diffusion problems. A small perturbation parameter {\epsilon} is multiplied with the second order spatial…
Studying systems where many individual bodies in motion interact with one another is a complex and interesting area. Simple mechanisms that may be determined for biological, chemical, or physical reasons can lead to astonishingly complex…
Integration against a probability distribution given its unnormalized density is a central task in Bayesian inference and other fields. We introduce new methods for approximating such expectations with a small set of weighted samples --…
We present a novel particle management method using the Characteristic Mapping framework. In the context of explicit evolution of parametrized curves and surfaces, the surface distribution of marker points created from sampling the…
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…