相关论文: A two-stage method for reconstruction of parameter…
Ordinary differential equations (ODEs) are widely used to describe dynamical systems in science, but identifying parameters that explain experimental measurements is challenging. In particular, although ODEs are differentiable and would…
We show that the Strang splitting method applied to a diffusion-reaction equation with inhomogeneous general oblique boundary conditions is of order two when the diffusion equation is solved with the Crank-Nicolson method, while order…
A singularly perturbed linear system of second order ordinary differential equations of reaction-diffusion type with given boundary conditions is considered. The leading term of each equation is multiplied by a small positive parameter.…
The Brinkman equations can be regarded as a combination of the Stokes and Darcy equations which model transitions between the fast flow in channels (governed by Stokes equations) and the slow flow in porous media (governed by Darcy's law).…
Callaway's dual relaxation times model, which takes into account the normal and resistive scatterings of phonon, is used to describe the heat conduction in materials like graphene. For steady-state problems, the Callaway model is usually…
This is a continuation of two recent publications of the authors about reconstruction procedures for 3-d phaseless inverse scattering problems. The main novelty of this paper is that the Born approximation for the case of the wave-like…
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…
Developing high-order numerical schemes for two-phase flow in porous media that preserve key physical properties remains a significant challenge in numerical analysis. In this article, we propose a general framework to construct fully…
This paper introduces a novel wave front tracking framework for reconstructing unknown flux functions in $2\times 2$ hyperbolic conservation laws, extending beyond the well-studied scalar case. By analyzing Riemann solutions at fixed…
Diffusion models have been demonstrated as strong priors for solving general inverse problems. Most existing Diffusion model-based Inverse Problem Solvers (DIS) employ a plug-and-play approach to guide the sampling trajectory with either…
A splitting scheme for backward doubly stochastic differential equations is proposed. The main idea is to decompose a backward doubly stochastic differential equation into a backward stochastic differential equation and a stochastic…
High-fidelity, high-resolution numerical simulations are crucial for studying complex multiscale phenomena in fluid dynamics, such as turbulent flows and ocean waves. However, direct numerical simulations with high-resolution solvers are…
A method of modelling the three-dimensional microstructure of random isotropic two-phase materials is proposed. The information required to implement the technique can be obtained from two-dimensional images of the microstructure. The…
In this work we consider an extension of a recently proposed structure preserving numerical scheme for nonlinear Fokker-Planck-type equations to the case of nonconstant full diffusion matrices. While in existing works the schemes are…
We introduce a methodology for performing parameter inference in high-dimensional, non-linear diffusion processes. We illustrate its applicability for obtaining insights into the evolution of and relationships between species, including…
The article considers parameter estimation constructing such as quasi-maximum likelyhood estimation and one step estimation in statistical models generated by solution of stochastic differential equation. It has been developed a software…
The mass flow rate of Poiseuille flow of rarefied gas through long ducts of two-dimensional cross-sections with arbitrary shape are critical in the pore-network modeling of gas transport in porous media. In this paper, for the first time,…
Diffusion-based models on continuous spaces have seen substantial recent progress through the mathematical framework of gradient flows, leveraging the Wasserstein-2 (${W}_2$) metric via the Jordan-Kinderlehrer-Otto (JKO) scheme. Despite the…
Lubrication equations allow to describe many structurin processes of thin liquid films. We develop and apply numerical tools suitable for their analysis employing a dynamical systems approach. In particular, we present a time integration…
We develop a cut Discontinuous Galerkin method (cutDGM) for a diffusion-reaction equation in a bulk domain which is coupled to a corresponding equation on the boundary of the bulk domain. The bulk domain is embedded into a structured,…