相关论文: A matched alternating direction implicit (ADI) met…

In this manuscript, an original numerical procedure for the nonlinear peridynamics on arbitrarily--shaped two-dimensional (2D) closed manifolds is proposed. When dealing with non parameterized 2D manifolds at the discrete scale, the problem…

A stable partitioned algorithm for fluid-structure interaction (FSI) problems that couple viscous incompressible flow with structural shells or beams is described. This added-mass partitioned (AMP) scheme uses Robin (mixed) interface…

We present a class of new explicit and stable numerical algorithms to solve the spatially discretized linear heat or diffusion equation. After discretizing the space and the time variables like conventional finite difference methods, we do…

We develop a numerical strategy to solve multi-dimensional Poisson equations on dynamically adapted grids for evolutionary problems disclosing propagating fronts. The method is an extension of the multiresolution finite volume scheme used…

Distinguishing signal of young gas rich circumstellar disks from stellar signal in near infrared light is a difficult task. Current techniques such as Angular Differential Imaging (ADI) and Polarimetric Differential Imaging (PDI) cope with…

We propose a new, unified approach to solving jump-diffusion partial integro-differential equations (PIDEs) that often appear in mathematical finance. Our method consists of the following steps. First, a second-order operator splitting on…

We consider a multilayer hyperbolic-parabolic PDE system which constitutes a coupling of 3D thermal - 2D elastic - 3D elastic dynamics, in which the boundary interface coupling between 3D fluid and 3D structure is realized via a 2D elastic…

The problem of increasing the accuracy of an approximate solution is considered for boundary value problems for parabolic equations. For ordinary differential equations (ODEs), nonstandard finite difference schemes are in common use for…

A new diffuse interface model for a two-phase flow of two incompressible fluids with different densities is introduced using methods from rational continuum mechanics. The model fulfills local and global dissipation inequalities and is also…

Tenfold improvements in computation speed can be brought to the alternating direction method of multipliers (ADMM) for Semidefinite Programming with virtually no decrease in robustness and provable convergence simply by projecting…

A fully implicit finite difference scheme has been developed to solve the hydrodynamic equations coupled with radiation transport. Solution of the time dependent radiation transport equation is obtained using the discrete ordinates method…

High fidelity simulations, e.g., large eddy simulation are often needed for accurately predicting pressure losses due to wake mixing in turbomachinery applications. An unsteady adjoint of such high fidelity simulations is useful for design…

In this paper, a hybrid quasi-static atomistic simulation method at finite temperature is developed, which combines the advantages of MD for thermal equilibrium and atomic-scale finite element method (AFEM) for efficient equilibration. Some…

A new time discretization scheme for the numerical simulation of two-phase flow governed by a thermodynamically consistent diffuse interface model is presented. The scheme is consistent in the sense that it allows for a discrete in time…

Alternating Direction Method of Multipliers (ADMM) has been used successfully in many conventional machine learning applications and is considered to be a useful alternative to Stochastic Gradient Descent (SGD) as a deep learning optimizer.…

In this paper, a direct finite element method is proposed for solving interface problems on unfitted meshes. This new method treats the two interface conditions as an $H^{\frac12}(\Gamma)\times H^{-\frac12}(\Gamma)$ pair for the mutual…

In this paper, a thermal-dynamical consistent model for mass transfer across permeable moving interfaces is proposed by using the energy variation method. We consider a restricted diffusion problem where the flux across the interface…

Thermal properties of a two-layered composite conductor are modified in case the interface is damaged. The present paper deals with nondestructive evaluation of perturbations of interface thermal conductance due to the presence of defects.…

The kinetics of interfaces in alloy solidification pose a classic free boundary problem. This paper introduces an approach that amalgamates the distinctive characteristics of sharp and diffuse interface models. The motion of the diffuse…

This work introduces novel unconditionally stable operator splitting methods for solving the time dependent nonlinear Poisson-Boltzmann (NPB) equation for the electrostatic analysis of solvated biomolecules. In a pseudo-transient…