Related papers: Compact implicit high resolution numerical method …
For the simulations of unsteady flow, the global time step becomes really small with a large variation of local cell size. In this paper, an implicit high-order gas-kinetic scheme (HGKS) is developed to remove the restrictions on the time…
The structural properties of mechanical metamaterials are typically studied with two-scale methods based on computational homogenization. Because such materials have a complex microstructure, enriched schemes such as second-order…
In this paper we consider a fully third order nonlinear boundary value problem which is of great interest of many researchers. First we establish the existence, uniqueness of solution. Next, we propose simple iterative methods on both…
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…
The direct deep learning simulation for multi-scale problems remains a challenging issue. In this work, a novel higher-order multi-scale deep Ritz method (HOMS-DRM) is developed for thermal transfer equation of authentic composite materials…
The paper is devoted to the numerical solution of elastoplastic constitutive initial value problems. An improved form of the implicit return-mapping scheme for nonsmooth yield surfaces is proposed that systematically builds on a…
We consider the geometric optics problem of finding a system of two reflectors that transform a spherical wavefront into a beam of parallel rays with prescribed intensity distribution. Using techniques from optimal transportation theory, it…
A novel numerical approach to solving the shallow-water equations on the sphere using high-order numerical discretizations in both space and time is proposed. A space-time tensor formalism is used to express the equations of motion…
This study concerns numerical methods for efficiently solving the Richards equation where different weak formulations and computational techniques are analyzed. The spatial discretizations are based on standard or mixed finite element…
We present an efficient transcription method for highly oscillatory optimal control problems. For these problems, the optimal state trajectory consists of fast oscillations that change slowly over the time horizon. Out of a large number of…
This work demonstrates algorithms to accurately compute solutions to thermal radiation transport problems using a reduced floating-point precision implementation of the Implicit Monte Carlo method. Several techniques falling into the…
We use high order finite difference methods to solve the wave equation in the second order form. The spatial discretization is performed by finite difference operators satisfying a summation-by-parts property. The focus of this work is on…
We propose a high order numerical homogenization method for dissipative ordinary differential equations (ODEs) containing two time scales. Essentially, only first order homogenized model globally in time can be derived. To achieve a high…
The Halpern iteration for solving monotone inclusion problems has gained increasing interests in recent years due to its simple form and appealing convergence properties. In this paper, we investigate the inexact variants of the scheme in…
The implicit compact finite-difference scheme was developed for evolutionary partial differential parabolic and Schr\"odinger-type equations and systems with a weak nonlinearity. To make a temporal step of the compact implicit scheme we…
The present study concerns the numerical homogenization of second order hyperbolic equations in non-divergence form, where the model problem includes a rapidly oscillating coefficient function. These small scales influence the large scale…
The solution of time-dependent hyperbolic conservation laws on cut cell meshes causes the small cell problem: standard schemes are not stable on the arbitrarily small cut cells if an explicit time stepping scheme is used and the time step…
The precise description of quantum nuclear fluctuations in atomistic modelling is possible by employing path integral techniques, which involve a considerable computational overhead due to the need of simulating multiple replicas of the…
In this paper, we introduce a mathematical model to describe the nanoparticles transport carried by a two-phase flow in a porous medium including gravity, capillary forces and Brownian diffusion. Nonlinear iterative IMPES scheme is used to…
Obtaining solutions to Optimal Transportation (OT) problems is typically intractable when the marginal spaces are continuous. Recent research has focused on approximating continuous solutions with discretization methods based on i.i.d.…