Related papers: A Compact Coupling Interface Method with Accurate …
In this paper we present an immersed weak Galerkin method for solving second-order elliptic interface problems on polygonal meshes, where the meshes do not need to be aligned with the interface. The discrete space consists of constants on…
Accurate representation of interfaces and flux exchange is vital for coupled multiphysics simulations across a broad range of applications. Currently, coupling approaches are limited by the underlying discretization or to specific physical…
This is the third paper on the study of gradient recovery for elliptic interface problem. In our previous works [H. Guo and X. Yang, 2016, arXiv:1607.05898 and {\it J. Comput. Phys.}, 338 (2017), 606--619], we developed {gradient recovery…
This paper presents a new narrow-stencil finite difference method for approximating the viscosity solution of second order fully nonlinear elliptic partial differential equations including Hamilton-Jacobi-Bellman equations. The proposed…
We propose a high-order FDTD scheme based on the correction function method (CFM) to treat interfaces with complex geometry without increasing the complexity of the numerical approach for constant coefficients. Correction functions are…
Stokes flow equations have been implemented successfully in practice for simulating problems with moving interfaces. Though computational methods produce accurate solutions and numerical convergence can be demonstrated using a resolution…
A second-order-accurate finite volume method, hybridized by blending an extended double-flux algorithm and a traditionally conservative scheme, is developed. In this scheme, hybrid convective fluxes as well as hybrid interpolation…
Many geometry processing techniques require the solution of partial differential equations (PDEs) on manifolds embedded in $\mathbb{R}^2$ or $\mathbb{R}^3$, such as curves or surfaces. Such manifold PDEs often involve boundary conditions…
We present an enhanced immersed interface method for simulating incompressible fluid flows in thin gaps between closely spaced immersed boundaries. This regime, common in engineered structures such as including tribological interfaces and…
Based upon two overlapped, body-unfitted meshes, a type of unified-field monolithic fictitious domain-finite element method (UFMFD-FEM) is developed in this paper for moving interface problems of dynamic fluid-structure interactions (FSI)…
In this work we analyze two classes of Density-Estimation techniques which can be used to consistently couple different kinetic models of the plasma-material interface, intended as the region of plasma immediately interacting with the first…
Rigid registration of multi-view and multi-platform LiDAR scans is a fundamental problem in 3D mapping, robotic navigation, and large-scale urban modeling applications. Data acquisition with LiDAR sensors involves scanning multiple areas…
Motivated by the study of the electrodynamics of particles, we propose in this work an arbitrary-order discrete de Rham scheme for the treatment of elliptic problems with potential and flux jumps across a fixed interface. The scheme…
In low-temperature high-density plasmas quantum effects of the electrons are becoming increasingly important. This requires the development of new theoretical and computational tools. Quantum Monte Carlo methods are among the most…
In this paper, an important discovery has been found for nonconforming immersed finite element (IFE) methods using the integral values on edges as degrees of freedom for solving elliptic interface problems. We show that those IFE methods…
Asymptotics-based configuration-interaction (CI) methods [G. Friesecke and B. D. Goddard, Multiscale Model. Simul. 7, 1876 (2009)] are a class of CI methods for atoms which reproduce, at fixed finite subspace dimension, the exact…
Recent results on supercomputers show that beyond 65K cores, the efficiency of molecular dynamics simulations of interfacial systems decreases significantly. In this paper, we introduce a dynamic cutoff method (DCM) for interfacial systems…
We introduce and analyze a lower envelope method (LEM) for the tracking of interfaces motion in multiphase problems. The main idea of the method is to define the phases as the regions where the lower envelope of a set of functions coincides…
The accurate modeling of topology changes remains a significant challenge in geometric Volume of Fluid (VOF) simulations. When using traditional single-plane reconstruction (PLIC), fluid structures smaller than the mesh size cannot be…
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…