Related papers: A Meshfree Generalized Finite Difference Method fo…
Data-driven techniques have a large potential to transform and accelerate the chemical sciences. However, chemical sciences also pose the unique challenge of very diverse, small, fuzzy datasets that are difficult to leverage in conventional…
Eulerian smoothed particle hydrodynamics (Eulerian SPH) is considered as a potential meshless alternative to a traditional Eulerian mesh-based method, i.e. finite volume method (FVM), in computational fluid dynamics (CFD). While researchers…
In this paper, we present a multiscale method for simulations of the multicontinua unsaturated flow problems in heterogeneous fractured porous media. The mathematical model is described by the system of Richards equations for each continuum…
This article presents a comparison of various implementations of the Lattice Discrete Particle Model (LDPM) for the numerical simulation of concrete and other heterogeneous quasibrittle materials. The comparison involves the use of…
Advances in deep learning have enabled physics-informed neural networks to solve partial differential equations. Numerical differentiation using the finite-difference (FD) method is efficient in physics-constrained designs, even in…
The increasing complexity and scale of photonic and electromagnetic devices demand efficient and accurate numerical solvers. In this work, we develop a parallel overlapping domain decomposition method (DDM) based on the finite-difference…
In this paper, we propose a coupled Discrete Empirical Interpolation Method (DEIM) and Generalized Multiscale Finite element method (GMsFEM) to solve nonlinear parabolic equations with application to the Allen-Cahn equation. The Allen-Cahn…
In this paper, we propose a multiscale empirical interpolation method for solving nonlinear multiscale partial differential equations. The proposed method combines empirical interpolation techniques and local multiscale methods, such as the…
This paper presents a novel stabilized mixed material point method (MPM) designed for the unified modeling of free-surface and seepage flow. The unified formulation integrates the Navier-Stokes equation with the Darcy-Brinkman-Forchheimer…
In this paper, we present an Online Generalized Multiscale Finite Element Method(Online GMsFEM) for heat and mass transfer problem in heterogeneous media with artificial ground freezing pipes. The mathematical model of the process is based…
Solving partial differential equations (PDE) is an indispensable part of many branches of science as many processes can be modelled in terms of PDEs. However, recent numerical solvers require manual discretization of the underlying equation…
In this paper, we address the numerical homogenization approximation of a free-boundary dam problem posed in a heterogeneous media. More precisely, we propose a generalized multiscale finite element (GMsFEM) method for the heterogeneous dam…
The finite element method, finite difference method, finite volume method and spectral method have achieved great success in solving partial differential equations. However, the high accuracy of traditional numerical methods is at the cost…
The Finite Element Method (FEM) is a powerful computational tool for solving partial differential equations (PDEs). Although commercial and open-source FEM software packages are widely available, an independent implementation of FEM…
We present a direct Poisson solver for massively parallel simulations on three-dimensional Cartesian grids with non-uniform spacing. The method uses a tensor-based formulation in which the operator is diagonalized numerically along two…
Accurate numerical simulations of interaction between fluid and solid play an important role in applications. The task is challenging in practical scenarios as the media are usually highly heterogeneous with very large contrast. To overcome…
In this paper, we consider an approximation method, and a novel general analysis, for second-order elliptic differential equations with heterogeneous multiscale coefficients. We obtain convergence of the Generalized Multi-scale Finite…
A multiscale numerical solver called the seamless-domain method (SDM) is used in linear heat conduction analysis of nonperiodic simulated fields. The practical feasibility of the SDM has been verified for use with periodic fields but has…
The performance evaluation of a potentially unstable slope involves two key components: the initiation of the slope failure and the post-failure runout. The Finite Element Method (FEM) excels at modeling the initiation of instability but…
In this paper, we investigate and design multiscale simulations for stochastic multiscale PDEs. As for the space, we consider a coarse grid and a known multiscale method, the Generalized Multiscale Finite Element Method (GMsFEM). In order…