Related papers: Coupling of multiscale and multi-continuum approac…

In this paper, the first large-scale application of multiscale-spectral generalized finite element methods (MS-GFEM) to composite aero-structures is presented. The crucial novelty lies in the introduction of A-harmonicity in the local…

This work is devoted to the development of an efficient and robust technique for accurate capturing of the electric field in multi-material problems. The formulation is based on the finite element method enriched by the introduction of…

In the field of brittle fracture animation, generating realistic destruction animations using physics-based simulation methods is computationally expensive. While techniques based on Voronoi diagrams or pre-fractured patterns are effective…

In this paper, we present a monolithic multigrid method for the efficient solution of flow problems in fractured porous media. Specifically, we consider a mixed-dimensional model which couples Darcy flow in the porous matrix with…

Multisequence Magnetic Resonance Imaging (MRI) provides a more reliable diagnosis in clinical applications through complementary information across sequences. However, in practice, the absence of certain MR sequences is a common problem…

We present a 3D hybrid method which combines the Finite Element Method (FEM) and the Spectral Boundary Integral method (SBIM) to model nonlinear problems in unbounded domains. The flexibility of FEM is used to model the complex,…

The finite element method (FEM) has several computational steps to numerically solve a particular problem, to which many efforts have been directed to accelerate the solution stage of the linear system of equations. However, the finite…

Simulation in media with multiple continua where each continuum interacts with every other is often challenging due to multiple scales and high contrast. One needs some types of model reduction. One of the approaches is multi-continuum…

In this paper, we develop a novel unfitted multiscale framework that combines two separate scales represented by only one single computational mesh. Our framework relies on a mixed zooming technique where we zoom at regions of interest to…

Time-evolving perforated domains arise in many engineering and geoscientific applications, including reactive transport, particle deposition, and structural degradation in porous media. Accurately capturing the macroscopic behavior of such…

The present work deals with the numerical resolution of coupled 3D-2D problems arising from the simulation of fluid flow in fractured porous media modeled via the Discrete Fracture and Matrix (DFM) model. According to the DFM model,…

In this paper a problem of numerical simulation of hydraulic fractures is considered. An efficient algorithm of solution is proposed for the plain strain model of hydraulic fracturing. The algorithm utilizes a FEM based subroutine to…

Accurate segmentation of long and thin tubular structures is required in a wide variety of areas such as biology, medicine, and remote sensing. The complex topology and geometry of such structures often pose significant technical…

This study presents a generalized multiscale multimesh finite element method ($\text{M}^2$-FEM) that addresses several long-standing challenges in the numerical simulation of integral structural theories, often used to model multiscale and…

The extended finite element method (XFEM) was introduced in 1999 to treat problems involving discontinuities with no or minimal remeshing through appropriate enrichment functions. This enables elements to be split by a discontinuity, strong…

In this article, we present a new unified finite element method (UFEM) for simulation of general Fluid-Structure interaction (FSI) which has the same generality and robustness as monolithic methods but is significantly more computationally…

This study evaluates four widely used fracture simulation methods, comparing their computational expenses and implementation complexities within the Finite Element (FE) framework when employed on heterogeneous solids. Fracture methods…

In this paper, we consider the quasi-gas-dynamic (QGD) model in a multiscale environment. The model equations can be regarded as a hyperbolic regularization and are derived from kinetic equations. So far, the research on QGD models has been…

In this paper, we propose a deep learning based reduced order modeling method for stochastic underground flow problems in highly heterogeneous media. We aim to utilize supervised learning to build a reduced surrogate model from the…

We introduce a novel hybrid methodology combining classical finite element methods (FEM) with neural networks to create a well-performing and generalizable surrogate model for forward and inverse problems. The residual from finite element…