Related papers: An Interface-enriched Generalized Finite Element M…
In recent years, the immersed finite element methods (IFEM) introduced in \cite{Li2003}, \cite{Li2004} to solve elliptic problems having an interface in the domain due to the discontinuity of coefficients are getting more attentions of…
We explore a new way to handle flux boundary conditions imposed on level sets. The proposed approach is a diffuse interface version of the shifted boundary method (SBM) for continuous Galerkin discretizations of conservation laws in…
The Finite element method (FEM) has long served as the computational backbone for topology optimization (TO). However, for designing structures undergoing large deformations, conventional FEM-based TO often exhibits numerical instabilities…
In this paper, we replace the asymptotic enrichments around the crack tip in the extended finite element method (XFEM) with the semi-analytical solution obtained by the scaled boundary finite element method (SBFEM). The proposed method does…
This article presents an error analysis of the recently introduced Frenet immersed finite element (IFE) method. The Frenet IFE space employed in this method is constructed to be locally conforming to the function space of the associated…
In this paper, we present a new immersed finite element scheme for solving elliptic interface problems on unfitted meshes by combining the skeletal finite element method (FEM) with the standard FEM. The skeletal FEM is used for the…
A higher-order accurate finite element method is proposed which uses automatically generated meshes based on implicit level-set data for the description of boundaries and interfaces in two and three dimensions. The method is an alternative…
Topology optimization methods face serious challenges when applied to structural design with fluid-structure interaction (FSI) loads, specially for high Reynolds fluid flow. This paper devises an explicit boundary method that employs…
In this paper, we study the development of efficient multiscale methods for flows in heterogeneous media. Our approach uses the Generalized Multiscale Finite Element (GMsFEM) framework. The main idea of GMsFEM is to approximate the solution…
In this paper, we present a mixed Generalized Multiscale Finite Element Method (GMsFEM) for solving flow in heterogeneous media. Our approach constructs multiscale basis functions following a GMsFEM framework and couples these basis…
Coupled multiphysics simulations for high-dimensional, large-scale problems can be prohibitively expensive due to their computational demands. This article presents a novel framework integrating a deep operator network (DeepONet) with the…
In the context of unfitted finite element discretizations the realization of high order methods is challenging due to the fact that the geometry approximation has to be sufficiently accurate. We consider a new unfitted finite element method…
Meshing complex engineering domains is a challenging task. Arbitrary polyhedral meshes can provide the much needed flexibility in automated discretization of such domains. The geometric property of the polyhedral meshes such as the…
One of the major issues in the computational mechanics is to take into account the geometrical complexity. To overcome this difficulty and to avoid the expensive mesh generation, geometrically unfitted methods, i.e. the numerical methods…
In this paper, we define new unfitted finite element methods for numerically approximating the solution of surface partial differential equations using bulk finite elements. The key idea is that the $n$-dimensional hypersurface, $\Gamma…
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…
Meshing of geometric domains having curved boundaries by affine simplices produces a polytopial approximation of those domains. The resulting error in the representation of the domain limits the accuracy of finite element methods based on…
We introduce a new paradigm for immersed finite element and isogeometric methods based on interpolating function spaces from an unfitted background mesh into Lagrange finite element spaces defined on a foreground mesh that captures the…
Element-based topology optimization algorithms capable of generating smooth boundaries have drawn serious attention given the significance of accurate boundary information in engineering applications. The basic framework of a new…
In the context of unfitted finite element discretizations the realization of high order methods is challenging due to the fact that the geometry approximation has to be sufficiently accurate. Recently a new unfitted finite element method…