Related papers: Phantom Domain Finite Element Method: A novel appr…
This manuscript presents the Quantum Finite Element Method (Q-FEM) developed for use in noisy intermediate-scale quantum (NISQ) computers and employs the variational quantum linear solver (VQLS) algorithm. The proposed method leverages the…
The Finite Element Method (FEM) is a well-established procedure for computing approximate solutions to deterministic engineering problems described by partial differential equations. FEM produces discrete approximations of the solution with…
The immersed finite element-finite difference (IFED) method is a computational approach to modeling interactions between a fluid and an immersed structure. This method uses a finite element (FE) method to approximate the stresses and forces…
An accurate, physically-based, and differentiable model of soft robots can unlock downstream applications in optimal control. The Finite Element Method (FEM) is an expressive approach for modeling highly deformable structures such as…
The paper studies several approaches to numerical integration over a domain defined implicitly by an indicator function such as the level set function. The integration methods are based on subdivision, moment--fitting, local…
The scaled boundary finite element method (SBFEM) is a semi-analytical computational scheme, which is based on the characteristics of the finite element method (FEM) and combines the advantages of the boundary element method (BEM). This…
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…
This paper proposes a strategy to solve the problems of the conventional s-version of finite element method (SFEM) fundamentally. Because SFEM can reasonably model an analytical domain by superimposing meshes with different spatial…
Computing the stiffness matrix for the finite element discretization of the nonlocal Laplacian on unstructured meshes is difficult, because the operator is nonlocal and can even be singular. In this paper, we focus on the $C^0$-piecewise…
Simulation of fracturing processes in porous rocks can be divided into two main branches: (i) modeling the rock as a continuum which is enhanced with special features to account for fractures, or (ii) modeling the rock by a discrete (or…
Multiscale Finite Element Methods (MsFEMs) are now well-established finite element type approaches dedicated to multiscale problems. They first compute local, oscillatory, problem-dependent basis functions that generate a suitable…
We propose a hybrid method, the Neural Enrichment Finite Element Method (NEFEM), designed for problems involving strong oscillations or interface problems with weak discontinuities. This method is based on the stable generalized finite…
This paper presents the implementation of the eXtended Finite Element Method (XFEM) in the general-purpose commercial software package COMSOL Multiphysics for multi-field thermo-hydro-mechanical problems in discontinuous porous media. To…
The paper outlines some recent developments of the boundary element method (BEM) that makes it more user friendly and suitable for a realistic simulation in geomechanics, especially for underground excavations and tunnelling. The…
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…
The numerical investigation of acoustic damping materials, such as foams, constitutes a valuable enhancement to experimental testing. Typically, such materials are modeled in a homogenized way in order to reduce the computational effort and…
In stress field analysis, the finite element analysis is a crucial approach, in which the mesh-density has a significant impact on the results. High mesh density usually contributes authentic to simulation results but costs more computing…
The potential of neural networks (NN) in engineering is rooted in their capacity to understand intricate patterns and complex systems, leveraging their universal nonlinear approximation capabilities and high expressivity. Meanwhile,…
In this study, we derived a three-dimensional scaled boundary finite element formulation for heat conduction problems. By incorporating Wachspress shape functions, a polyhedral scaled boundary finite element method (PSBFEM) was proposed to…
In this paper, we present a finite element method (FEM) framework enhanced by an operator-adapted wavelet decomposition algorithm designed for the efficient analysis of multiscale electromagnetic problems. Usual adaptive FEM approaches,…