Related papers: 3D finite element simulation of optical modes in V…
We introduce the Virtual Element Method (VEM) for elliptic eigenvalue problems. The main result of the paper states that VEM provides an optimal order approximation of the eigenmodes. A wide set of numerical tests confirm the theoretical…
The Finite Element Method (FEM) is widely used to solve discrete Partial Differential Equations (PDEs) in engineering and graphics applications. The popularity of FEM led to the development of a large family of variants, most of which…
We used numerical simulations based on the finite element method (FEM) to calculate both the amplitude and phase information of the scattered electric field from random rough surfaces, which can be directly compared to ellipsometric…
We present a computational framework for modeling large-scale particle-laden flows in complex domains with the goal of enabling simulations in medical-image derived patient specific geometries. The framework is based on a volume-filtered…
Numerical homogenization for mechanical multiscale modeling by means of the finite element method (FEM) is an elegant way of obtaining structure-property relations, if the behavior of the constituents of the lower scale is well understood.…
We consider fourth order singularly perturbed eigenvalue problems in one-dimension and the approximation of their solution by the $h$ version of the Finite Element Method (FEM). In particular, we use piecewise Hermite polynomials of degree…
The oversampling multiscale finite element method (MsFEM) is one of the most popular methods for simulating composite materials and flows in porous media which may have many scales. But the method may be inapplicable or inefficient in some…
This paper presents a novel approach for solving fourth-order phase-field models in brittle fracture mechanics using the Interior Penalty Finite Element Method (IP-FEM). The fourth-order model improves numerical stability and accuracy…
We consider, as a simple model problem, the application of Virtual Element Methods (VEM) to the linear Magnetostatic three-dimensional problem in the formulation of F. Kikuchi. In doing so, we also introduce new serendipity VEM spaces,…
We propose a novel efficient and robust Wavelet-based Edge Multiscale Finite Element Method (WEMsFEM) motivated by \cite{MR3980476,GL18} to solve the singularly perturbed convection-diffusion equations. The main idea is to first establish a…
We show that the DDR method can be interpreted as defining a computable consistent discrete $\mathrm{L}^2$ product on a conforming FES defined by PDEs. Without modifying the numerical method itself, this point of view provides an…
A finite element method is presented to compute time harmonic microwave fields in three dimensional configurations. Nodal-based finite elements have been coupled with an absorbing boundary condition to solve open boundary problems. This…
In this paper, we construct a combined multiscale finite element method (MsFEM) using the Local Orthogonal Decomposition (LOD) technique to solve the multiscale problems which may have singularities in some special portions of the…
Generalized or extended finite element methods (GFEM/XFEM) are in general badly conditioned and have numerous additional degrees of freedom (DOF) compared with the FEM because of introduction of enriched functions. In this paper, we develop…
As the capabilities of additive manufacturing techniques increase, topology optimization provides a promising approach to design geometrically sophisticated structures which can be directly manufactured. Traditional topology optimization…
The finite element methods (FEM) are important techniques in engineering for solving partial differential equations, but they depend heavily on element shape quality for stability and good performance. In this paper, we introduce the…
We propose a Pretrained Finite Element Method (PFEM),a physics driven framework that bridges the efficiency of neural operator learning with the accuracy and robustness of classical finite element methods (FEM). PFEM consists of a physics…
The phase field model is a widely used mathematical approach for describing crack propagation in continuum damage fractures. In the context of phase field fracture simulations, adaptive finite element methods (AFEM) are often employed to…
We present a methodology combining neural networks with physical principle constraints in the form of partial differential equations (PDEs). The approach allows to train neural networks while respecting the PDEs as a strong constraint in…
The Finite Element Method (FEM) is the gold standard for spatial discretization in numerical simulations for a wide spectrum of real-world engineering problems. Prototypical areas of interest include linear heat transfer and linear…