Related papers: Finite-element based electromagnetic field simulat…
This paper outlines an energy-minimization finite-element approach to the computational modeling of equilibrium configurations for nematic liquid crystals under free elastic effects. The method targets minimization of the system free energy…
We solve elliptic systems of equations posed on highly heterogeneous materials. Examples of this class of problems are composite structures and geological processes. We focus on a model problem which is a second-order elliptic equation with…
In this work a novel method for the analysis with trimmed CAD surfaces is presented. The method involves an additional mapping step and the attraction stems from its sim- plicity and ease of implementation into existing Finite Element (FEM)…
This paper describes the use of the corotational cut Finite Element Method (FEM) for real-time surgical simulation. Users only need to provide a background mesh which is not necessarily conforming to the boundaries/interfaces of the…
Finite element method (FEM) modeling of the volumetric expansion phenomenon associated with the accumulation of irradiation was performed on rocks in a concrete for nuclear power plant. The FEM mesh of sandstone, tuff, and granite was…
The subject of this work is an adaptive stochastic Galerkin finite element method for parametric or random elliptic partial differential equations, which generates sparse product polynomial expansions with respect to the parametric…
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…
In this paper, we present a new polygonal finite element method, called the Zipped Finite Element Method, for star-shaped polygons. The proposed approach constructs high-order shape functions as linear combinations of standard finite…
We are concerned with the fast simulation of random fields on closed surfaces in $\mathbb{R}^3$ which are generated by the (Whittle-) Mat\'ern class of covariance functions. To this end, we solve the underlying fractional stochastic partial…
We introduce a hybrid method to couple continuous Galerkin finite element methods and high-order finite difference methods in a nonconforming multiblock fashion. The aim is to optimize computational efficiency when complex geometries are…
We revise the structure-preserving finite element method in [K. Hu, Y. MA and J. Xu. (2017) Stable finite element methods preserving $\nabla \cdot \mathbf{B}=0$ exactly for MHD models. Numer. Math.,135, 371-396]. The revised method is…
The paper studies a finite element method for computing transport and diffusion along evolving surfaces. The method does not require a parametrization of a surface or an extension of a PDE from a surface into a bulk outer domain. The…
An inverse scattering problem is formulated for reconstructing optical properties of biological tissues. A recursive linearization algorithm is used to solve the inverse scattering problem. We employed the idea of finite element boundary…
Transient absorption and Raman scattering measurements on noble metal nanoparticles offer complimentary information on their vibrational modes and mechanical interactions with their surroundings. We have developed a comprehensive modeling…
In this paper, we study a generalized finite element method for solving second-order elliptic partial differential equations with rough coefficients. The method uses local approximation spaces computed by solving eigenvalue problems on…
Numerical simulations of waves in highly heterogeneous media have important applications, but direct computations are prohibitively expensive. In this paper, we develop a new generalized multiscale finite element method with the aim of…
Nanocomposites with tailored optical properties can provide a new degree of freedom for optical design. However, despite their potential these materials remain unused in bulk applications. Here we investigate the conditions under which they…
In this paper, we propose a new approach -- the Tempered Finite Element Method (TFEM) -- that extends the Finite Element Method (FEM) to classes of meshes that include zero-measure or nearly degenerate elements for which standard FEM…
We use the finite-element method for simulating light transmission through a 2D-periodic array of rectangular apertures in a film of highly conductive material. We report results with a relative error of the transmissivity lower than 0.01%.…
The paper presents a two-dimensional geometrically nonlinear formulation of a beam element that can accommodate arbitrarily large rotations of cross sections. The formulation is based on the integrated form of equilibrium equations, which…