Related papers: 3D finite element simulation of optical modes in V…
Motivated by problems where the response is needed at select localized regions in a large computational domain, we devise a novel finite element discretization that results in exponential convergence at pre-selected points. The two key…
An efficient finite element method (FEM) for calculating eigenvalues and eigenfunctions of quantum billiard systems is presented. We consider the FEM based on triangular $C_1$ continuity quartic interpolation. Various shapes of quantum…
This paper proposes the response surface method for finite element model updating. The response surface method is implemented by approximating the finite element model surface response equation by a multi-layer perceptron. The updated…
I formulate a general finite element method (FEM) for self-gravitating stellar systems. I split the configuration space to finite elements, and express the potential and density functions over each element in terms of their nodal values and…
Computational Fluid Dynamics (CFD) simulations are essential for analyzing and optimizing fluid flows in a wide range of real-world applications. These simulations involve approximating the solutions of the Navier-Stokes differential…
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…
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,…
This work provides an efficient virtual element scheme for the modeling of nonlinear elastodynamics undergoing large deformations. The virtual element method (VEM) has been applied to various engineering problems such as elasto-plasticity,…
This paper presents an asymptotically compatible error bound for the finite element method (FEM) applied to a nonlocal diffusion model. The analysis covers two scenarios: meshes with and without shape regularity. For shape-regular meshes,…
We introduce a family of Galerkin finite element methods which are constructed via recovery operators over element-wise discontinuous approximation spaces. This new family, termed collectively as recovered finite element methods (R-FEM) has…
The virtual element method (VEM) is a Galerkin approximation method that extends the finite element method to polytopal meshes. In this paper, we present two different conforming virtual element formulations for the numerical approximation…
The third medium contact has been proven to be an effective approach for simulating contact problems involving large deformations. Unlike traditional contact algorithms, the third medium contact introduces a third medium between two…
For the Lagrange interpolation over a triangular domain, we propose an efficient algorithm to rigorously evaluate the interpolation error constant under the maximum norm by using the finite element method (FEM). In solving the optimization…
We present an immersed boundary method to simulate the creeping motion of a rigid particle in a fluid described by the Stokes equations discretized thanks to a finite element strategy on unfitted meshes, called Phi-FEM, that uses the…
A hybrid computational approach that integrates the finite element method (FEM) with least squares support vector regression (LSSVR) is introduced to solve partial differential equations. The method combines FEM's ability to provide the…
Multiscale finite element methods for 2D/1D problems have been studied in this work to demonstrate their excellent ability to solve real-world problems. These methods are much more efficient than conventional 3D finite element methods and…
This paper summarizes the development of varFEM, which provides a realization of the programming style in FreeFEM by using the Matlab language.
Complex mechanic systems simulation is important in many real-world applications. The de-facto numeric solver using Finite Element Method (FEM) suffers from computationally intensive overhead. Though with many progress on the reduction of…
Many problems in science and engineering can be rigorously recast into minimizing a suitable energy functional. We have been developing efficient and flexible solution strategies to tackle various minimization problems by employing finite…
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…