Related papers: Finite Element-based Nonlinear Dynamic Optimizatio…
We present and analyze a linearized finite element method (FEM) for the dynamical incompressible magnetohydrodynamics (MHD) equations. The finite element approximation is based on mixed conforming elements, where Taylor--Hood type elements…
We consider an inverse problem involving the reconstruction of the solution to a nonlinear partial differential equation (PDE) with unknown boundary conditions. Instead of direct boundary data, we are provided with a large dataset of…
We propose a novel hybrid domain decomposition method that couples sub-domain-local high-fidelity finite element (FE) models with reduced order models (ROMs) using the Schwarz alternating method. By integrating the noninstrusive Operator…
To solve large-scale or high-resolution topology optimization problem, a novel algorithm is developed based on modified bi-directional evolutionary structure optimization (BESO) and extended finite element method (XFEM). Within XFEM, a set…
This paper presents a novel derivation of the direct parametrisation method for invariant manifolds able to build simulation-free reduced-order models for nonlinear piezoelectric structures, with a particular emphasis on applications to…
We investigate the dynamics of mechanical resonators subject to excitations comprising of an oscillating or harmonic part, whose amplitude decays exponentially in time. We call these complex frequency excitations and show that the resulting…
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,…
Nanomechanical resonators, machined out of Silicon-on-Insulator wafers, are operated in the nonlinear regime to investigate higher-order mechanical mixing at radio frequencies, relevant to signal processing and nonlinear dynamics on…
Mechanical resonators are widely used as precision clocks and sensitive detectors that rely on the stability of their eigenfrequencies. The phase noise is determined by different factors ranging from thermal noise and frequency noise of the…
A new Essentially Non-oscillatory (ENO) recovery algorithm is developed and tested in a Finite Volume method. The construction is hinged on a reformulation of the reconstruction as the solution to a variational problem. The sign property of…
In this work we propose an efficient and accurate multi-scale optical simulation algorithm by applying a numerical version of slowly varying envelope approximation in FEM. Specifically, we employ the fast iterative method to quickly compute…
Unfitted finite element methods, like CutFEM, have traditionally been implemented in a matrix-based fashion, where a sparse matrix is assembled and later applied to vectors while solving the resulting linear system. With the goal of…
This paper introduces an accurate edge-based smoothed finite element method (ES-FEM) for electromagnetic analysis for both two dimensional cylindrical and three dimensional cartesian systems, which shows much better performance in terms of…
We study circular nanomechanical graphene resonators by means of continuum elasticity theory, treating them as membranes. We derive dynamic equations for the flexural mode amplitudes. Due to geometrical nonlinearity these can be modeled by…
In this paper, a mechanistic data-driven approach is proposed to accelerate structural topology optimization, employing an in-house developed finite element convolutional neural network (FE-CNN). Our approach can be divided into two stages:…
This paper proposes a computational framework for the design optimization of stable structures under large deformations by incorporating nonlinear buckling constraints. A novel strategy for suppressing spurious buckling modes related to…
Carbon nanotubes and graphene allow fabricating outstanding nanomechanical resonators. They hold promise for various scientific and technological applications, including sensing of mass, force, and charge, as well as the study of quantum…
One predominant challenge in additive manufacturing (AM) is to achieve specific material properties by manipulating manufacturing process parameters during the runtime. Such manipulation tends to increase the computational load imposed on…
This work presents a Euler-Bernoulli beam finite element (FE) model to study the interlayer interaction mechanics of graphene nanoribbon (GNR) over a graphene substrate. The FE model is calibrated using molecular dynamics (MD) simulations…
In this paper, we consider numerical approximation of an electrically conductive ferrofluid model, which consists of Navier-Stokes equations, magnetization equation, and magnetic induction equation. To solve this highly coupled, nonlinear,…