Related papers: Explicit Time Stepping for the Wave Equation using…
This paper develops a high-accuracy algorithm for time fractional wave problems, which employs a spectral method in the temporal discretization and a finite element method in the spatial discretization. Moreover, stability and convergence…
Based on a recent novel formulation of parametric anisotropic curve shortening flow, we analyse a fully discrete numerical method of this geometric evolution equation. The method uses piecewise linear finite elements in space and a backward…
We study solution techniques for an evolution equation involving second order derivative in time and the spectral fractional powers, of order $s \in (0,1)$, of symmetric, coercive, linear, elliptic, second-order operators in bounded domains…
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…
The presence of corners in the computational domain, in general, reduces the regularity of solutions of parabolic problems and diminishes the convergence properties of the finite element approximation introducing a so-called "pollution…
The purpose of this research is to describe an efficient iterative method suitable for obtaining high accuracy solutions to high frequency time-harmonic scattering problems. The method allows for both refinement of local polynomial degree…
We provide a concise review of the exponentially convergent multiscale finite element method (ExpMsFEM) for efficient model reduction of PDEs in heterogeneous media without scale separation and in high-frequency wave propagation. ExpMsFEM…
This work introduces and analyzes a finite element scheme for evolution problems involving fractional-in-time and in-space differentiation operators up to order two. The left-sided fractional-order derivative in time we consider is employed…
We study a wave equation with a nonlocal time fractional damping term that models the effects of acoustic attenuation characterized by a frequency dependence power law. First we prove existence of a unique solution to this equation with…
An adaptive finite element method is presented for the elastic scattering of a time-harmonic plane wave by a periodic surface. First, the unbounded physical domain is truncated into a bounded computational domain by introducing the…
Transport and mixing properties of aperiodic flows are crucial to a dynamical analysis of the flow, and often have to be carried out with limited information. Finite-time coherent sets are regions of the flow that minimally mix with the…
This paper proposes an explicit computational method for solving a three-dimensional system of nonlinear elastodynamic sine-Gordon equations subject to appropriate initial and boundary conditions. The time derivative is approximated by…
In this research work, let us focus on the construction of numerical scheme based on radial basis functions finite difference (RBF-FD) method combined with the Laplace transform for the solution of fractional order dispersive wave…
Rigorous computer simulations of propagating electromagnetic fields have become an important tool for optical metrology and design of nanostructured optical components. A vectorial finite element method (FEM) is a good choice for an…
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…
This paper presents a novel methodology for fast simulation and analysis of transient heat transfer. The proposed methodology is suitable for real-time applications owing to (i) establishing the solution method from the viewpoint of…
In this work we present an extension of the Virtual Element Method with curved edges for the numerical approximation of the second order wave equation in a bidimensional setting. Curved elements are used to describe the domain boundary, as…
We present a ray-based finite element method (ray-FEM) by learning basis adaptive to the underlying high-frequency Helmholtz equation in smooth media. Based on the geometric optics ansatz of the wave field, we learn local dominant ray…
Local time-stepping methods permit to overcome the severe stability constraint on explicit methods caused by local mesh refinement without sacrificing explicitness. In \cite{DiazGrote09}, a leapfrog based explicit local time-stepping…
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…