Related papers: Convergence of infinite element methods for scalar…
In this paper, we propose and study the uniaxial perfectly matched layer (PML) method for three-dimensional time-domain electromagnetic scattering problems, which has a great advantage over the spherical one in dealing with problems…
A new approach for analyzing waveguide junctions containing conductive cylindrical objects is proposed. The algorithm is based on mode matching technique using local projection functions, which improves the numerical conditioning of the…
It is known that any {\em real coordinate transformation} (RCT) to compress waves in an unbounded domain into a bounded domain results in infinite oscillations that cannot be resolved by any grid-based method. In this paper, we intend to…
We discuss how the Perfectly Matched Layer (PML) can be adapted to numerical simulations of nonlinear and matter wave systems, such as Bose-Einstein condensates. We also present some examples which illustrate the benefits of using the PML…
Upper bound limit analysis allows one to evaluate directly the ultimate load of structures without performing a cumbersome incremental analysis. In order to numerically apply this method to thin plates in bending, several authors have…
In this work, we discuss and compare three methods for the numerical approximation of constant- and variable-coefficient diffusion equations in both single and composite domains with possible discontinuity in the solution/flux at…
This note is intended as a brief introduction to the theory and practice of perfectly matched layer (PML) absorbing boundaries for wave equations, originally developed for MIT courses 18.369 and 18.336. It focuses on the complex…
This paper introduces discrete-holomorphic Perfectly Matched Layers (PMLs) specifically designed for high-order finite difference (FD) discretizations of the scalar wave equation. In contrast to standard PDE-based PMLs, the proposed method…
This work investigates finite element approximations for a general class of elliptic hemivariational inequalities arising in semipermeable media. The proposed model incorporates non-isotropic and heterogeneous diffusion coefficients,…
Maxwell equations are solved in a layer comprising a finite number of homogeneous isotropic dielectric regions ended by anisotropic perfectly matched layers (PMLs). The boundary-value problem is solved and the dispersion relation inside the…
We suggest a unified spectrally matched optimal grid approach for finite-difference and finite-element approximation of the PML. The new approach allows to combine optimal discrete absorption for both evanescent and propagative waves.
This study focuses on solving the numerical challenges of imposing absorbing boundary conditions for dynamic simulations in the material point method (MPM). To attenuate elastic waves leaving the computational domain, the current work…
Surface acoustic wave (SAW) devices are widely used in modern communication equipment and SAW equations describe the critical physical processes of acoustic-electric conversion in SAW devices. It is very challenging to numerically solve…
The perfectly matched layer (PML) formulation is a prominent way of handling radiation problems in unbounded domain and has gained interest due to its simple implementation in finite element codes. However, its simplicity can be advanced…
In outdoor acoustics, the calculations of sound propagating in air can be computationally heavy if the domain is chosen large enough to fulfil the Sommerfeld radiation condition. By strategically truncating the computational domain with a…
We study overlapping Schwarz methods for the Helmholtz equation posed in any dimension with large, real wavenumber and smooth variable wave speed. The radiation condition is approximated by a Cartesian perfectly-matched layer (PML). The…
In this paper, we propose a discrete perfectly matched layer (PML) for the peridynamic scalar wave-type problems in viscous media. Constructing PMLs for nonlocal models is often challenging, mainly due to the fact that nonlocal operators…
We develop a new spatial semidiscrete multiscale method based upon the edge multiscale methods to solve semilinear parabolic problems with heterogeneous coefficients and smooth initial data. This method allows for a cheap spatial…
This paper concerns the analysis of a multiscale method for wave propagation problems in microscopically nonhomogeneous media. A direct numerical approximation of such problems is prohibitively expensive as it requires resolving the…
The main task in this paper is to prove that the perfectly matched layers (PML) method converges exponentially with respect to the PML parameter, for scattering problems with periodic surfaces. In [5], a linear convergence is proved for the…