Related papers: A recursive approach for the finite element comput…
This paper proposes a new method, in the frequency domain, to define absorbing boundary conditions for general two-dimensional problems. The main feature of the method is that it can obtain boundary conditions from the discretized equations…
A systematic expression quantifying the wave energy skewing phenomenon as a function of the mechanical characteristics of a non-isotropic structure is derived in this study. A structure of arbitrary anisotropy, layering and geometric…
We propose to homogenize a periodic (along one direction) structure, first in order to verify the quasi-static prediction of its response to an acoustic wave arising from mixing theory, then to address the question of what becomes of this…
Large statically indeterminate truss and frame structures exhibit complex load-bearing behavior, and redundancy matrices are helpful for their analysis and design. Depending on the task, the full redundancy matrix or only its diagonal…
It is known that the digital waveguide (DW) method for solving the wave equation numerically on a grid can be manipulated into the form of the standard finite-difference time-domain (FDTD) method (also known as the ``leapfrog'' recursion).…
Lagrangian coherent structures are effective barriers, sticky regions, that separate phase space regions of different dynamical behavior. The usual way to detect such structures is via finite-time Lyapunov exponents. We show that similar…
In this paper we prove a recursive characterisation of generic rigidity for frameworks periodic with respect to a partially variable lattice. We follow the approach of modelling periodic frameworks as frameworks on a torus and use the…
Numerical simulation of ultrasonic wave propagation provides an efficient tool for crack identification in structures, while it requires a high resolution and expensive time calculation cost in both time integration and spatial…
In this work, we present an efficient numerical implementation of the finite element method for modal analysis that leverages various symmetry operations, including spatial symmetry in point groups and space-time symmetry in…
The finite element method (FEM) has several computational steps to numerically solve a particular problem, to which many efforts have been directed to accelerate the solution stage of the linear system of equations. However, the finite…
We study the fundamental algorithmic rigidity problems for generic frameworks periodic with respect to a fixed lattice or a finite-order rotation in the plane. For fixed-lattice frameworks we give an $O(n^2)$ algorithm for deciding generic…
Computation of the spherical harmonic rotation coefficients or elements of Wigner's d-matrix is important in a number of quantum mechanics and mathematical physics applications. Particularly, this is important for the Fast Multipole Methods…
Previous studies of the response of the Moon to gravitational waves have been carried out using analytical or semi-analytical models assuming ideal lunar structures. Such models are advantageous for their high-speed calculation but fail to…
Online system identification algorithms are widely used for monitoring, diagnostics and control by continuously adapting to time-varying dynamics. Typically, these algorithms consider a model structure that lacks parsimony and offers…
A method is presented in which matrix elements for some processes are calculated recursively. This recursive calculational technique is based on the method of basis spinors.
In this work, two fast multipole boundary element formulations for the linear time-harmonic acoustic analysis of finite periodic structures are presented. Finite periodic structures consist of a bounded number of unit cell replications in…
We present a numerical approach to efficiently calculate spin-wave dispersions and spatial mode profiles in magnetic waveguides of arbitrarily shaped cross section with any non-collinear equilibrium magnetization which is translationally…
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…
This paper presents a new stochastic finite element method for computing structural stochastic responses. The method provides a new expansion of stochastic response and decouples the stochastic response into a combination of a series of…
We analyze and develop numerical methods for time-harmonic wave scattering in metallic waveguide structures of infinite extent. We show that radiation boundary conditions formulated via projectors onto outgoing modes determine the…