MATHICSE Technical Report : Analysis and computation of the elastic wave equation with random coefficients
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We analyze the recent Multi-index Stochastic Collocation (MISC) method for computing statistics of the solution of a partial differential equation (PDE) with random data, where the random coefficient is parametrized by means of a countable sequence of term ...
Though obliquely incident plane wave across rock fractures has been extensively investigated by theoretical analysis, the quantitative identification of each wave emerged from fractures has not been achieved either in numerical simulation or laboratory exp ...
A new finite element heterogeneous multiscale method (FE-HMM) is proposed for the numerical solution of the wave equation over long times in a rapidly varying medium. Our new FE-HMM-L method captures not only the short-time behavior of the wave field, well ...
In this paper, we carry out a numerical dispersion analysis for the linear two-dimensional elastodynamics equations approximated by means of NURBS-based Isogeometric Analysis in the framework of the Galerkin method; specifically, we consider the analysis o ...
Inspired by the BBM formula and by work of G. Leoni and D. Spector, we analyze the asymptotic behavior of two sequences of convex nonlocal functionals (Psi(n)(u)) and (Phi(n)(u)) which converge formally to the BV-norm of u. We show that pointwise convergen ...
Wave propagation in granular solids is found to have at least two regimes: a low-frequency ballistic signal and a high-frequency diffusive tail. The latter is attributed to granules clapping or elastic waves within the granules themselves. The low frequenc ...
The physical mechanism of elastic wave propagation through granular solids is investigated. Based on the symmetry of a one dimensional chain of spheres, spherical surface waves are considered to be responsible for the energy transport. A simple mathematica ...
We investigate smooth approximations of functions, with prescribed gradient behavior on a distinguished stratified subset of the domain. As an application, we outline how our results yield important consequences for a recently introduced class of stochasti ...
In everyday life of an engineer, CAD (Computer Aided Design) and FE (Finite Element) programs play an important role. The two different structures, CAD and FE programs, use different mathematical functions. In CAD programs, so called NURBS find their appli ...
We analyze the stochastic initial-boundary value problem for the elastic wave equation with random coefficients and deterministic data. We propose a stochastic collocation method for computing statistical moments of the solution or statistics of some given ...