22,529 research outputs found
On stability of discretizations of the Helmholtz equation (extended version)
We review the stability properties of several discretizations of the
Helmholtz equation at large wavenumbers. For a model problem in a polygon, a
complete -explicit stability (including -explicit stability of the
continuous problem) and convergence theory for high order finite element
methods is developed. In particular, quasi-optimality is shown for a fixed
number of degrees of freedom per wavelength if the mesh size and the
approximation order are selected such that is sufficiently small and
, and, additionally, appropriate mesh refinement is used near
the vertices. We also review the stability properties of two classes of
numerical schemes that use piecewise solutions of the homogeneous Helmholtz
equation, namely, Least Squares methods and Discontinuous Galerkin (DG)
methods. The latter includes the Ultra Weak Variational Formulation
Enhanced error estimator based on a nearly equilibrated moving least squares recovery technique for FEM and XFEM
In this paper a new technique aimed to obtain accurate estimates of the error
in energy norm using a moving least squares (MLS) recovery-based procedure is
presented. We explore the capabilities of a recovery technique based on an
enhanced MLS fitting, which directly provides continuous interpolated fields,
to obtain estimates of the error in energy norm as an alternative to the
superconvergent patch recovery (SPR). Boundary equilibrium is enforced using a
nearest point approach that modifies the MLS functional. Lagrange multipliers
are used to impose a nearly exact satisfaction of the internal equilibrium
equation. The numerical results show the high accuracy of the proposed error
estimator
A 2.5D BEM-FEM using a spectral approach to study scattered waves in fluid–solid interaction problems
42nd International Conference on Boundary Elements and other Mesh Reduction Methods, BEM/MRM 2019; ITeCons-University of Coimbra, Coimbra; Portugal; 2 July 2019 through 4 July 2019.
- Publicado en WIT Transactions on Engineering Sciences, Volume 126, 2019, Pages 111-123This work presents a two-and-a-half dimensional (2.5D) spectral formulation based on the finite element method (FEM) and the boundary element method (BEM) to study wave propagation in acoustic and elastic waveguides. The analysis involved superposing two dimensional (2D) problems with different longitudinal wavenumbers. A spectral finite element (SFEM) is proposed to represent waveguides in solids with arbitrary cross-section. Moreover, the BEM is extended to its spectral formulation (SBEM) to study unbounded fluid media and acoustic enclosures. Both approaches use Lagrange polynomials as element shape functions at the Legendre–Gauss–Lobatto (LGL) points. The fluid and solid subdomains are coupled by applying the appropriate boundary conditions at the limiting interface. The proposed method is verified by means of a benchmark problem regarding the scattering of waves by an elastic inclusion. The convergence and the computational effort are evaluated for different h-p strategies. Numerical results show good agreement with the reference solution. Finally, the proposed method is used to study the pressure field generated by an array of elastic fluid-filled scatterers immersed in an acoustic mediumMinisterio de Economía y Competitividad BIA2016-75042-C2-1-
Timescale effect estimation in time-series studies of air pollution and health: A Singular Spectrum Analysis approach
A wealth of epidemiological data suggests an association between
mortality/morbidity from pulmonary and cardiovascular adverse events and air
pollution, but uncertainty remains as to the extent implied by those
associations although the abundance of the data. In this paper we describe an
SSA (Singular Spectrum Analysis) based approach in order to decompose the
time-series of particulate matter concentration into a set of exposure
variables, each one representing a different timescale. We implement our
methodology to investigate both acute and long-term effects of
exposure on morbidity from respiratory causes within the urban area of Bari,
Italy.Comment: Published in at http://dx.doi.org/10.1214/07-EJS123 the Electronic
Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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