494 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
Evolution of Voronoi-based Fuzzy Controllers
A fuzzy controller is usually designed by formulating the knowledge of a human expert into a set of linguistic variables and fuzzy rules. One of the most successful methods to automate the fuzzy controllers development process are evolutionary algorithms. In this work, we propose a so-called ``approximative'' representation for fuzzy systems, where the antecedent of the rules are determined by a multivariate membership function defined in terms of Voronoi regions. Such representation guarantees the -completeness property and provides a synergistic relation between the rules. An evolutionary algorithm based on this representation can evolve all the components of the fuzzy system, and due to the properties of the representation, the algorithm (1) can benefit from the use of geometric genetic operators, (2) does not need genetic repair algorithms, (3) guarantees the completeness property and (4) can implement previous knowledge in a simple way by using adaptive a priori rules. The proposed representation is evaluated on an obstacle avoidance problem with a simulated mobile robot
A priori convergence estimates for a rough Poisson-Dirichlet problem with natural vertical boundary conditions
Stents are medical devices designed to modify blood flow in aneurysm sacs, in
order to prevent their rupture. Some of them can be considered as a locally
periodic rough boundary. In order to approximate blood flow in arteries and
vessels of the cardio-vascular system containing stents, we use multi-scale
techniques to construct boundary layers and wall laws. Simplifying the flow we
turn to consider a 2-dimensional Poisson problem that conserves essential
features related to the rough boundary. Then, we investigate convergence of
boundary layer approximations and the corresponding wall laws in the case of
Neumann type boundary conditions at the inlet and outlet parts of the domain.
The difficulty comes from the fact that correctors, for the boundary layers
near the rough surface, may introduce error terms on the other portions of the
boundary. In order to correct these spurious oscillations, we introduce a
vertical boundary layer. Trough a careful study of its behavior, we prove
rigorously decay estimates. We then construct complete boundary layers that
respect the macroscopic boundary conditions. We also derive error estimates in
terms of the roughness size epsilon either for the full boundary layer
approximation and for the corresponding averaged wall law.Comment: Dedicated to Professor Giovanni Paolo Galdi 60' Birthda
Computing the lower and upper bounds of Laplace eigenvalue problem: by combining conforming and nonconforming finite element methods
This article is devoted to computing the lower and upper bounds of the
Laplace eigenvalue problem. By using the special nonconforming finite elements,
i.e., enriched Crouzeix-Raviart element and extension , we get
the lower bound of the eigenvalue. Additionally, we also use conforming finite
elements to do the postprocessing to get the upper bound of the eigenvalue. The
postprocessing method need only to solve the corresponding source problems and
a small eigenvalue problem if higher order postprocessing method is
implemented. Thus, we can obtain the lower and upper bounds of the eigenvalues
simultaneously by solving eigenvalue problem only once. Some numerical results
are also presented to validate our theoretical analysis.Comment: 19 pages, 4 figure
Estimation of expiratory time constants via fuzzy clustering
Objective. In mechanically ventilated patients the expiratorytime constant provides information about respiratory mechanics. In thepresent study a new method, fuzzy clustering, is proposed to determine expiratory time constants. Fuzzy clustering differs from other methods since it neither interferes with expiration nor presumes any functional relationship between the variables analysed. Furthermore, time constantbehaviour during expiration can be assessed, instead of an average timeconstant. The time constants obtained with fuzzy clustering are comparedto time constants conventionally calculated from the same expirations.
Methods. 20 mechanically ventilated patients, including 10 patients with COPD, were studied. The data of flow, volume and pressure were sampled. From these data, four local linear models were detected by fuzzy clustering. The
A Finite Element Computation of the Gravitational Radiation emitted by a Point-like object orbiting a Non-rotating Black Hole
The description of extreme-mass-ratio binary systems in the inspiral phase is
a challenging problem in gravitational wave physics with significant relevance
for the space interferometer LISA. The main difficulty lies in the evaluation
of the effects of the small body's gravitational field on itself. To that end,
an accurate computation of the perturbations produced by the small body with
respect the background geometry of the large object, a massive black hole, is
required. In this paper we present a new computational approach based on Finite
Element Methods to solve the master equations describing perturbations of
non-rotating black holes due to an orbiting point-like object. The numerical
computations are carried out in the time domain by using evolution algorithms
for wave-type equations. We show the accuracy of the method by comparing our
calculations with previous results in the literature. Finally, we discuss the
relevance of this method for achieving accurate descriptions of
extreme-mass-ratio binaries.Comment: RevTeX 4. 18 pages, 8 figure
Asymptotics of Eigenvalues and Eigenfunctions for the Laplace Operator in a Domain with Oscillating Boundary. Multiple Eigenvalue Case
We study the asymptotic behavior of the solutions of a spectral problem for
the Laplacian in a domain with rapidly oscillating boundary. We consider the
case where the eigenvalue of the limit problem is multiple. We construct the
leading terms of the asymptotic expansions for the eigenelements and verify the
asymptotics
Efficient Analysis of High Dimensional Data in Tensor Formats
In this article we introduce new methods for the analysis of high dimensional data in tensor formats, where the underling data come from the stochastic elliptic boundary value problem. After discretisation of the deterministic operator as well as the presented random fields via KLE and PCE, the obtained high dimensional operator can be approximated via sums of elementary tensors. This tensors representation can be effectively used for computing different values of interest, such as maximum norm, level sets and cumulative distribution function. The basic concept of the data analysis in high dimensions is discussed on tensors represented in the canonical format, however the approach can be easily used in other tensor formats. As an intermediate step we describe efficient iterative algorithms for computing the characteristic and sign functions as well as pointwise inverse in the canonical tensor format. Since during majority of algebraic operations as well as during iteration steps the representation rank grows up, we use lower-rank approximation and inexact recursive iteration schemes
A hysteretic multiscale formulation for nonlinear dynamic analysis of composite materials
This article has been made available through the Brunel Open Access Publishing Fund.A new multiscale finite element formulation
is presented for nonlinear dynamic analysis of heterogeneous
structures. The proposed multiscale approach utilizes
the hysteretic finite element method to model the microstructure.
Using the proposed computational scheme, the micro-basis functions, that are used to map the microdisplacement components to the coarse mesh, are only evaluated once and remain constant throughout the analysis procedure. This is accomplished by treating inelasticity at the micro-elemental level through properly defined hysteretic evolution equations. Two types of imposed boundary conditions are considered for the derivation of the multiscale basis functions, namely the linear and periodic boundary conditions. The validity of the proposed formulation as well as its computational efficiency are verified through illustrative numerical experiments
Recommended from our members
Plane wave discontinuous Galerkin methods: exponential convergence of the hp-version
We consider the two-dimensional Helmholtz equation with constant coefficients on a domain with piecewise analytic boundary, modelling the scattering of acoustic waves at a sound-soft obstacle. Our discretisation relies on the Trefftz-discontinuous Galerkin approach with plane wave basis functions on meshes with very general element shapes, geometrically graded towards domain corners. We prove exponential convergence of the discrete solution in terms of number of unknowns
- …