1,720,982 research outputs found
An Algorithm for the Anisotropic Adaptivity of Unstructured Triangular Meshes
No full textIt is well recognized today the importance of anisotropic meshes when it is solved a
problem whose solution exhibits a substantial anisotropy. Most of the times it is better to build
these meshes adaptively, and a corresponding algorithm is proposed in this paper. A comparison
is made with the existing leading algorithms for the adaptive refinement of isotropic meshes, i.e.
regular refinement and longest-edge bisection
Adaptivity in Space and Time for Shallow Water Equations
No full textIn this paper, adaptive algorithms for time and space discretizations are added to an existing
solution method previously applied to the Venice lagoon tidal
circulation problem. An analysis of the interactions between space and
time discretizations adaptation algorithms is presented. In particular
it turns out that both error estimation in space and time must be
present for maintaining the adaptation efficient. Several advantages,
for adaptivity and for time decoupling of the equations,
offered by the operator splitting adopted for shallow waters equations
solution are put in evidenc
A Fast Numerical Homogenization Algorithm for Finite Element Analysis
No full textA numerical homogenization method is here presented to solve problems
governed by partial differential equations with coefficients that are
generic functions in . It consists of a recursive finite elements discretization and an
algebraic homogenization. This method takes advantages for speed and memory
occupation from the hierarchy of elements and nodes defined by
the recursive discretization. It turns out that using state-of-the-art
general linear algebra techniques, all non-numerical data manipulations that are
typically done before real computations, can be avoided
A Linear System Solver for Adaptive FEM
No full textIn this paper it is presented an approximate direct solver
for systems of linear equations arising from finite element
discretizations.
The approximation is implemented using estimates arising from
functional analysis or matrix analysis of the differential problem
discretized using finite elements, or of its discrete counter-part.
It results an advantage in terms of less matrix updates during the
factorization, and possibly less {\it fill-in} and less equations to
be included in the factorization (with a considerable computational
saving, in this case). This last advantage arise frequently during
successive updates of the solution after refinement/un-refinement
steps in an adaptive analysis.
The basic principle underlying the method here proposed is related to
the knowledge of the Green's function associated to the differential
problem discretized by finite elements.
Early experimentation shows the method to be promising
Least squares FEM approximation and subgrid extraction for convection dominated problems
No full textAs it is well known, the Galerkin FEM gives an oscillating solution in convection dominated problems.
The oscillations grow in magnitude with the Peclet number and may even totally hide the true solution.
The cure commonly used is to modify a-priori the formulation of the problem, by adding a stabilizing term to avoid an oscillating solution. This is called a stabilized method.
Here, instead, we analyze these oscillations from a least squares perspective and propose a post-processing technique that both stabilizes the solution and partially resolve the sub grid scales
The Best -Approximation Weighted-Residuals Method for Finite Element Approximations
No full textIn this article it is presented a Petrov-Galerkin method which gives a least-squares solution, useful for that problems for which the standard Galerkin method wildly oscillates and does not give an optimal approximation.
The method proposed computes the weighting-functions that give the
best-approximation in the norm induced by the inner product used to
formulate the weighted residuals.
We give an efficient implementation of this method using a space of linear finite elements
An Adaptive Method for Shallow Water Equations with an Application to the Venice Lagoon
No full textAn algorithm for the study of the shallow water equations has been
presented in many papers and applied to the field data of the Venice
lagoon. The interest for an adaptive procedure is evident in all the
problems of CFD; here we consider the shallow water problem and a model
is developed to introduce the adaptive procedure for studying with
greater precision some local phenomena of critical behaviour without
an excessive growth in the number of nodes, in the amount of work done
a-priori and in general in the complexity of the calculations.
Some numerical results of the application to the Venice lagoon are presented
The Best-Approximation Weighted-Residuals Method for the steady convection diffusion reaction problem
No full textIn this paper we present an analytical, parameter-free, Petrov-Galerkin method that gives stable solutions of convection dominated boundary-value problems. We call it the Best Approximation Weighted Residuals (BAWR) method since it gives the best approximation in the norm induced by the inner-product used to build the weighted-residuals approximation. The method computes the optimal weighting functions by solving suitable adjoint problems. Moreover, through a localization technique it becomes computationally efficient without loosing accuracy. The analysis is confirmed by numerical results
An anisotropic unstructured triangular adaptive mesh algorithm based on error and error gradient information
No full textIn this paper, an algorithm based on unstructured triangular meshes using standard refinement patterns for anisotropic adaptive meshes is presented. It consists of three main actions: anisotropic refinement, solution-weighted smoothing and patch unrefinement. Moreover, a hierarchical mesh formulation is used. The main idea is to use the error and error gradient on each mesh element to locally control the anisotropy of the mesh. The proposed algorithm is tested on interpolation and boundary-value problems with a discontinuous solution. (C) 2008 IMACS. Published by Elsevier B.V. All rights reserved
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