1,721,013 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 Recursive algorithm by the moments method to evaluate a class of numerical integrals over an infinite interval
No full textA special recursive algorithm is built by a three-term recursive formula with coefficients evaluated by the moments method. A new functional c(·) is studied over any function space that contains the polynomial space and it is shown that such a functional is positive definite, enabling us to use the advantages of such a property on the zeros of orthogonal polynomials for such a functional. A comparison is presented of the numerical advantages of such a method with respect to the Laguerre polynomials
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
Can irregular subdivisions preserve convexity?
No full textThis paper presents a subdivision scheme on triangles that we call variable subdivision scheme. The scheme can be seen as an iterative scheme to generate interpolating surfaces that can be irregular in some case. Moreover, it seems to be suitable to preserve the convexity of the Bézier net defined over the triangle since it is exchangeable with the mid-point splitting. This property is proved by means of the algorithm used to define the schem
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
The modified bordering method to evaluate eigenvalues and eigenvectors of normal matrices.
No full textA bordering procedure is here proposed to evaluate the eigensystem of hermitian matrices, and more in general of normal matrices, when the spectral decomposition is known of then–1×n–1 principal minor. The procedure is also applicable to special real and nonsymmetric matrices here named quasi-symmetric. The computational cost to write the characteristic polynomial isO(n 2), using a new set of recursive formulas. A modified Brent algorithm is used to find the roots of the polynomial. The eigenvectors are evaluated in a direct way with a computational cost ofO(n 2) for each one. Some numerical considerations indicate where numerical difficulties may occur. Numerical results are given comparing this method with the Givens-Householder one
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