1,721,015 research outputs found
Description of the Meshless Local Petrov-Galerkin approach
No full textIn this paper we describe the Meshless Local Petrov-Galerkin (MLPG) method
and its numerical implementation for the solution of elliptic
problems
Elementi Finiti Misti e Volumi Finiti per la soluzione del problema di flusso e trasporto di contaminanti radioattivi pesanti in mezzi porosi
No full textIn questo lavoro \`e stato sviluppato un metodo numerico
accurato ed efficiente per
risolvere problemi accoppiati di flusso e trasporto
di contaminanti radioattivi
in acque sotterranee. Lo studio \`e finalizzato,
soprattutto, allo studio del sito pi\`u contaminato del mondo,
il lago Karachai, negli Urali del Sud (Russia). Questo
lago fu utilizzato, fin dagli anni cinquanta, per immagazzinarvi
residui radioattivi provenienti
da esperimenti nucleari e, successivamente,
come discarica dei rifiuti liquidi radioattivi
della centrale nucleare di Mayak
Mixed finite elements and finite volumes for solutions to flow and transport problem of heavy radioactive contaminants in porous media
No full textIn questo lavoro \`e stato sviluppato un metodo numerico
accurato ed efficiente per
risolvere problemi accoppiati di flusso e trasporto
di contaminanti radioattivi
in acque sotterranee. Lo studio \`e finalizzato,
soprattutto, allo studio del sito pi\`u contaminato del mondo,
il lago Karachai, negli Urali del Sud (Russia)
Programmare in Matlab. Guida passo dopo passo
No full textProgrammare vuol dire saper tradurre un algoritmo in un linguaggio specializzato in modo che il computer possa risolvere per noi problemi molto complicati e, in molti casi, difficilmente risolvibili con carta e penna. Questo libro insegna come risolvere problemi di matematica e di ingegneria lavorando in MATLAB e applicando metodi numerici di base (quali, ad esempio, metodi per risolvere zeri di funzione, per interpolare e approssimare dati, per integrare funzioni o risolvere semplici equazioni differenziali o affrontare problemi di algebra lineare). Numerosi esercizi completano ogni capitolo
A numerical study of the virtual element method in anisotropic diffusion problems
No full textIn this paper, we present the Virtual Element Method (VEM) for the solution of strongly anisotropic diffusion equations. In the VEM, the bilinear form associated with the diffusion equations is decomposed into two parts: a consistency term and a stability term. Therefore, the local stiffness matrix is the sum of two matrices: a consistency matrix and a stability matrix. Both matrices are constructed by using suitable projection operators that are computable from the degrees of freedom.
The VEM stiffness matrix becomes very ill-conditioned in presence of a strong anisotropy of the diffusion tensor coefficient, leading to a loss of convergence, an effect known in the literature as mesh locking.
In this work, we compare different choices of the stabilization, the basis fuctions and the elliptic projection operator, in order to alleviate the mesh locking phenomenon.
To this end, we use orthonormal basis functions for the space of polynomials of degree k and
an elliptic projection operator that is weighted with respect to the diffusion tensor.
Moreover, the VEM with k=1 needs a particular treatment to avoid locking.
Numerical experiments with different values of k confirm the validity of the proposed approach
Laboratorio di calcolo numerico. Apllicazioni con Matlab e Octave
No full textsupporto didattico per gli studenti di Ingegneri
An analysis of monotonicity conditions in the mixed hybrid finite element method on unstructured triangulations
No full textIn this paper we consider the mixed hybrid finite element method on unstructured triangular grids and evaluate its, monotonicity properties by using a non standard set of basis functions for the C velocity approximation space.
The mixed hybrid discretization of the steady-state diffusion equation produces a system matrix that depends only on the inner product of the outward normals to the edges of the triangulation and not oil the choice of the velocity space basis. This property is used to study the characteristics of the system matrix. It is well known that this matrix is of type M if the angles of the triangulation are not bigger than pi/2. An M-matrix has a nonnegative inverse. i.e. all the elements are nonnegative. This implies the existence of a discrete maximum principle and thus monotonicity of the discretization. We show that, when the triangulation is of Delaunay type and satisfies the property that no circumcenters of boundary elements with Dirichlet conditions lie outside the domain, the inverse of the final matrix is always positive, even in the presence of obtuse angles
A virtual element generalization on polygonal meshes of the Scott-Vogelius finite element method for the 2-D Stokes problem
Full text linkThe Virtual Element Method (VEM) is a Galerkin approximation method that extends the Finite Element Method (FEM) to polytopal meshes. In this paper, we present a conforming formulation that generalizes the Scott-Vogelius finite element method for the numerical approximation of the Stokes problem to polygonal meshes in the framework of the virtual element method. In particular, we consider a straightforward application of the virtual element approximation space for scalar elliptic problems to the vector case and approximate the pressure variable through discontinuous polynomials. We assess the effectiveness of the numerical approximation by investigating the convergence on a manufactured solution problem and a set of representative polygonal meshes. We numerically show that this formulation is convergent with optimal convergence rates except for the lowest-order case on triangular meshes, where the method coincides with the P-1 - P-0 Scott-Vogelius scheme, and on square meshes, which are situations that are well-known to be unstable
Numerical performance of preconditioning techniques for the solution of complex sparse linear systems
No full textPreconditioning techniques based on ILU decomposition, on Frobenius norm minimization and on factorized sparse approximate inverse are considered. These algorithms are applied with conjugate gradient-type methods, namely Bi-CGSTAB, QMR and TFQMR for the solution of complex, large, sparse linear systems. The results of numerical experiments in scalar environment with matrices arising from transport in porous media, quantum chemistry, structural dynamics and electromagnetism are analysed. The preconditioner that appears most significant in parallel environment (based on factorized sparse approximate inverse) is then employed on a Cray T3E supercomputer. The experimental results show the satisfactory parallel performance of the proposed algorithm
High Order Godunov Mixed Methods on tetrahedral meshes for density driven flow simulations in porous media
No full textTwo-dimensional Godunov mixed methods have been shown to be effective for the numerical solution of density-dependent flow and transport problems in groundwater even when concentration gradients are high and the process is dominated by density effects. This class of discretization approaches solves the flow equation by means of the mixed finite element method, thus guaranteeing mass conserving velocity fields, and discretizes the transport equation by mixed finite element and finite volumes techniques combined together via appropriate time splitting. In this paper, we extend this approach to three dimensions employing tetrahedral meshes and introduce a spatially variable time stepping procedure that improves computational efficiency while preserving accuracy by adapting the time step size according to the local Courant-Friedrichs-Lewy (CFL) constraint. Careful attention is devoted to the choice of a truly three-dimensional limiter for the advection equation in the time-splitting technique, so that to preserve second order accuracy in space (in the sense that linear functions are exactly interpolated). The three-dimensional Elder problem and the salt-pool problem, recently introduced as a new benchmark for testing three-dimensional density models, provide assessments with respect to accuracy and reliability of this numerical approach
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