Search results for "Discretization"
showing 10 items of 237 documents
MAST-2D diffusive model for flood prediction on domains with triangular Delaunay unstructured meshes
2011
Abstract A new methodology for the solution of the 2D diffusive shallow water equations over Delaunay unstructured triangular meshes is presented. Before developing the new algorithm, the following question is addressed: it is worth developing and using a simplified shallow water model, when well established algorithms for the solution of the complete one do exist? The governing Partial Differential Equations are discretized using a procedure similar to the linear conforming Finite Element Galerkin scheme, with a different flux formulation and a special flux treatment that requires Delaunay triangulation but entire solution monotonicity. A simple mesh adjustment is suggested, that attains t…
A thermodynamically consistent nonlocal formulation for damaging materials
2002
A thermodynamically consistent nonlocal formulation for damaging materials is presented. The second principle of thermodynamics is enforced in a nonlocal form over the volume where the dissipative mechanism takes place. The nonlocal forces thermodynamically conjugated are obtained consistently from the free energy. The paper indeed extends to elastic damaging materials a formulation originally proposed by Polizzotto et al. for nonlocal plasticity. Constitutive and computational aspects of the model are discussed. The damage consistency conditions turn out to be formulated as an integral complementarity problem and, consequently, after discretization, as a linear complementarity problem. A n…
Step-by-step integration for fractional operators
2018
Abstract In this paper, an approach based on the definition of the Riemann–Liouville fractional operators is proposed in order to provide a different discretisation technique as alternative to the Grunwald–Letnikov operators. The proposed Riemann–Liouville discretisation consists of performing step-by-step integration based upon the discretisation of the function f(t). It has been shown that, as f(t) is discretised as stepwise or piecewise function, the Riemann–Liouville fractional integral and derivative are governing by operators very similar to the Grunwald–Letnikov operators. In order to show the accuracy and capabilities of the proposed Riemann–Liouville discretisation technique and th…
On the Stochastic Response of a Fractionally-damped Duffing Oscillator
2012
A numerical method is presented to compute the response of a viscoelastic Duffing oscillator with fractional derivative damping, subjected to a stochastic input. The key idea involves an appropriate discretization of the fractional derivative, based on a preliminary change of variable, that allows to approximate the original system by an equivalent system with additional degrees of freedom, the number of which depends on the discretization of the fractional derivative. Unlike the original system that, due to the presence of the fractional derivative, is governed by non-ordinary differential equations, the equivalent system is governed by ordinary differential equations that can be readily h…
Incremental elastoplastic analysis for active macro-zones
2012
SUMMARY In this paper a strategy to perform incremental elastoplastic analysis using the symmetric Galerkin boundary element method for multidomain type problems is shown. The discretization of the body is performed through substructures, distinguishing the bem-elements characterizing the so-called active macro-zones, where the plastic consistency condition may be violated, and the macro-elements having elastic behaviour only. Incremental analysis uses the well-known concept of self-equilibrium stress field here shown in a discrete form through the introduction of the influence matrix (self-stress matrix). The nonlinear analysis does not use updating of the elastic response inside each plas…
Asymptotic preserving IMEX finite volume schemes for low Mach number Euler equations with gravitation
2017
In this paper we will present and analyze a new class of the IMEX finite volume schemes for the Euler equations with a gravity source term. We will in particular concentrate on a singular limit of weakly compressible flows when the Mach number M1. In order to efficiently resolve slow dynamics we split the whole nonlinear system in a stiff linear part governing the acoustic and gravity waves and a non-stiff nonlinear part that models nonlinear advection effects. For time discretization we use a special class of the so-called globally stiffly accurate IMEX schemes and approximate the stiff linear operator implicitly and the non-stiff nonlinear operator explicitly. For spatial discretization t…
Inversion Formulas for the Discretized Hilbert Transform on the Unit Circle
1998
A discrete version of the Hilbert transform on the unit circle is considered. Its Moore--Penrose inverse with respect to suitable scalar products is derived for different side conditions. Furthermore, stability of the pseudo-inverse is studied. These results allow the efficient computation of approximate solutions of singular integral equations with Hilbert kernel. Furthermore, the stability analysis of such methods becomes much easier even for graded meshes which are useful for weakly singular solutions.
Numerical Study of Two Sparse AMG-methods
2003
A sparse algebraic multigrid method is studied as a cheap and accurate way to compute approximations of Schur complements of matrices arising from the discretization of some symmetric and positive definite partial differential operators. The construction of such a multigrid is discussed and numerical experiments are used to verify the properties of the method.
Multiresolution based on weighted averages of the hat function I: Linear reconstruction techniques
1998
In this paper we analyze a particular example of the general framework developed in [A. Harten, {\it SIAM J. Numer. Anal}., 33 (1996) pp. 1205--1256], the case in which the discretization operator is obtained by taking local averages with respect to the hat function. We consider a class of reconstruction procedures which are appropriate for this multiresolution setting and describe the associated prediction operators that allow us to climb up the ladder from coarse to finer levels of resolution. In Part I we use data-independent (linear) reconstruction techniques as our approximation tool. We show how to obtain multiresolution transforms in bounded domains and analyze their stability with r…
Weighted ENO interpolation and applications
2004
Abstract Data-dependent interpolatory techniques such as essentially non-oscillatory (ENO) technique [J. Comput. Phys. 71 (1987) 231] have long been used as a reconstruction process in multiresolution schemes. In this work we analyze the weighted ENO (WENO) technique introduced by Liu et al. in the context of conservation laws [J. Comput. Phys. 115 (1994) 200] and improved by Jiang and Shu [J. Comput. Phys. 126 (1996) 202], and apply it to the compression of images, using multiresolution techniques.