Search results for "Numerical Analysis"
showing 10 items of 883 documents
Semipredictable dynamical systems
2015
A new class of deterministic dynamical systems, termed semipredictable dynamical systems, is presented. The spatiotemporal evolution of these systems have both predictable and unpredictable traits, as found in natural complex systems. We prove a general result: The dynamics of any deterministic nonlinear cellular automaton (CA) with $p$ possible dynamical states can be decomposed at each instant of time in a superposition of $N$ layers involving $p_{0}$, $p_{1}$,... $p_{N-1}$ dynamical states each, where the $p_{k\in \mathbb{N}}$, $k \in [0, N-1]$ are divisors of $p$. If the divisors coincide with the prime factors of $p$ this decomposition is unique. Conversely, we also prove that $N$ CA w…
Active controlled structural systems under delta-correlated random excitation: linear and nonlinear case
2006
Abstract Reduction of structural vibration in active controlled dynamical system is usually performed by means of convenient control forces dependent of the dynamic response. In this paper the existent studies will be extended to dynamical systems subjected to non-Gaussian random process accounting for the time delay involved in the application of active control actions. Control forces acting with time-delay effects will be expanded in Taylor series evaluating response statistics by means of the extended Ito differential rule to consider the effects of the non-normality of the input processes. Numerical application provided shows the feasibility of the proposed method to analyze stochastic …
Mixed mode failure analysis of bonded joints with rate dependent interface models
2006
The recent developments in joining technologies and the increasing use of composites materials in structural design justify the wide interest of structural mechanics researchers in bonded joints. Joints often represent the weakness zone of the structure and appropriate and rigorous mechanical models are required in order to describe deformation, durability and failure. The present work is devoted to the theoretical formulation and numerical implementation of an interface model suitable to simulate the time-dependent behaviour of bonded joints. The interface laws are formulated in the framework of viscoplasticity for generalized standard materials and describe the softening response of the j…
A posteriori error estimates for a Maxwell type problem
2009
In this paper, we discuss a posteriori estimates for the Maxwell type boundary-value problem. The estimates are derived by transformations of integral identities that define the generalized solution and are valid for any conforming approximation of the exact solution. It is proved analytically and confirmed numerically that the estimates indeed provide a computable and guaranteed bound of approximation errors. Also, it is shown that the estimates imply robust error indicators that represent the distribution of local (inter-element) errors measured in terms of different norms. peerReviewed
On the numerical solution of axisymmetric domain optimization problems by dual finite element method
1994
Shape optimization of an axisymmetric three-dimensional domain with an elliptic boundary value state problem is solved. Since the cost functional is given in terms of the cogradient of the solution, a dual finite element method based on the minimum of complementary energy principle is used. © 1994 John Wiley & Sons, Inc.
Convergence of a finite volume scheme for the compressible Navier–Stokes system
2019
We study convergence of a finite volume scheme for the compressible (barotropic) Navier–Stokes system. First we prove the energy stability and consistency of the scheme and show that the numerical solutions generate a dissipative measure-valued solution of the system. Then by the dissipative measure-valued-strong uniqueness principle, we conclude the convergence of the numerical solution to the strong solution as long as the latter exists. Numerical experiments for standard benchmark tests support our theoretical results.
The MAST FV/FE scheme for the simulation of two-dimensional thermohaline processes in variable-density saturated porous media
2009
A novel methodology for the simulation of 2D thermohaline double diffusive processes, driven by heterogeneous temperature and concentration fields in variable-density saturated porous media, is presented. The stream function is used to describe the flow field and it is defined in terms of mass flux. The partial differential equations governing system is given by the mass conservation equation of the fluid phase written in terms of the mass-based stream function, as well as by the advection-diffusion transport equations of the contaminant concentration and of the heat. The unknown variables are the stream function, the contaminant concentration and the temperature. The governing equations sy…
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…
Mathematical and numerical analysis of initial boundary valueproblem for a linear nonlocal equation
2019
We propose and study a numerical scheme for bounded distributional solutions of the initial boundary value problem for the anomalous diffusion equation ∂t u +Lμu = 0 in a bounded domain supplemented with inhomogeneous boundary conditions. Here Lμ is a class of nonlocal operators including fractional Laplacian. ⃝c 2019 InternationalAssociation forMathematics andComputers in Simulation (IMACS). Published by ElsevierB.V.All rights reserved.
A normalized iterative Smoothed Particle Hydrodynamics method
2020
Abstract In this paper we investigate on a normalized iterative approach to improve the Smoothed Particle Hydrodynamics (SPH) estimate of a function. The method iterates on the residuals of an initial SPH approximation to obtain a more accurate solution. The iterative strategy preserves the matrix-free nature of the method, does not require changes on the kernel function and it is not affected by disordered data distribution. The iterative refinement is further improved by ensuring linear approximation order to the starting iterative values. We analyze the accuracy and the convergence of the method with the standard and normalized formulation giving evidence of the enhancements obtained wit…