Search results for " numerical analysis"
showing 10 items of 106 documents
Bòvedas tabicadas: experimental and numerical analysis
2008
A class of thin vaults, the so-called “bovedas tabicadas”, which represent one of the most common Spanish traditional building techniques at the end of XIX century are studied here, treating the relevant analysis problem through a numerical, as well as an experimental, approach. At first the problem is studied by searching for the behaviour of the material effecting suitable experiments. Once the constitutive behaviour of the materials and the structural elements are experimentally characterized, a semi inverse method for the identification of the optimum mechanical parameters to assign to an equivalent homogeneous ideal material through analysis reproducing the executed experimental tests …
Modeling wave propagation in elastic solids via high-order accurate implicit-mesh discontinuous Galerkin methods
2022
A high-order accurate implicit-mesh discontinuous Galerkin framework for wave propagation in single-phase and bi-phase solids is presented. The framework belongs to the embedded-boundary techniques and its novelty regards the spatial discretization, which enables boundary and interface conditions to be enforced with high-order accuracy on curved embedded geometries. High-order accuracy is achieved via high-order quadrature rules for implicitly-defined domains and boundaries, whilst a cell-merging strategy addresses the presence of small cut cells. The framework is used to discretize the governing equations of elastodynamics, written using a first-order hyperbolic momentum-strain formulation…
A numerical approach to Blow-up issues for dispersive perturbations of Burgers' equation
2014
We provide a detailed numerical study of various issues pertaining to the dynamics of the Burgers equation perturbed by a weak dispersive term: blow-up in finite time versus global existence, nature of the blow-up, existence for "long" times, and the decomposition of the initial data into solitary waves plus radiation. We numerically construct solitons for fractionary Korteweg-de Vries equations.
Functional A Posteriori Error Estimates for Time-Periodic Parabolic Optimal Control Problems
2015
This article is devoted to the a posteriori error analysis of multiharmonic finite element approximations to distributed optimal control problems with time-periodic state equations of parabolic type. We derive a posteriori estimates of the functional type, which are easily computable and provide guaranteed upper bounds for the state and co-state errors as well as for the cost functional. These theoretical results are confirmed by several numerical tests that show high efficiency of the a posteriori error bounds. peerReviewed
Nonlinear hyperbolic equations in surface theory: integrable discretizations and approximation results
2006
A numerical scheme is developed for solution of the Goursat problem for a class of nonlinear hyperbolic systems with an arbitrary number of independent variables. Convergence results are proved for this difference scheme. These results are applied to hyperbolic systems of differential-geometric origin, like the sine-Gordon equation describing the surfaces of the constant negative Gaussian curvature (K-surfaces). In particular, we prove the convergence of discrete K--surfaces and their Backlund transformations to their continuous counterparts. This puts on a firm basis the generally accepted belief (which however remained unproved untill this work) that the classical differential geometry of…
Numerical study of the transverse stability of the Peregrine solution
2020
We generalise a previously published approach based on a multi-domain spectral method on the whole real line in two ways: firstly, a fully explicit 4th order method for the time integration, based on a splitting scheme and an implicit Runge--Kutta method for the linear part, is presented. Secondly, the 1D code is combined with a Fourier spectral method in the transverse variable both for elliptic and hyperbolic NLS equations. As an example we study the transverse stability of the Peregrine solution, an exact solution to the one dimensional nonlinear Schr\"odinger (NLS) equation and thus a $y$-independent solution to the 2D NLS. It is shown that the Peregrine solution is unstable against all…
Numerical study of shock formation in the dispersionless Kadomtsev-Petviashvili equation and dispersive regularizations
2013
The formation of singularities in solutions to the dispersionless Kadomtsev-Petviashvili (dKP) equation is studied numerically for different classes of initial data. The asymptotic behavior of the Fourier coefficients is used to quantitatively identify the critical time and location and the type of the singularity. The approach is first tested in detail in 1+1 dimensions for the known case of the Hopf equation, where it is shown that the break-up of the solution can be identified with prescribed accuracy. For dissipative regularizations of this shock formation as the Burgers' equation and for dispersive regularizations as the Korteweg-de Vries equation, the Fourier coefficients indicate as …
Spatial Besov regularity for stochastic partial differential equations on Lipschitz domains
2010
We use the scale of Besov spaces B^\alpha_{\tau,\tau}(O), \alpha>0, 1/\tau=\alpha/d+1/p, p fixed, to study the spatial regularity of the solutions of linear parabolic stochastic partial differential equations on bounded Lipschitz domains O\subset R^d. The Besov smoothness determines the order of convergence that can be achieved by nonlinear approximation schemes. The proofs are based on a combination of weighted Sobolev estimates and characterizations of Besov spaces by wavelet expansions.
A new incremental method of computing the limit load in deformation plasticity models
2015
The aim of this paper is to introduce a new incremental procedure that can be used for numerical evaluation of the limit load. Existing incremental type methods are based on parametrization of the energy by the loading parameter $\zeta\in[0,\zeta_{lim})$, where $\zeta_{lim}$ is generally unknown. In the new method, the incremental procedure is operated in terms of an inverse mapping and the respective parameter $\alpha$ is changing in the interval $(0,+\infty)$. Theoretically, in each step of this algorithm, we obtain a guaranteed lower bound of $\zeta_{lim}$. Reduction of the problem to a finite element subspace associated with a mesh $\mathcal T_h$ generates computable bound $\zeta_{lim,h…
Improved Global-Local Method for Ultrasonic Guided Wave Scattering Predictions in Composite Waveguides and Defects
2023
Abstract As structures increase in complexity, in the use of high-performing materials and designs, their health assessment becomes increasingly challenging. Ultrasonic guided waves (UGWs) have shown to be very promising in the inspection of large (i.e. aerospace components) attenuating (i.e. composite materials) structures and have been successfully employed for damage detection in a variety of fields. The intrinsic complex nature of UGWs, due to their dispersive behavior, combined with the structural complexity of the applications, though, makes the interpretation of UGW inspections very challenging. Numerical simulations of UGW propagation become crucial to this end and have been address…