Solano, F.; Guevara-Jordan, J.; Rojas, O.; Otero, B.; Rodriguez, R. Journal of computational and applied mathematics Vol. 295, p. 2-12 DOI: 10.1016/j.cam.2015.09.037 Data de publicació: 2016-03-15 Article en revista
A new mimetic finite difference scheme for solving the acoustic wave equation is presented. It combines a novel second order tensor mimetic discretizations in space and a leapfrog approximation in time to produce an explicit multidimensional scheme. Convergence analysis of the new scheme on a staggered grid shows that it can take larger time steps than standard finite difference schemes based on ghost points formulation. A set of numerical test problems gives evidence of the versatility of the new mimetic scheme for handling general boundary conditions. (C) 2015 Elsevier B.V. All rights reserved.
A new mimetic finite difference scheme for solving the acoustic wave equation is presented. It combines a novel second order tensor mimetic discretizations in space and a leapfrog approximation in time to produce an explicit multidimensional scheme. Convergence analysis of the new scheme on a staggered grid shows that it can take larger time steps than standard finite difference schemes based on ghost points formulation. A set of numerical test problems gives evidence of the versatility of the new mimetic scheme for handling general boundary conditions.
We present two fourth-order compact finite difference (CFD) discretizations of the velocity–pressure formulation of the acoustic wave equation in 2-D rectangular grids. The first method uses standard implicit CFD on nodal meshes and requires solving tridiagonal linear systems along each grid line, while the second scheme employs a novel set of mimetic CFD operators for explicit differentiation on staggered grids. Both schemes share a Crank–Nicolson time integration decoupled by the Peaceman–Rachford splitting technique to update discrete fields by alternating the coordinate direction of CFD differentiation (ADI-like iterations). For comparison purposes, we also implement a spatially fourth-order FD scheme using non compact staggered mimetic operators in combination to second-order leap-frog time discretization. We apply these three schemes to model acoustic motion under homogeneous boundary conditions and compare their experimental convergence and execution times, as grid is successively refined. Both CFD schemes show four-order convergence, with a slight superiority of the mimetic version, that leads to more accurate results on fine grids. Conversely, the mimetic leap-frog method only achieves quadratic convergence and shows similar accuracy to CFD results exclusively on coarse grids. We finally observe that computation times of nodal CFD simulations are between four and five times higher than those spent by the mimetic CFD scheme with similar grid size. This significant performance difference is attributed to solving those embedded linear systems inherent to implicit CFD.
Gibert, Karina; Sevilla-Villanueva, Beatriz; Sànchez-Marrè, M. Journal of computational and applied mathematics Vol. 292, p. 623-633 DOI: 10.1016/j.cam.2015.01.031 Data de publicació: 2016-01-15 Article en revista
Cluster interpretation is an important step for a proper understanding of a set of classes, independently of whether they have been automatically discovered or expert-based. An understanding of classes is crucial for the further use of classes as the basis of a decision-making process.; The abundant work on cluster validity found in the literature is mainly focused on the validation of clusters from the structural point of view. However, structural validation does not ensure that the clustering is useful, since meaningfulness is the key to guaranteeing that classes can support further decisions. In previous works, special significance tests taken from the field of multivariate analysis were introduced in an interpretation methodology for automatically assessing relevant variables in particular classes.; In this paper, we present the interpretation of nested partitions and the relationships between both interpretations are studied. In particular, the inconsistencies produced in interpretation when a second partition refines the first one with a higher level of granularity are studied, diagnosed, and a modification of the original methodology is provided to guarantee consistency in these cases. The relevant characteristics detected in a parent class must also be inherited in subclasses, or at least in some of them.; The proposal is evaluated using a real data set on baseline health conditions and dietary habits of a sample of the general population. (C) 2015 Elsevier B.V. All rights reserved.
We consider a methodology based on B-splines scaling functions to numerically invert Fourier or Laplace transforms of functions in the space L-2(R). The original function is approximated by a finite combination of jth order B-splines basis functions and we provide analytical expressions for the recovered coefficients. The methodology is particularly well suited when the original function or its derivatives present peaks or jumps due to discontinuities in the domain. We will show in the numerical experiments the robustness and accuracy of the method. (C) 2014 Elsevier B.V. All rights reserved.
A local convergence analysis for a generalized family of two step Secant-like methods with frozen operator for solving nonlinear equations is presented. Unifying earlier methods such as Secant’s, Newton, Chebyshev-like, Steffensen and other new variants the family of iterative schemes is built up, where a profound and clear study of the computational efficiency is also carried out. Numerical examples and an application using multiple precision and a stopping criterion are implemented without using any known root. Finally, a study comparing the order, efficiency and elapsed time of the methods suggested supports the theoretical results claimed.
García, O.; Vehí, J.; Campos, J.; Henriques, A.; Casas, J. Journal of computational and applied mathematics Vol. 218, num. 1, p. 43-52 DOI: 10.1016/j.cam.2007.04.047 Data de publicació: 2008-08 Article en revista
An efficient health monitoring system for damage detection in civil engineering structures using on-line monitoring data is being developed to identify any possible damage in short time. The present work is based on the treatment of uncertainties, which is one of the basic common difficulties faced when modelling structures. A methodology, based on interval analysis (IA) theory [R.E. Moore, Interval Analysis, Prentice-Hall, Englewood Cliffs, NJ, 1966] applied to a numerical constraint satisfaction problem (CSP) [J.R. Casas, J.C. Matos, J.A. Figueiras, J. Vehí, O. García, P. Herrero, Bridge monitoring and assessment under uncertainty via interval analysis, in: Ninth International Conference On Structural Safety And Reliability—ICOSSAR2005, 2005. pp. 487–494], is implemented in the damage detection [J.R. Casas, J.C. Matos, J.A. Figueiras, J. Vehí, O. García, P. Herrero, Bridge monitoring and assessment under uncertainty via interval analysis, in: Ninth International Conference On Structural Safety And Reliability—ICOSSAR2005, 2005. pp. 487–494] and modelling system of a long-term monitoring project in order to achieve such an objective. An algorithm is being developed for using such methodology with the obtained data.
Such methodology has been first checked in the laboratory with a simple reinforced concrete structure (loaded up to failure). The obtained results are useful for identifying the load where the structure presents changes in its behaviour. The majority of the structures present a linear elastic behaviour throughout their life. However, they tend to deteriorate; such degradation reflects on results obtained from the long term monitoring system. Structural assessment was successfully performed in this case, enabling its application to real structures.
We present a new overlapping Dirichlet/Robin Domain Decomposition method. The method uses Dirichlet and Robin transmission conditions on the interfaces of an overlapping partitioning of the computational domain. We derive interface equations to study the convergence of the method and show its properties through four numerical examples. The mathematical framework is general and can be applied to derive overlapping versions of all the classical nonoverlapping methods.