Pedro Enrique Barrilao González

A general spline differential quadrature method based on quasi-interpolation

The differential quadrature method is a numerical discretization technique for the approximation of derivatives. The classical method is polynomial-based, and there is a natural restriction in the number of grid points involved. A general spline-based method is proposed to avoid this problem. For any degree a Lagrangian spline interpolant is defined having a fundamental function with small support. A quasi-interpolant is used to achieve the optimal approximation order. That two-stage scheme is detailed for the cubic, quartic, quintic and sextic cases and compared with another methods that appear in the literature.

An in-depth study on WENO-based techniques to improve parameter extraction procedures in MOSFET transistors

WENO-based techniques, along with some particular polynomial interpolation procedures, have been employed to improve parameter extraction in Metal Oxide Semiconductor Field Effect Transistors (MOSFETs), in particular for the determination of the threshold voltage. The limitations detected in conventional numerical methods to calculate derivatives of experimental data are overcome with this new application of WENO-based techniques. The numerical noise that comes up in the experimental and simulated data usually employed to characterize MOSFETs transistors is strongly reduced. The need for an accurate determination of the threshold voltage motivates the use of this advanced numerical approach that solves many of the issues that affect the conventional parameter extraction procedures currently in use in the microelectronics industry. In addition, also the influence of DIBL effects on the threshold voltage in short channel MOSFETs has been analyzed with this smart weighted ENO procedure.

On spline-based differential quadrature

In the paper Barrera et al. (2014), a boolean sum differential quadrature method (DQM) was proposed by combining a spline interpolation operator having a fundamental function with minimal compact support and a spline quasi-interpolation operator reproducing the polynomials in the spline space. It is a general framework that provides results that differ from the ones obtained by defining specific schemes with structures which depend on the degree of the B-spline to be considered. The main drawback of these boolean sum DQMs is that the number of evaluation points increases quickly with the degree of the B-spline due to the use of a quasi-interpolation operator. We propose a different construction avoiding this problem and derive explicit results for low degree B-splines.

Parallelization of implicit-explicit runge-kutta methods for cluster of PCs

Several physical phenomena of great importance in science and engineering are described by large partly stiff differential systems where the stiff terms can be easily separated from the remaining terms. Implicit-Explicit Runge-Kutta (IMEXRK) methods have proven to be useful solving these systems efficiently. However, the application of these methods still requires a large computational effort and their parallel implementation constitutes a suitable way to achieve acceptable response times. In this paper, a technique to parallelize and implement efficiently IMEXRK methods on PC clusters is proposed. This technique has been used to parallelize a particular IMEXRK method and an efficient parallel implementation of the resultant scheme has been derived in a structured manner by following a component-based approach. Several numerical experiments which have been performed on a cluster of dual PCs reveal the good speedup and the satisfactory scalability of the parallel solver obtained.

A hole filling method for surfaces by using C1-Powell-Sabin splines. Estimation of the smoothing parameters

Abstract: Let D@?R^2 be a polygonal domain, H be a subdomain of D and f@?C^1(D@?-H@?). In this paper we propose a method to reconstruct f over the whole D@? using a technique based on the minimization of an energy functional J. More precisely, we construct a new C^1-Powell-Sabin spline function f^* over D@? that approximates f outside H, and fills the hole of f inside H. The resulting filling patch strongly depends on the values of two smoothing parameters involved in the functional J. We give a criteria to select optimum values of the parameters and we present some graphical and numerical examples.

Derivation of a State-Space Model by Functional Data Analysis

SummaryBy approximating a stochastic process by means of spline interpolation of its sample-paths, a time dependent state-space model is introduced. Then we derive the expression of the associated transition matrix that allows to obtain a discrete model useful in applications. In order to essay the behaviour of the proposed models simulations on a narrow-band process are developed. Finally, the paper includes an application with real data obtained from the Stock Market of Madrid.

Filling holes with geometric and volumetric constraints

Abstract We propose and analyze different methods to reconstruct a function that is defined outside a sub-domain (hole) of a given domain. The reconstructed function is a smooth Powell–Sabin spline that is defined also inside this hole, filling then this lack of information, and, at the same time, fulfills certain global geometric considerations and other local volume constraints on the hole. We give several examples and we include a technique to estimate the volume of the function inside the hole by using just the data of the function where it is known, that is, outside the hole.

Approximation of patches by Cr-finite elements of Powell–Sabin type

In this work we develop a method to extend a function that is defined in a finite set of disjoint patches to a bigger domain containing all of them. The way to extend the function is by minimizing an energy functional which controls the closeness of the extended function to the original one over the patches, as well as the smoothness of the final reconstructed function. We show the existence and uniqueness of solution of this problem and we give a convergence result as well as several graphical and numerical examples.