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Università degli Studi di Napoli "Federico II"
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Ingeniería, investigación y tecnología, 2009
Recent numer ical studies have proved that multiquadric collo ca tion methods can achieve expo ne... more Recent numer ical studies have proved that multiquadric collo ca tion methods can achieve expo nen tial rate of conver gence for elliptic prob lems. Although some investi ga tions has been performed for time dependent prob lems, the influ ence of the shape param eter of the multiquadric kernel on the conver gence rate of these schemes has not been studied. In this article, we inves ti gate this issue and the influence of the Péclet number on the rate of conver gence for a convec tion diffu sion problem by using both an explicit and implicit multiquadric collo ca tion tech niques. We found that for low to moderate Péclet number an expo nen tial rate of convergence can be attained. In addi tion, we found that increasing the value of the Péclet number produces a value reduc tion of the coef fi cient that deter mines the expo nential rate of conver gence. More over, we numer i cally showed that the optimal value of the shape param eter decreases monotonically when the diffusive coefficient is reduced.
Series on Advances in Mathematics for Applied Sciences, 2009
A novel method for detection of lines in a digital image used in line scale calibration process i... more A novel method for detection of lines in a digital image used in line scale calibration process is described. The line images are recorded by a moving microscope and a CCD camera. This method is based on the center of the line instead of the edges of the line. Line detection is one of the most important problems in the line scale calibration. This method uses a Gabor filter for each row in the digital image. Likewise, based on robust statistics, some outlier points due to imperfections in the mark on the scale are ignored.
Numerical Methods for Partial Differential Equations, 2009
During the last years, there has been increased interest in developing efficient radial basis fun... more During the last years, there has been increased interest in developing efficient radial basis function (RBF) algorithms to solve partial differential problems of great scale. In this article, we are interested in solving large PDEs problems, whose solution presents rapid variations. Our main objective is to introduce a RBF dynamical domain decomposition algorithm which simultaneously performs a node adaptive strategy. This algorithm is based on the RBFs unsymmetric collocation setting. Numerical experiments performed with the multiquadric kernel function, for two stationary problems in two dimensions are presented.
Ingeniería, investigación y tecnología, 2009
Recent numer ical studies have proved that multiquadric collo ca tion methods can achieve expo ne... more Recent numer ical studies have proved that multiquadric collo ca tion methods can achieve expo nen tial rate of conver gence for elliptic prob lems. Although some investi ga tions has been performed for time dependent prob lems, the influ ence of the shape param eter of the multiquadric kernel on the conver gence rate of these schemes has not been studied. In this article, we inves ti gate this issue and the influence of the Péclet number on the rate of conver gence for a convec tion diffu sion problem by using both an explicit and implicit multiquadric collo ca tion tech niques. We found that for low to moderate Péclet number an expo nen tial rate of convergence can be attained. In addi tion, we found that increasing the value of the Péclet number produces a value reduc tion of the coef fi cient that deter mines the expo nential rate of conver gence. More over, we numer i cally showed that the optimal value of the shape param eter decreases monotonically when the diffusive coefficient is reduced.
Series on Advances in Mathematics for Applied Sciences, 2009
A novel method for detection of lines in a digital image used in line scale calibration process i... more A novel method for detection of lines in a digital image used in line scale calibration process is described. The line images are recorded by a moving microscope and a CCD camera. This method is based on the center of the line instead of the edges of the line. Line detection is one of the most important problems in the line scale calibration. This method uses a Gabor filter for each row in the digital image. Likewise, based on robust statistics, some outlier points due to imperfections in the mark on the scale are ignored.
Numerical Methods for Partial Differential Equations, 2009
During the last years, there has been increased interest in developing efficient radial basis fun... more During the last years, there has been increased interest in developing efficient radial basis function (RBF) algorithms to solve partial differential problems of great scale. In this article, we are interested in solving large PDEs problems, whose solution presents rapid variations. Our main objective is to introduce a RBF dynamical domain decomposition algorithm which simultaneously performs a node adaptive strategy. This algorithm is based on the RBFs unsymmetric collocation setting. Numerical experiments performed with the multiquadric kernel function, for two stationary problems in two dimensions are presented.