Implementation and analysis of multigrid schemes with finite elements for elliptic optimal control problems

The detailed implementation and analysis of a finite element multigrid scheme for the solution of elliptic optimal control problems is presented. A particular focus is in the definition of smoothing strategies for the case of constrained control problems. For this setting, convergence of the multigrid scheme is discussed based on the BPX framework. Results of numerical experiments are reported to illustrate and validate the optimal efficiency and robustness of the performance of the present multigrid strategy.     

Solution of the finite element vector Helmholtz equation by means of eigenvalue displacement

In this paper, after an examination of the spectrum of the system matrix of the discrete vector Helmholtz equation, a novel technique that makes edge finite element matrices more suitable for Lanczos-based solvers is introduced. This technique works by displacing the eigenvalues related to static modes to a more favorable part of the spectrum. The displacement is achieved by means of a matrix that is added to the system matrix.     

The effects of a left bundle-branch block on ventricular repolarization dispersion

Patients with left bundle-branch block (LBBB) often present electrocardiographic abnormalities and, therefore, are excluded from studies concerning electrocardiographic evaluation of ventricular repolarization. The aim of the study was to assess whether LBBB could influence dispersion of ventricular repolarization. Surface electrocardiograms of 16 patients (9 males and 7 females, mean age 58 +/- 14 years) with episodes of intermittent LBBB were analyzed. Six patients were affected by coronary artery disease, 6 by hypertensive cardiomyopathy and 4 by dilated cardiomyopathy. Maximal QT and JT corrected intervals, QT and JT dispersion, and QT and JT dispersion corrected for heart rate, were obtained before and after LBBB. We observed a significant prolongation of maximal QT (412 +/- 29 vs 433 +/- 25 ms; p < 0.05), and of maximal corrected QT (457 +/- 37 vs 497 +/- 56 ms; p < 0.05) after LBBB. Maximal JT interval, also corrected for heart rate, did not show any significant modification after LBBB. Moreover, we did not observe any significant difference in electrocardiographic parameters of dispersion of repolarization. Our results seem to indicate that LBBB did not alter significantly dispersion of ventricular repolarization. QT dispersion is considered an important marker of risk for incidence of ventricular arrhythmias. If our results will be confirmed in larger groups of patients, analysis of QT dispersion could be extended even to patients with LBBB.     

Trigonometric approximations for the computation of Radar cross sections

Trigonometric approximation methods for the interpolation of the far field of a scatterer lit up by plane waves are presented. The Wacker method, commonly used to determine the far field of an antenna from spherical near field measurements, is adapted to decompose the scattered field in a finite series of vector spherical harmonics. The decomposition coefficients are used to assess the accuracy of the computed field and to efficiently store the far field profile. These coefficients are approximated by trigonometric functions up to a given order which can be estimated from the geometry of the scatterer. In this way an efficient procedure for the interpolation of monostatic and bistatic radar cross sections is obtained.     

Analysis of Iterative Methods for Solving a Ginzburg-Landau Equation

Very recently we have proposed to use a complex Ginzburg-Landau equation for high contrast inpainting, to restore higher dimensional (volumetric) data (which has applications in frame interpolation), improving sparsely sampled data and to fill in fragmentary surfaces. In this paper we review digital inpainting algorithms and compare their performance with a Ginzburg-Landau inpainting model. For the solution of the Ginzburg-Landau equation we compare the performance of several numerical algorithms. A stability and convergence analysis is given and the consequences for applications to digital inpainting are discussed.First online version published in June, 2005     

FEM analysis of unbounded electromagnetic scattering by the Robiniteration procedure

A new accurate procedure for the FEM solution of unbounded electromagnetic scattering problems is described. The scatterers are enclosed in a fictitious boundary on which a Robin condition is initially guessed, and then iteratively improved using the Green formula. The method does not present interior resonances and is easy to implement     

Finite-element solution to electromagnetic scattering problems bymeans of the Robin boundary condition iteration method

A new numerical method, called the Robin boundary condition iteration (RBCI), is proposed for the finite-element (FE) solution of electromagnetic scattering problems in open boundary domains. The unbounded domain is truncated to a bounded one by means of a fictitious boundary that contains the scatterer and on which a suitable nonhomogeneous Robin (mixed) boundary condition is assumed for the Helmholtz equation in the bounded domain. The Robin condition is expressed by means of an integral formula (the second Green identity) in terms of the field in the interior of the bounded domain, with the integration surface being a surface strictly enclosed by the truncation boundary. The discretized differential and integral equations are then coupled together to solve the problem. The formulation is completely immune from the well-known interior resonance problems. A simple and effective iterative solving scheme is described. Examples are also provided to validate RBCI and compare it with other methods