Application of the Jacobi Davidson method for spectral low-rank preconditioning in computational electromagnetics problems

[EN] We consider the numerical solution of linear systems arising from computational electromagnetics applications. For large scale problems the solution is usually obtained iteratively with a Krylov subspace method. It is well known that for ill conditioned problems the convergence of these methods can be very slow or even it may be impossible to obtain a satisfactory solution. To improve the convergence a preconditioner can be used, but in some cases additional strategies are needed. In this work we study the application of spectral lowrank updates (SLRU) to a previously computed sparse approximate inverse preconditioner.The updates are based on the computation of a small subset of the eigenpairs closest to the origin. Thus, the performance of the SLRU technique depends on the method available to compute the eigenpairs of interest. The SLRU method was first used using the IRA s method implemented in ARPACK. In this work we investigate the use of a Jacobi Davidson method, in particular its JDQR variant. The results of the numerical experiments show that the application of the JDQR method to obtain the spectral low-rank updates can be quite competitive compared with the IRA s method.Mas Marí, J.; Cerdán Soriano, JM.; Malla Martínez, N.; Marín Mateos-Aparicio, J. (2015). Application of the Jacobi Davidson method for spectral low-rank preconditioning in computational electromagnetics problems. Journal of the Spanish Society of Applied Mathematics. 67:39-50. doi:10.1007/s40324-014-0025-6S395067Bergamaschi, L., Pini, G., Sartoretto, F.: Computational experience with sequential, and parallel, preconditioned Jacobi–Davidson for large sparse symmetric matrices. J. Comput. Phys. 188(1), 318–331 (2003)Carpentieri, B.: Sparse preconditioners for dense linear systems from electromagnetics applications. PhD thesis, Institut National Polytechnique de Toulouse, CERFACS (2002)Carpentieri, B., Duff, I.S., Giraud, L.: Sparse pattern selection strategies for robust Frobenius-norm minimization preconditioners in electromagnetism. Numer. Linear Algebr. Appl. 7(7–8), 667–685 (2000)Carpentieri, B., Duff, I.S., Giraud, L.: A class of spectral two-level preconditioners. SIAM J. Sci. Comput. 25(2), 749–765 (2003)Carpentieri, B., Duff, I.S., Giraud, L., Magolu monga Made, M.: Sparse symmetric preconditioners for dense linear systems in electromagnetism. Numer. Linear Algebr. Appl. 11(8–9), 753–771 (2004)Carpentieri, B., Duff, I.S., Giraud, L., Sylvand, G.: Combining fast multipole techniques and an approximate inverse preconditioner for large electromagnetism calculations. SIAM J. Sci. Comput. 27(3), 774–792 (2005)Darve, E.: The fast multipole method I: error analysis and asymptotic complexity. SIAM J. Numer. Anal. 38(1), 98–128 (2000)Fokkema, D.R., Sleijpen, G.L., Van der Vorst, H.A.: Jacobi–Davidson style QR and QZ algorithms for the reduction of matrix pencils. SIAM J. Sci. Comput. 20(1), 94–125 (1998)Greengard, L., Rokhlin, V.: A fast algorithm for particle simulations. J. Comput. Phys. 73(3), 325–348 (1987)Grote, M., Huckle, T.: Parallel preconditioning with sparse approximate inverses. SIAM J. Sci. Comput. 18(3), 838–853 (1997)Harrington, R.: Origin and development of the method of moments for field computation. IEEE Antenna Propag. Mag. (1990)Kunz, K.S., Luebbers, R.J.: The finite difference time domain method for electromagnetics. SIAM J. Sci. Comput. 18(3), 838–853 (1997)Maxwell, J.C.: A dynamical theory of the electromagnetic field. Roy. S. Trans. CLV, (1864). Reprinted in Tricker, R. A. R. The Contributions of Faraday and Maxwell to Electrial Science, Pergamon Press (1966)Marín, J., Malla M.: Some experiments preconditioning via spectral low rank updates for electromagnetism applications. In: Proceedings of the international conference on preconditioning techniques for large sparse matrix problems in scientific and industrial applications (Preconditioning 2007), Toulouse (2007)Meijerink, J.A., van der Vorst, H.A.: An iterative solution method for linear systems of which the coefficient matrix is a symmetric M-matrix. Math. Comput. 31, 148–162 (1977)Sorensen, D.C., Lehoucq, R.B., Yang, C.: ARPACK users’ guide: solution of large-scale eigenvalue problems with implicitly restarted Arnoldi methods. SIAM, Philadelphia (1998)Rao, S.M., Wilton, D.R., Glisson, A.W.: Electromagnetic scattering by surfaces of arbitrary shape. IEEE Trans. Antenna Propag. 30, 409–418 (1982)Saad, Y.: Iterative methods for sparse linear systems. PWS Publishing Company, Boston (1996)Silvester, P.P., Ferrari, R.L.: Finite elements for electrical engineers. Cambridge University Press, Cambridge (1990)Sleijpen, S.L., van der Vorst, H.A.: A Jacobi–Davidson iteration method for linear eigenvalue problems. SIAM J. Matrix Anal. Appl. 17, 401–425 (1996)van der Vorst, H.A.: Bi-CGSTAB: a fast and smoothly converging variant of Bi-CG for the solution of non-symmetric linear systems. SIAM J. Sci. Stat. Comput. 12(6), 631–644 (1992

A hybrid fuzzy sliding-mode control for a three-phase shunt active power filter

This document is the Accepted Manuscript version of the following article: Mohamed Abdeldjabbar Kouadria, Tayeb Allaoui, and Mouloud Denai, ‘A hybrid fuzzy sliding-mode control for a three-phase shunt active power filter’, Energy Systems, Vol. 8 (2): 297-308, March 2016. The final publication is available at Springer via http://dx.doi.org/10.1007/s12667-016-0198-4.This paper describes the hybrid fuzzy sliding-mode control (HFSMC) for a three phase shunt active shunt filter for the power quality improvement. The Power Quality (PQ) problems in power distribution systems are not new but only recently the effects of these problems have gained public awareness. These non-linear loads are constructed by nonlinear devices in which the current is not proportional to the applied voltage. For the harmonic elimination different methods are used, but in this paper a novel fuzzy logic controller for a three-phase shunt active power filter for the power quality improvement such as reactive power and harmonic current compensation generated due to nonlinear loads. The hybrid fuzzy sliding-mode control (HFSMC) approach is proposed such that it can be applied with advantages to both fuzzy and sliding-mode controller. Simulation results are presented to demonstrate the effectiveness of the control strategy. The results are found to be quite satisfactory to mitigate harmonic distortions, reactive power compensation and power quality improvement.Peer reviewedFinal Accepted Versio

A global method for coupling transport with chemistry in heterogeneous porous media

Modeling reactive transport in porous media, using a local chemical equilibrium assumption, leads to a system of advection-diffusion PDE's coupled with algebraic equations. When solving this coupled system, the algebraic equations have to be solved at each grid point for each chemical species and at each time step. This leads to a coupled non-linear system. In this paper a global solution approach that enables to keep the software codes for transport and chemistry distinct is proposed. The method applies the Newton-Krylov framework to the formulation for reactive transport used in operator splitting. The method is formulated in terms of total mobile and total fixed concentrations and uses the chemical solver as a black box, as it only requires that on be able to solve chemical equilibrium problems (and compute derivatives), without having to know the solution method. An additional advantage of the Newton-Krylov method is that the Jacobian is only needed as an operator in a Jacobian matrix times vector product. The proposed method is tested on the MoMaS reactive transport benchmark.Comment: Computational Geosciences (2009) http://www.springerlink.com/content/933p55085742m203/?p=db14bb8c399b49979ba8389a3cae1b0f&pi=1

Prognostic and therapeutic significance of carbohydrate antigen 19-9 as tumor marker in patients with pancreatic cancer

In pancreatic cancer ( PC) accurate determination of treatment response by imaging often remains difficult. Various efforts have been undertaken to investigate new factors which may serve as more appropriate surrogate parameters of treatment efficacy. This review focuses on the role of carbohydrate antigen 19- 9 ( CA 19- 9) as a prognostic tumor marker in PC and summarizes its contribution to monitoring treatment efficacy. We undertook a Medline/ PubMed literature search to identify relevant trials that had analyzed the prognostic impact of CA 19- 9 in patients treated with surgery, chemoradiotherapy and chemotherapy for PC. Additionally, relevant abstract publications from scientific meetings were included. In advanced PC, pretreatment CA 19- 9 levels have a prognostic impact regarding overall survival. Also a CA 19- 9 decline under chemotherapy can provide prognostic information for median survival. A 20% reduction of CA 19- 9 baseline levels within the first 8 weeks of chemotherapy appears to be sufficient to define a prognostic relevant subgroup of patients ('CA 19- 9 responder'). It still remains to be defined whether the CA 19- 9 response is a more reliable method for evaluating treatment efficacy compared to conventional imaging. Copyright (c) 2006 S. Karger AG, Basel

Order-of-magnitude speedup for steady states and traveling waves via Stokes preconditioning in Channelflow and Openpipeflow

Steady states and traveling waves play a fundamental role in understanding hydrodynamic problems. Even when unstable, these states provide the bifurcation-theoretic explanation for the origin of the observed states. In turbulent wall-bounded shear flows, these states have been hypothesized to be saddle points organizing the trajectories within a chaotic attractor. These states must be computed with Newton's method or one of its generalizations, since time-integration cannot converge to unstable equilibria. The bottleneck is the solution of linear systems involving the Jacobian of the Navier-Stokes or Boussinesq equations. Originally such computations were carried out by constructing and directly inverting the Jacobian, but this is unfeasible for the matrices arising from three-dimensional hydrodynamic configurations in large domains. A popular method is to seek states that are invariant under numerical time integration. Surprisingly, equilibria may also be found by seeking flows that are invariant under a single very large Backwards-Euler Forwards-Euler timestep. We show that this method, called Stokes preconditioning, is 10 to 50 times faster at computing steady states in plane Couette flow and traveling waves in pipe flow. Moreover, it can be carried out using Channelflow (by Gibson) and Openpipeflow (by Willis) without any changes to these popular spectral codes. We explain the convergence rate as a function of the integration period and Reynolds number by computing the full spectra of the operators corresponding to the Jacobians of both methods.Comment: in Computational Modelling of Bifurcations and Instabilities in Fluid Dynamics, ed. Alexander Gelfgat (Springer, 2018

An outcome analysis of self-expandable metallic stents in central airway obstruction: a cohort study

<p>Abstract</p> <p>Background</p> <p>Self-expandable metallic stents (SEMSs) have provided satisfactory management of central airway obstruction. However, the long-term benefits and complications of this management modality in patients with benign and malignant obstructing lesions after SEMS placement are unclear. We performed this cohort study to analyze the outcomes of Ultraflex SEMSs in patients with tracheobronchial diseases.</p> <p>Methods</p> <p>Of 149 patients, 72 with benign and 77 with malignant tracheobronchial disease received 211 SEMSs (benign, 116; malignant, 95) and were retrospectively reviewed in a tertiary hospital.</p> <p>Results</p> <p>The baseline characteristics of patients who received SEMS implantation for benign conditions and those who underwent implantation for malignant conditions were significantly different. These characteristics included age (mean, 63.9 vs. 58; <it>p </it>< 0.01), gender (male, 62% vs. 90%; <it>p </it>< 0.0001), smoking (47% vs. 85%; <it>p </it>< 0.0001), forced expiratory volume in 1 second (mean, 0.9 vs. 1.47 L/s; <it>p </it>< 0.0001), follow-up days after SEMS implantation (median; 429 vs. 57; <it>p </it>< 0.0001), and use of covered SEMS (36.2% vs. 94.7%; <it>p </it>< 0.0001). Symptoms improved more after SEMS implantation in patients with benign conditions than in those with malignant conditions (76.7% vs. 51.6%; <it>p </it>< 0.0001). The overall complication rate after SEMS implantation in patients with benign conditions was higher than that in patients with malignancy (42.2% vs. 21.1%; <it>p </it>= 0.001). Successful management of SEMS migration, granulation tissue formation, and SEMS fracture occurred in 100%, 81.25%, and 85% of patients, respectively.</p> <p>Conclusions</p> <p>Patients who received SEMS implantation owing to benign conditions had worse lung function and were older than those who received SEMS for malignancies. There was higher complication rate in patients with benign conditions after a longer follow-up period owing to the nature of the underlying diseases.</p

Prevention of type 2 diabetes in adults with impaired glucose tolerance: the European Diabetes Prevention RCT in Newcastle upon Tyne, UK

<p>Abstract</p> <p>Background</p> <p>Diabetes prevalence is increasing. The Finnish Diabetes Prevention Study (DPS) showed a 58% reduction in Type 2 Diabetes (T2D) incidence in adults with impaired glucose tolerance (IGT). The European Diabetes Prevention Study (EDIPS) extends the DPS to different European populations, using the same study design. In the Newcastle arm of this study (EDIPS-Newcastle), we tested the hypothesis that T2D can be prevented by lifestyle intervention and explored secondary outcomes in relation to diabetes incidence.</p> <p>Methods</p> <p>We recruited 102 participants (42 men and 60 women, mean age 57 years, mean BMI 34 kgm^-2) with IGT to EDIPS-Newcastle and randomised to Intervention and usual care Control groups. The intervention included individual motivational interviewing aimed at: weight reduction, increase in physical activity, fibre and carbohydrate intake and reduction of fat intake (secondary outcomes). The primary outcome was diagnosis of T2D.</p> <p>Results</p> <p>Mean duration of follow-up was 3.1 years. T2D was diagnosed in 16 participants (I = 5, C = 11). Absolute incidence of T2D was 32.7 per 1000 person-years in the Intervention-group and 67.1 per 1000 person-years in the Control-group. The overall incidence of diabetes was reduced by 55% in the Intervention-group, compared with the Control-group: RR 0.45 (95%CI 0.2 to 1.2).</p> <p>Explanatory survival analysis of secondary outcomes showed that those who sustained beneficial changes for two or more years reduced their risk of developing T2D.</p> <p>Conclusion</p> <p>Our results are consistent with other diabetes prevention trials. This study was designed as part of a larger study and although the sample size limits statistical significance, the results contribute to the evidence that T2D can be prevented by lifestyle changes in adults with IGT. In explanatory analysis small sustained beneficial changes in weight, physical activity or dietary factors were associated with reduction in T2D incidence.</p> <p>Trial Registration</p> <p>International Standard Randomised Controlled Trial Number registry (ISRCTN)</p> <p>Registry number: ISRCTN 15670600</p> <p><url>http://www.controlled-trials.com/isrctn/search.html?srch=15670600&sort=3&dir=desc&max=10</url></p