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

Guidelines for investigating causality of sequence variants in human disease

The discovery of rare genetic variants is accelerating, and clear guidelines for distinguishing disease-causing sequence variants from the many potentially functional variants present in any human genome are urgently needed. Without rigorous standards we risk an acceleration of false-positive reports of causality, which would impede the translation of genomic research findings into the clinical diagnostic setting and hinder biological understanding of disease. Here we discuss the key challenges of assessing sequence variants in human disease, integrating both gene-level and variant-level support for causality. We propose guidelines for summarizing confidence in variant pathogenicity and highlight several areas that require further resource development

Jacobi-Davidson Methods and Preconditioning with Applications in Pole-zero Analysis

this paper, Sect. 2 introduces the pole-zero problem. Section 3 gives an overview of conventional methods used in pole-zero analysis, and describes the Jacobi-Davidson style methods as an alternative. In Sect. 4, the methods will be compared by numerical results, concluding with some future research topic

Families of Poles in the Netherlands (FPN) survey. Wave 1.

The release of formal restrictions on the free movement of Central and Eastern Europeans that started with the end of the Cold War and the eastward enlargement of the European Union in the 2000s have led to new migration flows in Europe. In the Netherlands, in absolute terms, Poles are the largest group amongst emigrants from the central and eastern European countries which accessed the European Union in 2004. The Families of Poles in the Netherlands (FPN) survey aims to develop a database which allows examining different aspects of Polish migrant family life, including family formation, generational interdependencies, espoused family obligations and life outcomes. The sampling frame of the FPN study was population registers (Basisregistratie Personen, BRP). Names and addresses of sample members were drawn by Statistics Netherlands based on the following criteria: the potential respondent was born in Poland, registered in the Netherlands for the first time in 2004 or later, and was between 18 and 49 years old at the time of the most recent registration. In total 1131 Polish migrants participated in the survey. The fieldwork started in October 2014 and lasted until the end of April 2015. A blueprint for the survey is the questionnaire of the Generations and Gender Surveys (GGS). The FPN data can be thus matched with the Polish and Dutch GGS, and Onderzoek Gezinsvorming data (OG; a longitudinal data on fertility and family formation executed in the Netherlands) to reveal the impact of contextual and policy influences on, among others, family relationships. To study the determinants of family solidarity and migration choices, following changes in respondents’ situations over time is necessary. Therefore, the FPN has a panel character – the second wave of the survey will be repeated in 2017. The FPN survey was carried out by the Erasmus University Rotterdam and is a part of Pearl Dykstra’s ERC Advanced Investigator project “Families in Context”. Financial support from the European Research Council, Advanced Investigator Grant “Families in Context” (grant agreement no. 324211) is gratefully acknowledged. The data from the FPN are accessible via the DANS website to researchers affiliated with academic and (semi-)government organizations. No one has any exclusive right or priority to use the FPN to work on any research question