Geodesic
Multiple solution of systems of linear algebraic equations by an iterative method with the adaptive recalculation of the preconditioner
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 8, pp. 1395-1400 
R. R. Akhunov; T. R. Gazizov; S. P. Kuksenko. Multiple solution of systems of linear algebraic equations by an iterative method with the adaptive recalculation of the preconditioner. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 8, pp. 1395-1400. http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_8_a2/
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     title = {Multiple solution of systems of linear algebraic equations by an iterative method with the adaptive recalculation of the preconditioner},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_8_a2/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The mean time needed to solve a series of systems of linear algebraic equations (SLAEs) as a function of the number of SLAEs is investigated. It is proved that this function has an extremum point. An algorithm for adaptively determining the time when the preconditioner matrix should be recalculated when a series of SLAEs is solved is developed. A numerical experiment with multiply solving a series of SLAEs using the proposed algorithm for computing 100 capacitance matrices with two different structures — microstrip when its thickness varies and a modal filter as the gap between the conductors varies — is carried out. The speedups turned out to be close to the optimal ones.

[1] Calgaro C., Chehab J. P., Saad Y., “Incremental incomplete LU factorizations with applications to time-dependent PDEs”, Numer. Lin. Algebra with Appl., 17:5 (2010), 811–837 | DOI | MR | Zbl

[2] Akhunov P. P., Kuksenko S. P., Gazizov T. R., “Uskorenie mnogokratnogo resheniya SLAU iteratsionnym metodom pri vychislenii emkosti mikropoloskovoi linii v shirokom diapazone izmeneniya ee razmerov”, Chisl. metody i voprosy organizatsii vychislenii. XXVII, Zap. nauchn. seminarov S.-Peterburgskogo otdeleniya matem. in-ta im. V. A. Steklova RAN, 428, 2014, 32–41

[3] Akhunov P. P., Kuksenko S. P., Gazizov T. R., “Mnogokratnoe reshenie SLAU iteratsionnym metodom s pereformirovaniem matritsy predobuslovlivaniya”, Chisl. metody i voprosy organizatsii vychislenii. XXVII, Zap. nauchn. seminarov S.-Peterburgskogo otdeleniya matem. in-ta im. V. A. Steklova RAN, 428, 2014, 42–48

[4] Van der Vorst H., “Bi-CGSTAB: a fast and smoothly converging variant of Bi-CG for solution of nonsymmetric linear systems”, SIAM J. Sci. Statistical Comput., 13 (1992), 631–644 | DOI | MR | Zbl

[5] Kuksenko S. P., Zabolotskii A. M., Melkozerov A. O., Gazizov T. R., “Novye vozmozhnosti sistemy modelirovaniya elektromagnitnoi sovmestimosti TALGAT”, Dokl. Tomsk. gos. un-ta sistem upr. i radioelektroniki, 2 (2015), 45–50 | Zbl

[6] Gazizov T. R., “Analytic expressions for Mom calculation of capacitance matrix of two dimensional system of conductors and dielectrics having arbitrary oriented boundaries”, Proc. of the 2001 IEEE EMC Symposium (Montreal, Canada, August 13–17, 2001), v. 1, 151–155

[7] Zabolotsky A. M., Gazizov T. R., Melkozerov A. O., Orlov P. E., Dolganov E. S., “Improved design of modal filter for electronics protection”, Proc. of 31-th Int. conf. on lightning protection (Vienna, Austria, September 2–7, 2012)