Geodesic
Multiple solution of systems of linear algebraic equations by an iterative method with recomputed preconditioner
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXVII, Tome 428 (2014), pp. 42-48 
R. R. Akhunov; S. P. Kuksenko; T. R. Gazizov. Multiple solution of systems of linear algebraic equations by an iterative method with recomputed preconditioner. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXVII, Tome 428 (2014), pp. 42-48. http://geodesic.mathdoc.fr/item/ZNSL_2014_428_a3/
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     title = {Multiple solution of systems of linear algebraic equations by an iterative method with recomputed preconditioner},
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     year = {2014},
     volume = {428},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2014_428_a3/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

An algorithm for multiple solution of systems of linear algebraic equations by preconditioned BiCGStab method is proposed. When the number of iterations for solving a current system becomes too large, the precontioner is recomputed. Results of numerical experiments on computing the capacitance matrices of a microstrip line in a wide range of its sizes, demonstrating the possibility of a considerable reduction of the total solution time, are presented.

[1] S. P. Kuksenko, T. R. Gazizov, “Sovershenstvovanie algoritma vychisleniya metodom momentov ëmkostnykh matrits struktury provodnikov i dielektrikov v diapazone znachenii dielektricheskoi pronitsaemosti”, Elektromagn. volny i elektron. sistemy, 10 (2012), 13–21

[2] R. S. Surovtsev, S. P. Kuksenko, T. R. Gazizov, “Uskorenie mnogokratnogo resheniya SLAU s chastichno izmenyayuscheisya matritsei”, Dokl. Tomskogo gos. univ. sistem upravl. i radioelektr, 2011, no. 2(24), chast 1, 141–144

[3] R. R. Akhunov, S. P. Kuksenko, T. R. Gazizov, “Uskorenie mnogokratnogo resheniya SLAU iteratsionnym metodom pri vychislenii ëmkosti mikropoloskovoi linii v shirokom diapazone izmeneniya eë razmerov”, Zap. nauchn. semin. POMI, 428, 2014, 32–41

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

[5] R. R. Akhunov, S. P. Kuksenko, V. K. Salov, T. R. Gazizov, “Mnogokratnoe reshenie SLAU s chastichno izmenyayuscheisya matritsei iteratsionnym metodom”, Zap. nauchn. semin. POMI, 419, 2013, 16–25

[6] Gazizov T. R., Melkozerov A. O., Gazizov T. T., Kuksenko S. P., Zabolotskii A. M., Ashirbakiev R. I., Lezhnin Ev. V., Salov V. K., Lezhnin Eg. V., Orlov P. E., Kalimulin I. F., Surovtsev R. S., Komnatnov M. E., Gazizov R. R., Akhunov R. R., Svidetelstvo o gosudarstvennoi registratsii programmy dlya EVM No 2013619615, TALGAT 2012, Zayavka No 2013617773. Data postupleniya 29 avgusta 2013 g. Zaregistrirovano v Reestre programm dlya EVM 11 oktyabrya 2013 g.

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