Geodesic
Acceleration of multiple iterative solution of linear algebraic systems in computing the capacitance of a microstrip line in a wide range of its sizes
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXVII, Tome 428 (2014), pp. 32-41 
R. R. Akhunov; S. P. Kuksenko; T. R. Gazizov. Acceleration of multiple iterative solution of linear algebraic systems in computing the capacitance of a microstrip line in a wide range of its sizes. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXVII, Tome 428 (2014), pp. 32-41. http://geodesic.mathdoc.fr/item/ZNSL_2014_428_a2/
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     title = {Acceleration of multiple iterative solution of linear algebraic systems in computing the capacitance of a~microstrip line in a~wide range of its sizes},
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Multiple solution of systems of linear algebraic equations by the BiCGStab method is considered. For the problem of computing the capacitance matrix of a microstrip line in a range of its sizes, two acceleration methods are suggested. The first one consists in using the solution of a previous system as the initial guess for the current system. The second one consists in applying to all systems a preconditioner computed for the first system. The efficiency of these acceleration methods in solving a large series of linear systems with small changes in arbitrary matrix entries is demonstrated on numerical experiments.

[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 elektr. sist., 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. un-ta sistem upravleniya i radioelektroniki, 2011, no. 2(24), chast 1, 141–144

[3] 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 Symp. (Montreal, Canada, August 13–17, 2001), v. 1, 2001, 151–155

[4] 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

[5] V. K. Salov, T. R. Gazizov, O. A. Nikitina, “Convergence of multiple iterative solution of linear algebraic systems with a fully varying matrix using a single calculated initial preconditioner”, Innovative Information Technologies, Materials of the International Scientific-Practical Conference (April 21–25, 2014, Prague, Czech Republic), Part 2, 2014, 452–457

[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] 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

[8] S. P. Kuksenko, T. R. Gazizov, “Dense linear system solution by preconditioned iterative methods in computational electromagnetics”, 19th Int. Zurich Symp. Electromagn. Compatibility, 2008, 918–921

[9] R. R. Akhunov, S. P. Kuksenko, T. R. Gazizov, “Mnogokratnoe reshenie SLAU iteratsionnym metodom s pereformirovaniem matritsy predobuslovlivaniya”, Zap. nauchn. semin. POMI, 428, 2014, 42–48