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Zh. Vychisl. Mat. Mat. Fiz., 2015, Volume 55, Number 8, Pages 1320–1328 (Mi zvmmf10247)  

This article is cited in 14 scientific papers (total in 14 papers)

On an algorithm for solving parabolic and elliptic equations

N. D'Ascenzoa, V. I. Savelievb, B. N. Chetverushkinc

a Deutsche Elektronen Synchrotron (DESY), Hamburg, 22206, Germany
b Immanuel Kant Baltic Federal University, Kaliningrad, 236041, Russia
c Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya pl. 4, Moscow, 125047, Russia

Abstract: The present-day rapid growth of computer power, in particular, parallel computing systems of ultrahigh performance requires a new approach to the creation of models and solution algorithms for major problems. An algorithm for solving parabolic and elliptic equations is proposed. The capabilities of the method are demonstrated by solving astrophysical problems on high-performance computer systems with massive parallelism.

Key words: high-performance computations, numerical algorithms, parabolic and elliptic equations.

DOI: https://doi.org/10.7868/S0044466915080037

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English version:
Computational Mathematics and Mathematical Physics, 2015, 55:8, 1290–1297

Bibliographic databases:

UDC: 519.633
Received: 19.02.2015

Citation: N. D'Ascenzo, V. I. Saveliev, B. N. Chetverushkin, “On an algorithm for solving parabolic and elliptic equations”, Zh. Vychisl. Mat. Mat. Fiz., 55:8 (2015), 1320–1328; Comput. Math. Math. Phys., 55:8 (2015), 1290–1297

Citation in format AMSBIB
\by N.~D'Ascenzo, V.~I.~Saveliev, B.~N.~Chetverushkin
\paper On an algorithm for solving parabolic and elliptic equations
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2015
\vol 55
\issue 8
\pages 1320--1328
\jour Comput. Math. Math. Phys.
\yr 2015
\vol 55
\issue 8
\pages 1290--1297

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 52, no. 7, 2016, 817–823  crossref  mathscinet  zmath  isi  elib  scopus
    2. 95, no. 1, 2017, 68–71  crossref  mathscinet  zmath  isi
    3. B. N. Chetverushkin, N. G. Churbanova, A. A. Kuleshov, A. A. Lyupa, M. A. Trapeznikova, “Application of kinetic approach to porous medium flow simulation in environmental hydrology problems on high-performance computing systems”, Russ. J. Numer. Anal. Math. Model, 31:4 (2016), 187–196  crossref  mathscinet  zmath  isi  elib  scopus
    4. B. Chetverushkin, N. D'Ascenzo, A. Saveliev, V. Saveliev, “A kinetic model for magnetogasdynamics”, Math. Models Comput. Simul., 9:5 (2017), 544–553  mathnet  crossref  elib
    5. T. E. Moiseev, E. E. Myshetskaya, V. F. Tishkin, “O blizosti reshenii nevozmuschënnykh i giperbolizirovannykh uravnenii teploprovodnosti dlya razryvnykh nachalnykh dannykh”, Preprinty IPM im. M. V. Keldysha, 2017, 086, 15 pp.  mathnet  crossref
    6. B. N. Chetverushkin, N. D'Ascenzo, A. V. Saveliev, V. I. Saveliev, “Novel kinetically consistent algorithm for magneto gas dynamics”, Appl. Math. Lett., 72 (2017), 75–81  crossref  mathscinet  zmath  isi
    7. B. Chetverushkin, N. D'Ascenzo, A. Saveliev, V. Saveliev, “Novel kinetic consistent MHD algorithm for high performance computing”, Coupled Problems in Science and Engineering VII, Coupled Problems 2017, eds. M. Papadrakakis, E. Onate, B. Schrefler, Int. Center Numerical Methods Engineering, 2017, 924–938  isi
    8. B. N. Chetverushkin, M. V. Yakobovskii, “Vychislitelnye algoritmy i arkhitektura sistem vysokoi proizvoditelnosti”, Preprinty IPM im. M. V. Keldysha, 2018, 052, 12 pp.  mathnet  crossref  elib
    9. B. N. Chetverushkin, “Giperbolicheskaya kvazigazodinamicheskaya sistema”, Matem. modelirovanie, 30:2 (2018), 81–98  mathnet  elib
    10. B. N. Chetverushkin, N. D'Ascenzo, A. V. Saveliev, V. I. Saveliev, “Kinetic model and magnetogasdynamics equations”, Comput. Math. Math. Phys., 58:5 (2018), 691–699  mathnet  crossref  crossref  isi  elib
    11. B. N. Chetverushkin, A. V. Saveliev, V. I. Saveliev, “A quasi-gasdynamic model for the description of magnetogasdynamic phenomena”, Comput. Math. Math. Phys., 58:8 (2018), 1384–1394  mathnet  crossref  crossref  isi  elib
    12. B. N. Chetverushkin, “Problems and prospects of supercomputer technologies in the near future”, Her. Russ. Acad. Sci., 88:6 (2018), 448–453  crossref  isi  scopus
    13. Jedamzik K., Saveliev A., “Stringent Limit on Primordial Magnetic Fields From the Cosmic Microwave Background Radiation”, Phys. Rev. Lett., 123:2 (2019), 021301  crossref  isi
    14. B. N. Chetverushkin, A. E. Lutskii, V. P. Osipov, “Zakony sokhraneniya i kompaktnaya kvazigazodinamicheskaya sistema”, Matem. modelirovanie, 31:12 (2019), 21–32  mathnet  crossref  elib
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