Construction of Multivariate Interpolation Hermite Polynomials for Finite Element Method

Galmandakh Chuluunbaatar; Alexander A. Gusev; Ochbadrakh Chuluunbaatar; Vladimir P. Gerdt; Sergue I. Vinitsky; Vladimir L. Derbov; Andrzej Góźdź; Pavel M. Krassovitskiy; Luong Le Hai

doi:10.1051/epjconf/202022602007

All issues

Volume 226 (2020)

EPJ Web Conf., 226 (2020) 02007

Abstract

Open Access

Issue		EPJ Web Conf. Volume 226, 2020 Mathematical Modeling and Computational Physics 2019 (MMCP 2019)


Article Number		02007
Number of page(s)		4
Section		Mathematical Modeling, Numerical Methods, and Simulation
DOI		https://doi.org/10.1051/epjconf/202022602007
Published online		20 January 2020

EPJ Web of Conferences 226, 02007 (2020)
https://doi.org/10.1051/epjconf/202022602007

Construction of Multivariate Interpolation Hermite Polynomials for Finite Element Method

Galmandakh Chuluunbaatar¹^,2, Alexander A. Gusev¹^★, Ochbadrakh Chuluunbaatar¹^,3^★★, Vladimir P. Gerdt¹^,2, Sergue I. Vinitsky¹^,2^★★★, Vladimir L. Derbov⁴, Andrzej Góźdź⁵, Pavel M. Krassovitskiy¹^,6 and Luong Le Hai⁷

¹ Joint Institute for Nuclear Research, Dubna, Russia
² Peoples’ Friendship University of Russia (RUDN University), Moscow, Russia
³ Institute of Mathematics and Digital Technologies, Mongolian Academy of Sciences, Ulaanbaatar, Mongolia
⁴ Saratov State University, Saratov, Russia
⁵ Institute of Physics, University of M. Curie-Skłodowska, Lublin, Poland
⁶ Institute of Nuclear Physics, Almaty, Kazakhstan
⁷ Ho Chi Minh city University of Education, Ho Chi Minh city, Vietnam

^★ e-mail: gooseff@jinr.ru
^★★ e-mail: chuka@jinr.ru
^★★★ e-mail: vinitsky@theor.jinr.ru

Published online: 20 January 2020

Abstract

A new algorithm for constructing multivariate interpolation Hermite polynomials in analytical form in a multidimensional hypercube is presented. These polynomials are determined from a specially constructed set of values of the polynomials themselves and their partial derivatives with continuous derivatives up to a given order on the boundaries of the finite elements. The effciency of the finite element schemes, algor thms and programs is demonstrated by solving the Helmholtz problem for a cube.

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