Symbolic-Numerical Algorithms for Solving Elliptic Boundary-Value Problems Using Multivariate Simplex Lagrange Elements

We propose new symbolic-numerical algorithms implemented in Maple-Fortran environment for solving the self-adjoint elliptic boundary-value problem in a d-dimensional polyhedral finite domain, using the high-accuracy finite element method with multivariate Lagrange elements in the simplexes. The high-order fully symmetric PI-type Gaussian quadratures with positive weights and no points outside the simplex are calculated by means of the new symbolic-numerical algorithms implemented in Maple. Quadrature rules up to order 8 on the simplexes with dimension d=3-6 are presented. We demonstrate the efficiency of algorithms and programs by benchmark calculations of a low part of spectra of exactly solvable Helmholtz problems for a cube and a hypercube. © 2018, Springer Nature Switzerland AG.

Authors
Gusev A.A.1 , Gerdt V.P. 1, 2 , Chuluunbaatar O. 1, 3 , Chuluunbaatar G. 1, 2 , Vinitsky S.I. 1, 2 , Derbov V.L.4 , Góźdź A.5 , Krassovitskiy P.M.1, 6
Journal
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Language
English
Pages
197-213
Status
Published
DOI
10.1007/978-3-319-99639-4_14
Volume
11077 LNCS
Year
2018
Organizations
  • 1 Joint Institute for Nuclear Research, Dubna, Russian Federation
  • 2 RUDN University, 6 Miklukho-Maklaya St., Moscow, 117198, Russian Federation
  • 3 Institute of Mathematics, National University of Mongolia, Ulaanbaatar, Mongolia
  • 4 N.G. Chernyshevsky Saratov National Research State University, Saratov, Russian Federation
  • 5 Institute of Physics, University of M. Curie–Skłodowska, Lublin, Poland
  • 6 Institute of Nuclear Physics, Almaty, Kazakhstan
Keywords
Elliptic boundary-value problem; Finite element method; Helmholtz equation for cube and hypercube; High-order fully symmetric Gaussian quadratures; Multivariate simplex lagrange elements
Date of creation
19.10.2018
Date of change
19.10.2018
Short link
https://repository.rudn.ru/en/records/article/record/7370/
Share

Other records