Open AccessThe implementation of the boundary element method to the Helmholtz equation of acoustics
Author(s) -
Sergey Sivak,
M.E. Royak,
Ilya M. Stupakov,
Aleksandr S. Aleksashin,
Ekaterina Voznjuk
Publication year - 2021
Publication title -
informacionno-upravlâûŝie sistemy
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.202
H-Index - 6
eISSN - 2541-8610
pISSN - 1684-8853
DOI - 10.31799/1684-8853-2021-2-13-19
Subject(s) - helmholtz equation , method of fundamental solutions , boundary knot method , boundary element method , singular boundary method , mathematics , finite element method , mathematical analysis , boundary (topology) , discretization , boundary value problem , helmholtz free energy , computer science , physics , quantum mechanics , thermodynamics
To solve the Helmholtz equation is important for the branches of engineering that require the simulation of wave phenomenon. Numerical methods allow effectiveness’ enhancing of the related computations. Methods: To find a numerical solution of the Helmholtz equation one may apply the boundary element method. Only the surface mesh constructed for the boundary of the three-dimensional domain of interest must be supplied to make the computations possible. This method’s trait makes it possible toconduct numerical experiments in the regions which are external in relation to some Euclidian three-dimensional subdomain bounded in the three-dimensional space. The later also provides the opportunity of not using additional geometric techniques to consider the infinitely distant boundary. However, it’s only possible to use the boundary element methods either for the homogeneous domains or for the domains composed out of adjacent homogeneous subdomains. Results: The implementation of the boundary elementmethod was committed in the program complex named Quasar. The discrepancy between the analytic solution approximation and the numerical results computed through the boundary element method for internal and external boundary value problems was analyzed. The results computed via the finite element method for the model boundary value problems are also provided for the purpose of the comparative analysis done between these two approaches. Practical relevance: The method gives an opportunityto solve the Helmholtz equation in an unbounded region which is a significant advantage over the numerical methods requiring the volume discretization of computational domains in general and over the finite element method in particular. Discussion: It is planned to make a coupling of the two methods for the purpose of providing the opportunity to conduct the computations in the complex regions with unbounded homogeneous subdomain and subdomains with substantial inhomogeneity inside.