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Сибирский государственный университет
науки и технологий имени академика М.Ф. Решетнева

Сибирский аэрокосмический журнал
ISSN 2712-8970 (Print) ISSN 2782-5760 (on-line)

Сведения об образовательной организации

UDK 519.632 Vestnik SibGAU. 2014, No. 3(55), P. 73–77
HERMITE BICUBIC COLLOCATION METHOD IN DOMAIN WITH CURVILINEAR BOUNDARY
V. A. Kireev
Siberian Federal University 79, Svobodnyi prosp., Krasnoyarsk, 660041, Russian Federation Е-mail: kireevvit@gmail.com
In this paper the collocation method with Hermite bicubic basis functions is considered, applied to the first bound-ary value problem for an elliptic equation in a domain with a curved boundary. The collocation method has some ad-vantages compared with Galerkin finite element method: no need to compute the integrals for the determination of the coefficients of the stiffness matrix. Hermite bicubic functions belongs to the class C1. The consistent with the boundary mesh is constructed for solving the problem. The grid is consistent with the border so that two nodes in irregular cells were lying on a curvilinear boundary. This approach allows to reduce the total number of basis functions in the do-main. As an internal collocation nodes the points of the set of Gauss are taken. The collocation points are distributed evenly on a curvilinear boundary. Under such arrangement, the total number of collocation points equal the total num-ber of basis functions with the given boundary conditions. The problem is reduced to solution of a linear system Au=f where A is a square matrix. The results of numerical experiments of solving Poisson equation with different right sides show that the algorithm of solution has the convergence of high order.
collocation method, Hermite bicubic basis, second order elliptic equation, curved boundary.
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Kireev Vitaliy Aleksandrovich – postgraduate student, Institute of Mathematics and fundamental informatics, Siberian Federal University. E-mail: kireevvit@gmail.com.