Finite-Difference Operators for 2D problems

• Autorzy: Sobczyk T.

Identyfikatory

DOI

10.24425/bpasts.2020.135387

• Języki publikacji: EN

Abstrakty

EN

This paper presents the concept of using algorithms for reducing the dimensions of finite-difference equations of two-dimensional (2D) problems, for second-order partial differential equations. Solutions are predicted as two-variable functions over the rectangular domain, which are periodic with respect to each variable and which repeat outside the domain. Novel finite-difference operators, of both the first and second orders, are developed for such functions. These operators relate the value of derivatives at each point to the values of the function at all points distributed uniformly over the function domain. A specific feature of the novel operators follows from the arrangement of the function values as well as the values of derivatives, which are rectangular matrices instead of vectors. This significantly reduces the dimensions of the finite-difference operators to the numbers of points in each direction of the 2D area. The finite-difference equations are created exemplary elliptic equations. An original iterative algorithm is proposed for reducing the process of solving finite-difference equations to the multiplication of matrices.

Słowa kluczowe

EN

second-order partial differential equations; 2D finite-difference operators; finite-difference equation; iterative algorithms

PL

równania różniczkowe cząstkowe drugiego rzędu; operatory różnic skończonych 2D; algorytm iteracyjny; metoda różnic skończonych

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2020
• Tom: Vol. 68, nr 6
• Strony: 1535--1541
• Opis fizyczny: Bibliogr. 19 poz.

Twórcy

autor

Sobczyk T.

• Cracow University of Technology, Institute on Electromechanical Energy Conversion, ul. Warszawska 24, 31-155 Cracow, Poland

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).