The fictitious domain method and homotopy as a new alternative for multidimensional partial differential equations in domains of arbitrary shape

Gavrilyuk, IP
1Makarov, VL
1Institute of Mathematics of the NAS of Ukraine, Kyiv
Dopov. Nac. akad. nauk Ukr. 2019, 11:8-16
Section: Mathematics
Language: Ukrainian

The ideas of the method of fictitious domains and of homotopy are united with the aim to reduce the solution of multidimensional partial differential equations in an arbitrary domain to an exponentially convergent sequence of problems in a parallelepiped (rectangle in the 2D case). This makes it possible to reduce the amount of computational work due to the absence of the need for the triangulation of a domain.

Keywords: boundary-value problem for a partial differential equation, domain of arbitrary shape, exponential convergence rate, fictitious domain method, homotopy, parallelepiped

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