TY - JOUR
AU - V.L. Makarov
AU - I. P. Gavrilyuk
PY - 2020/02/15
Y2 - 2020/07/12
TI - The fictitious domain method and homotopy as a new alternative for multidimensional partial differential equations in domains of any shape
JF - Ukrainsâ€™kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 72
IS - 2
SE - Research articles
DO -
UR - http://umj.imath.kiev.ua/index.php/umj/article/view/1101
AB - UDC 517.9; 519.63The ideas of the fictitious domain method and homotopy are combined with an aim to reduce the solution of boundary-value problems for multidimensional partial differential equations (PDE) in domains of any shape to an exponentially convergent sequence of PDEs in a parallelepiped (in a rectangle, in the 2D case). This allows us to reduce the computational costs due to the elimination of the necessity of triangulation of the domain by a grid with $N$ inner nodes (e.g., the Delaunay algorithm in the 2D case requires ${\mathcal {O}}(N \log{N})$ operations).
ER -