»ã±¨±êÌâ (Title)£ºEfficient spectral-Galerkin methods for PDEs in three-dimensional complex geometries£¨ÓÐЧµÄÆ×Galerkin²½ÖèÇó½âÈýά¸´ÔÓÇøÓòƫ΢·Ö·½³Ì£©

»ã±¨ÈË (Speaker)£ºÍõÖÐÇì ½ÌÊÚ£¨ÉϺ£Àí¹¤´óѧ£©

»ã±¨¹¦·ò (Time)£º2023Äê11ÔÂ17ÈÕ(ÖÜÎå) 13:00-15:30

»ã±¨µØÖ· (Place)£ºÌÚѶ»áÒ飺968-592-891

Ô¼ÇëÈË(Inviter)£ºÎ⻪

Ö÷°ì²¿ÃÅ£ºÀíѧԺÊýѧϵ

»ã±¨ÌáÒª£ºIn this paper, we introduce a new spherical coordinate transformation, which transforms three-dimensional curved geometries into a unit sphere. This transformation plays an important role in spectral approximations of differential equations in three-dimensional curved geometries. Some basic properties of the spherical coordinate transformation are given. As examples, we consider an elliptic equation in three-dimensional curved geometries, prove the existence and uniqueness of the weak solution, construct the Fourier-Legendre spectral-Galerkin scheme and analyze the optimal convergence of numerical solutions under $H^1$-norm. We also apply the suggested approach to the Gross¨CPitaevskii equation in three-dimensional curved geometries and present some numerical results. The proposed algorithm is very effective and easy to implement for problems in three-dimensional curved geometries. Abundant numerical results show that our spectral-Galerkin method possesses high order accuracy.