»ã±¨±êÌâ (Title)£ºOverlapping Schwarz Methods in H(curl;¦¸)£¨H(curl;¦¸)ÖеijÁµþSchwarz²½Ö裩

»ã±¨ÈË (Speaker)£º ÁºÆô¸Õ ²©Ê¿ºó×êÑÐÔ±£¨Í¬¼Ã´óѧ£©

»ã±¨¹¦·ò (Time)£º2024Äê11ÔÂ15ÈÕ(ÖÜÎå) 10:00

»ã±¨µØÖ· (Place)£ºÐ£±¾²¿GJ304

Ô¼ÇëÈË(Inviter)£ºÀîÐÂÏé

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»ã±¨ÌáÒª£ºOverlapping Schwarz method is one of the most important methods for computing the large-scale discrete problems arising from partial differential equations. The previous proved bound is C(1+H^2/¦Ä^2) for the condition number of the overlapping domain decomposition methods in H(curl; ¦¸), where H and ¦Ä are the sizes of subdomains and overlaps respectively. But all numerical results indicate that the best bound is C(1+H/¦Ä). In this talk, we shall solve this long-standing open problem by proving that is indeed the best bound. Based on the overlapping Schwarz methods, we shall propose a two¨Clevel preconditioned Helmholtz subspace iterative (PHSI) method for solving algebraic eigenvalue problems resulting from edge element approximation of Maxwell eigenvalue problems. The two-level PHSI method may compute simple eigenpairs, multiple eigenpairs and clustered eigenpairs. This is a joint work with Prof. Xuejun Xu and Prof. Shangyou Zhang.