»ã±¨±êÌ⣺һ¸öÇó½âÒþʽ½çÃæÍÖÔ²ÐÍƫ΢·Ö·½³Ì»ùÓÚ½¨¸Äº¯ÊýµÄÎÞºËÌìǵ»ý·Ö²½Ö裨A correction function-based kernel-free boundary integral method for elliptic PDEs with implicitly defined interfaces£©

»ã±¨ÈË (Speaker)£ºÓ¦ÎÄ¿¡ ½ÌÊÚ£¨ÉϺ£½»Í¨´óѧ£©

»ã±¨¹¦·ò (Time)£º2023Äê11ÔÂ7ÈÕ(Öܶþ) 10£º00

»ã±¨µØÖ· (Place)£ºÌÚѶ»áÒ飺440-650-222

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In this talk, I will present a new version of the kernel-free boundary integral£¨KFBI£©method for elliptic PDEs with implicitly defined irregular boundaries and interfaces. The KFBI method evaluates boundary or volume integrals indirectly by solving equivalent but much simpler interface problems. A correction function is introduced for both evaluation of right hand side correction terms and interpolation of a non-smooth potential function. It allows the new method to avoid computation of high-order partial derivatives on interfaces or boundaries, greatly reducing the algorithm complexity and improving the efficiency, especially for fourth-order methods in three space dimensions. Challenging numerical examples including high-contrast coefficients, arbitrarily close interfaces and heterogeneous interface problems, will be reported to demonstrate the efficiency and accuracy of the method.