自伴不定问题的WOPSIP方法的两水平加性Schwarz预条件子(英文)  

A two-level additive Schwarz preconditioner with WOPSIP methods for non-self-adjoint and indefinite problems

作　　者：王春梅[1,2] 颜世建[1] 

机构地区：[1]南京师范大学数学科学学院,南京210023 [2]南京师范大学泰州学院,泰州225300

出　　处：《黑龙江大学自然科学学报》2014年第3期296-301,共6页Journal of Natural Science of Heilongjiang University

基　　金：Supported by the Project of Graduate Education Innovation of Jiangsu Province(CXZZ13-0387)

摘　　要：弱过度惩罚对称内罚方法(WOPSIP),是一种间断有限元方法,其主要特点是它满足能量范数和L2范数的正确的误差估计,且它不要求调整罚参数。此外,由于双线性形式比较简单,使得WOPSIP方法的编程比较简单,且程序易于实现并行。提出了非自伴不定问题的WOPSIP方法的两水平加性Schwarz预条件子。条件数有界,界为(1+maxiHiδi)2,其中Hi和δi分别为子区域Ωi的直径和相邻子区域之间的重叠度。The weakly over-penalized symmetric interior penalty （WOPSIP） method has the unique feature that （i） it satisfies the correct error estimates in both the energy norm and the L2 norm, and （ii） it does not require the tuning of a penalty parameter. Furthermore, the simplicity of the bilinear form makes the programming of the WOPSIP method very easy, and the matrix representing the bilinear form also has an interesting structure with built-in parallelism. A two-level additive Schwarz preeonditioner with WOPSIP methods for non-self-adjoint and indefinite problems is proposed and analyzed. The condi-tion number is bounded by（1＋maxiHi/δi）^2, where Hi and δi are respectively the diameter of subdomain Ωi and the amount of overlap between neighboring subdomains.

关 键 词：非自伴不定 两水平 加性Schwarz 预条件子 弱过度惩罚 内罚 

分 类 号：O241.6[理学—计算数学]