Condition Number of Acoustic Infinite Element

Abstract

Various shape function and weight function of infinite element are researched and summarized into eight methods, and then various infinite element methods can be summarized as general equation, the condition number of which can reflect merits of infinite method. Condition number of various methods versus frequency and the node number are calculated in this paper. Finally, most optimal infinite element method is summed up. The infinite element method [1-12] is among the most successful techniques used to solve boundary-value problems on unbounded domains and whose solutions satisfy some condition at infinity. Two ideas make the infinite element method attractive: the idea of partition and the idea of approximation. The partition idea covers unbounded domains by attaching infinite strips to finite element partitions of bounded domains. More mature versions of infinite element method involved the approximation idea. These ideas make it possible that the finite element/infinite element method yields significantly greater computational efficiency than other methods such as the boundary element method. There have been a large number of infinite element methods, in which some methods have obvious advantages and some methods have fewer advantages. However, there is less research literature about merits of various infinite element methods appear at home and abroad. Thus, condition number of matrix equation is applied to verify merits of various infinite methods in this paper.