應用分形有限元方法於外域聲場計算

Abstract

應用二級分形有限元方法計算了外域聲場。用一人工邊界把外域聲場分為兩部分，人工邊界以內使用常規有限元方法，人工邊界以外的無限大區域使用分形有限元方法。使用分形有限元方法的優點是：一方面形成幾何自相似網格使得相鄰層之間的單元剛度矩陣和質量矩陣具有非常簡單的關係；另一方面引用自動滿足無限遠輻射條件的全域插值函數把節點自由度變換為一組廣義坐標，因而計算量可以大大減少。數值算例表明：該方法對於計算無限大外域聲場是有效的。

The fractal finite element method is extended to solve exterior acoustic problems. An artificial boundary is introduced to divide the exterior domain into two parts. The conventional finite element method is adopted within the artificial boundary, and the fractal finite element method is employed in the outer region beyond the artificial boundary. Because of the facts that the relationships of element matrices between the adjacent fractal layers are very simple and the node degrees of freedom are transformed into a set of general coordinates by using the global interpolation functions, which satisfy automatically Sommerfeld's radiation conditions, the computer time can be reduced greatly by the fractal finite element method. The numerical results show that this method is effective in solving exterior acoustic problems.