【摘要】 本文从二维声软高频散射问题的边界积分方程出发,利用密度函数在凸区域外散射的关于波数k→+∞的渐近分析,将其由高振荡性转化为低振荡性,进而得到一个第二类Fredholm积分方程的解.通过选取积分区间[0,2π]的配置点,按照多项式(明区域)与几何(暗区域)增加(或减少),得到其收敛性为O(k-1/(24))(k>>1).此外,数值例子表明本文的数值方法非常有效.更多还原

【Abstract】 Based on the boundary integral equation reduced from the sound-soft high frequency scattering problem in two dimensions,we firstly convert the density to slow oscillatory from high oscillatory by using the asymptotic behaviour as k→ +∞ of density in a strictly convex bounded region.Furthermore,the equivalence of second Fredholm integral equation is obtained.Using the composite mesh with a polynomial grading on the illuminated zone and a geometric grading on the shadow zone,we obtain that the convergence is O(k^1/24)（k>> 1）.Moreover,examples are given for demonstrating that our method has good accuracy.更多还原