CAJ | 학술논문

针对多区域中声波的传播问题,其中每个散射区域的介质是相同的,将散射区域内的声波用一种单双层混合位势的形式来表示,再应用 Green 定理表示出外部介质区域中的声波,并形成相应的边界积分方程.如果区域个数为M 时,传统的边界元方法最终将形成2M 个边界积分方程并对应2M 个未知函数,而本文的边界元方法最终只形成 M 个边界积分方程以及对应 M 个未知函数,从而使得求解的方程和未知数的个数都减少了一倍.最后,通过对数值算例的求解,验证了该方法的可行性及精确性.
침대다구역중성파적전파문제,기중매개산사구역적개질시상동적,장산사구역내적성파용일충단쌍층혼합위세적형식래표시,재응용 Green 정리표시출외부개질구역중적성파,병형성상응적변계적분방정.여과구역개수위M 시,전통적변계원방법최종장형성2M 개변계적분방정병대응2M 개미지함수,이본문적변계원방법최종지형성 M 개변계적분방정이급대응 M 개미지함수,종이사득구해적방정화미지수적개수도감소료일배.최후,통과대수치산례적구해,험증료해방법적가행성급정학성.
In this paper,we discuss the acoustic transmission problem in multiple domains. We denote the acoustic in the scattering domains in the form of combined double and single-layer potentials and each domain’s mediums is the same, and then get the acoustic in the outer domain and boundary integral equation by Green theory. The traditional boundary element method will eventually form 2M boundary integral equations with 2M unknowns if there are M domains. However, we obtain a set of M equations with M unknowns and half of the equations can be reduced by applying the method in this paper. Finally, the numerical examples were given to test the accuracy and feasibility of the method.