一类混合边界条件的裂缝散射问题及数值模拟

A Scattering Problem of a Crack with Mixed Boundary Conditions and Its Numerical Simulations

考虑时谐电磁波对非常薄的无限长圆柱理想导体的散射问题,该散射体在水平截面上抽象为平面上的曲线段(即裂缝).假设曲线段是光滑的,且其2侧赋予不同的边界条件(混合边界条件),首先证明了散射问题解的唯一性;然后通过位势理论与积分方程方法,将问题转化为等价的奇异积分方程组并证明了解的存在性;最后,通过求解奇异积分方程组给出了混合边界裂缝散射问题的数值模拟.

Consider a scattering problem of time-harmonic electromagnetic plane waves from a thin infinitely long cylindrical obstacle. The thin obstacle is a curve segment referred to as crack. Assuming that the crack is smooth,and both sides of the crack have different boundary conditions（ mixed boundary conditions）,the uniqueness of the solution is firstly given for the scattering problem. Then the scattering problem is transformed into an equivalent system of hypersingular integral equations by the potential theory and the integral equation method,and the existence of the solution is also proved. Finally,numerical simulations of the scattering problem for the mixed boundary crack are presented by solving the system of hypersingular integral equations.