标题： 一种电磁和声学散射的自旋积分方程 显示英文标题

标题： A spin integral equation for electromagnetic and acoustic scattering

摘要： 我们提出一种新的积分方程，用于解决对完美导体的麦克斯韦散射问题。 同样的算法也适用于声软和声硬的赫尔姆霍兹散射问题，事实上后两者可以在三维空间中并行求解。 我们的积分方程在内部虚假共振处不会失效，并且使用没有代数或微分约束的函数空间。 在边界上需要求逆的算子涉及一个与三维柯西奇异积分密切相关的主要奇异积分算子，并且在自然函数空间上是有界的，并且关于波数解析依赖。 我们的算子作用于取复数二乘二矩阵值的函数，利用场的自旋表示。 显示英文摘要

摘要： We present a new integral equation for solving the Maxwell scattering problem against a perfect conductor. The very same algorithm also applies to sound-soft as well as sound-hard Helmholtz scattering, and in fact the latter two can be solved in parallel in three dimensions. Our integral equation does not break down at interior spurious resonances, and uses spaces of functions without any algebraic or differential constraints. The operator to invert at the boundary involves a singular integral operator closely related to the three dimensional Cauchy singular integral, and is bounded on natural function spaces and depend analytically on the wave number. Our operators act on functions with pairs of complex two by two matrices as values, using a spin representation of the fields.