多体波散射问题的数值求解及具有所需折射系数材料的制备
Numerical solution of many-body wave scattering problem and creating materials with a desired refraction coefficient
AI总结：
研究了多小粒子对标量波的散射及具有特定折射系数材料的制备，采用渐近与数值方法求解声波散射问题，在假设下给出了数值结果。
摘要：
研究了由多个小粒子引起的标量波散射及制备具有所需折射系数的材料。在假设$ka \ll 1, ζ_m = \frac{h(x_m)}{a^κ}, d = O(a^{\frac{2-κ}{3}}), M = O(\frac{1}{a^{2-κ}}), κ\in [0,1)$下，声波散射问题在渐近和数值条件下得到解决。数值结果展示了粒子数量为$10^4, 10^5$和$10^6$的情况。
英文摘要：
Scalar wave scattering by many small particles with impedance boundary condition and creating material with a desired refraction coefficient are studied. The acoustic wave scattering problem is solved asymptotically and numerically under the assumptions $ka \ll 1, ζ_m = \frac{h(x_m)}{a^κ}, d = O(a^{\frac{2-κ}{3}}), M = O(\frac{1}{a^{2-κ}}), κ\in [0,1)$, where $k = 2π/λ$ is the wave number, $λ$ is the wave length, $a$ is the radius of the particles, $d$ is the distance between neighboring particles, $M$ is the total number of the particles embedded in a bounded domain $Ω\subset \RRR$, $ζ_m$ is the boundary impedance of the m\textsuperscript{th} particle $D_m$, $h \in C(D)$, $D := \bigcup_{m=1}^M D_m$, is a given arbitrary function which satisfies Im$h \le 0$, $x_m \in Ω$ is the position of the m\textsuperscript{th} particle, and $1 \leq m \leq M$. Numerical results are presented for which the number of particles equals $10^4, 10^5$, and $10^6$.
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