Numerical solution of many-body wave scattering problem and creating materials with a desired refraction coefficient
For researchers in wave propagation and metamaterials, it provides a numerical method to design materials with prescribed refraction coefficients using many small scatterers.
This paper solves the scalar wave scattering problem for many small particles with impedance boundary conditions and demonstrates numerically that materials with a desired refraction coefficient can be created, handling up to 10^6 particles.
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 $10^6$.