Numerical solution of many-body wave scattering problem and creating materials with a desired refraction coefficient

Abstract

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 $ka\ll 1,{\zeta }_m=\frac{h(x_m)}{a^{\kappa }},d=O(a^{\frac{2-\kappa }{3}}),M=O(\frac{1}{a^{2-\kappa }}),\kappa \in [0,1)$, where $k=2\pi /\lambda$ is the wave number, $\lambda$ 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 $Ω\subset \RRR$, ${\zeta }_m$ 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$h\le 0$, $x_m\in \Omega$ is the position of the m\textsuperscript{th} particle, and $1\le m\le M$. Numerical results are presented for which the number of particles equals $10^4,10^5$, and $10^6$.

References in corpus (2)

• Many-body wave scattering by small bodies and applications
• Wave scattering by many small particles embedded in a medium

Cited by in corpus (2)

• A Fast Algorithm for Solving Scalar Wave Scattering Problem by Billions of Particles
• Simple Method for Evaluating Singular Integrals