  Scalar wave scattering by many small particles of arbitrary shapes with
impedance boundary condition is studied. The problem is solved asymptotically
and numerically under the assumptions a << d << lambda, where k = 2pi/lambda is
the wave number, lambda is the wave length, a is the characteristic size of the
particles, and d is the smallest distance between neighboring particles. A fast
algorithm for solving this wave scattering problem by billions of particles is
presented. The algorithm comprises the derivation of the (ORI) linear system
and makes use of Conjugate Orthogonal Conjugate Gradient method and Fast
Fourier Transform. Numerical solutions of the scalar wave scattering problem
with 1, 4, 7, and 10 billions of small impedance particles are achieved for the
first time. In these numerical examples, the problem of creating a material
with negative refraction coefficient is also described and a recipe for
creating materials with a desired refraction coefficient is tested.
