## An efficient $$\mathcal O(N)$$ algorithm for computing $$\mathcal O(N^2)$$ acoustic wave interactions in large $$N$$-obstacle three dimensional configurations.(English)Zbl 1311.65156

Summary: We develop and implement a fast and memory efficient scheme for simulating the wave interactions between large numbers of particles. This is crucial for iteratively computing a time harmonic acoustic field exterior to a configuration of the particles. The main focus of this article is on efficient computation of the wave interactions between the particles in any iterative multiple scattering approach. We develop our algorithm in four stages and demonstrate the efficiency of our interaction evaluation algorithm at each stage for configurations with several thousand convex and non-convex particles. Using this efficient approach, we simulate the full large particle wave propagation models using a flexible generalized minimal residual (GMRES) based inner-outer preconditioned multiple scattering iterative technique on a single compute node.

### MSC:

 65N38 Boundary element methods for boundary value problems involving PDEs 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation 65F08 Preconditioners for iterative methods 76M15 Boundary element methods applied to problems in fluid mechanics 76Q05 Hydro- and aero-acoustics

BETL; BEM++
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### References:

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