Domain decomposition method for solution of acoustic-structure finite element method for distributed computation

Abstract

A new Domain Decomposition Method (DDM) is proposed, which breaks an Acoustic-Structure Finite Element Model (ASFEM) into multiple non-symmetric sections, computes the scattering by each one as an independent system, and combines all the solutions of the individual segments to get the entire scattering solution. In general, the approach to get a finite element solution for acoustic scattering from an underwater target uses the Helmholtz equation as the governing equation and non-reflecting absorbing or radiation boundary conditions to truncate the infinite exterior region. The solution is obtained in the frequency domain and is stationary by nature. Our purpose here is to devise a hybrid, stationary, ASFEM solution using the DDM to enable more efficient use of memory for very complex targets. Taking advantage of the stationary of the solution and using multi-grid meshes with a mapping function to update boundary conditions on the surface of separated sections, the final solution for all the decoupled sections is determined iteratively, taking sufficient steps to reach equilibrium in all sections. The method can make it possible to get a solution for an ASFEM whose geometry is not symmetric in any space direction and requires too many elements to run on a single processor due to the limited memory size. It can also be used to reduce the run time of an ASFEM solution using a distributed computational system.