A weak-form interpolation meshfree method for computing underwater acoustic radiation

Abstract An improved interpolating element-free Galerkin (IIEFG) method coupled with Modified Dirichlet-to-Neumann (MDtN) boundary condition is presented in this paper for use in computing underwater acoustic radiation. In the scheme of the IIEFG-MDtN approach, the improved interpolating moving least-square technology is employed to construct the shape function with the aim of improving the interpolation accuracy, and the MDtN boundary condition is used to meet the Sommerfeld radiation condition required at infinity and remove the difficulties arisen as the truncated DtN boundary condition is employed in computation. It is the key feature of this weak-form meshfree method that no connectivity of nodes or mesh is required for acoustic field variable interpolations while the prediction accuracy is significantly improved. The factors including the size of the influence domain, shape parameters and the number of terms used in the MDtN map, which affect the performance of this proposed method, are studied numerically. Typical numerical examples are presented to test the properties of the IIEFG-MDtN approach. The results indicate the devised method is outstanding to cope with underwater acoustic radiation prediction and can achieve higher accuracy and faster convergency compared to the finite element method.