Partition of unity

Physics

Finite element method

Mathematics

Domain (mathematical analysis)

Boundary (topology)

Structural engineering

Motion (physics)

Algorithm

Engineering

Radiation

Mathematical analysis

Interpolation (computer graphics)

Boundary value problem

Meshfree methods

Acoustic radiation

Computation

Quantum mechanics

Boundary element method

Classical mechanics

Polynomial

International Journal of Computational Methods

To improve the accuracy of the standard finite element (FE) solutions for acoustic radiation computation, this work presents the coupling of a radial point interpolation method (RPIM) with the standard FEM based on triangular (T3) mesh to give a coupled “FE-Meshfree” Trig3-RPIM element for two-dimensional acoustic radiation problems. In this coupled Trig3-RPIM element, the local approximation (LA) is represented by the polynomial-radial basis functions and the partition of unity (PU) concept is satisfied using the standard FEM shape functions. Incorporating the present coupled Trig3-RPIM element with the appropriate non-reflecting boundary condition, the two-dimensional acoustic radiation problems in exterior unbounded domain can be successfully solved. The numerical results demonstrate that the present coupled Trig3-RPIM have significant superiorities over the standard FEM and can be regarded as a competitive numerical techniques for exterior acoustic computation.

A Coupled FE-Meshfree Triangular Element for Acoustic Radiation Problems