A streamlined meshless method handling Helmholtz equation on 3D geometries

We apply a modified meshless discretization scheme to the Helmholtz equation on 3D geometries. The rational Exponential Basis Functions (EBFs) and Non-Uniform Rational B-Splines (NURBS) are efficiently utilized to approximate the solution and geometry, respectively. The scheme is based on interpolation of the solution via collocating the rational EBFs on a sample cloud of regular nodes. The resulting library rational shape functions are effectively used to enforce the compatibility and boundary conditions in the internal and boundary clouds conforming to the domain boundaries. The accuracy of the method is demonstrated through comparing the results to Finite Element Method (FEM).

Keywords:

3D Helmholtz equation , rational Exponential Basis Functions , meshless method.