Meshfree isoparametric finite point interpolation method (IFPIM) with weak and strong forms for evaporative laser drilling

An isoparametric finite point interpolation method (IFPIM) with weak and strong forms has been developed to analyze evaporative laser drilling. The method is based on isoparametric finite point representation of the unknowns in the influence domain. The local influence domains are mapped onto a master domain where the shape functions and their derivatives are known. The solution in the master domain is approximated by a linear combination of shape functions. The present method employs a simple strong form in the domain and a weak form on the boundary. Three different types of boundary conditions considered are of essential, convection, and laser irradiation type. The problem is geometrically nonlinear because the domain is not known a priori due to material removal in drilling. An iterative scheme is used to solve the nonlinear problem. The material removal is handled by redistributing points in the domain. This renders the point distribution non-uniform as in random distribution. The numerical results show excellent agreement with those by FEM and BEM in terms of groove shape, temperature and heat flux distributions, and amount of material removal. The results are superior to those from the isoparametric finite point interpolation methods with only strong forms.