Radial basis functions with compactly support and multizone decomposition: Applications to environmental modelling

This paper presents the application of the radial basis functions (RBF) for solving a set of non-linear hydrodynamics model for marine environments. Two different techniques, namely compact support and multizone decomposition, are used to improve the conditioning of the resultant coefficient matrix which is a full matrix due to the use of the global radial basis functions. The idea of the compactly supported radial basis function (CSRBF) is to reduce the full matrix to a banded sparse matrix. The multizone approach is similar to the commonly used domain decomposition. The resulting sparse or smaller matrix has shown to improve in both stability and computational efficiency. Both techniques are verified by comparing with the global multiquadric radial basis function applied to a linear and a real non-linear two-dimensional hydrodynamic model in simulating the tidal current and water flow circulation patterns.