Interpolation techniques based on the local radial basis function differential quadrature (LRBF-DQ) method are proposed to interpolate the field values with arbitrarily given scattered data. The interpolation of more unknown field data from the limited known data is becoming an important research subject nowadays for the large-scale engineering analysis and design problems. Three new methods that utilize the field gradient, the governing equation, and both of them are undertaken. The geometric characteristics of the field values can therefore be taken into consideration by the field gradient. In the meantime the physical principle is able to be satisfied with the introduction of the governing equation whose merit is absent in the traditional interpolation techniques, such as the linear polynomial fitting (LPF) and the quadratic polynomial fitting (QPF) methods. The last method will take the advantages of both the methods of gradient and governing equation, namely the geometric characteristics and physical laws. Two numerical examples governed respectively by the three-dimensional (3D) Poisson and the 3D advection–diffusion equations are performed to demonstrate the accuracy and the stability of the present methods. The results are compared with those by the LPF and the QPF methods which show the current interpolation methods are more accurate and robust than the conventional ones.
On influence aspect of parameter in scattered data approximation problem using multiquadric radial basis function
