Toward a computational multiresolution analysis for radial point interpolation meshless method

In this work, the application of Daubechies' scaling functions (DSFs) in computational engineering, particulary radial point interpolation meshless method (RPIM) in electromagnetic engineering, is studied. This analysis indicates some shortcomings of DSFs in computational engineering. In fact, the DSFs take the role of shape functions in RPIM, but they do not hold some general properties of shape functions. Modifying these shortcomings according to engineering requirements as time consumption rate, new scaling (shape) functions are derived, and testing them into two important classes of electromagnetic problems, that is, incident wave on dielectrics and scatterers, gives good agreement with exact solutions. Copyright (c) 2014 John Wiley & Sons, Ltd.