An Efficient Procedure for the Projection of a Given Field onto Hierarchical Vector Basis Functions of Arbitrary Order

Abstract

In contrast to interpolatory basis functions, the projection of a given field onto hierarchical vector basis functions is rather difficult and could be costly if not done with some effort at efficiency. The lack of any interpolatory points for the hierarchal basis functions is the underlying reason for the necessity of a more involved method compared to that for interpolatory basis functions. We present a method to project an arbitrary given field onto hierarchical vector basis functions that is an extension of a projection method proposed in an earlier paper by Webb. The main improvements of the new procedure are its ability to project a given field residing in a volume onto the vector basis functions of an arbitrary order as well as its ability to handle an arbitrary geometrical element mapping scheme that enables the use of tetrahedrons with curvilinear faces. The procedure is efficient in that it projects the field by solving a series of small and easily manageable systems of equations. Moreover, the memory requirement is kept low by utilizing universal matrices that can be reused throughout the computational domain.