Seminars

Tuesday April 19th, Byron 106 at 14:00am


Construction of partition of unity bases for piecewise polynomial
space using linear algebraic approach

by

Tae-Wan Kim

Department of Naval Architecture and Ocean Engineering, Research Institute of Marine Systems Engineering, Seoul National University

We present a method to compute a partition-of-unity basis of the space of piecewise polynomial function with given regularity and degree on a axis-aligned box subdivision of a domain. We solve a linear system of constraint equations of the polynomial coefficients representing the basis. The system is usually underdetermined, that means there are many bases which satisfy the system. The method can be applied to any domain, extending to any partitions the traditional construction of B-spline basis. Furthermore, by specifying some additional constraints related to geometric properties, we obtain a a unique solution, which turns out to be equivalent to the B- spline basis from the traditional method.