Bulletin of the Polish Academy of Sciences: Technical Sciences

Abstract

We focus on two and three-dimensional isogeometric finite element method computations with tensor product C k B-spline basis functions. We consider the computational cost of the multi-frontal direct solver algorithm executed over such tensor product grids. We present an algorithm for estimation of the number of floating-point operations per mesh node resulting from the execution of the multi-frontal solver algorithm with the ordering obtained from the element partition trees. Next, we propose an algorithm that introduces C 0 separators between patches of elements of a given size based on the stimated number of flops per node. We show that the computational cost of the multi-frontal solver algorithm executed over the computational grids with C 0 separators introduced is around one or two orders of magnitude lower, while the approximability of the functional space is improved. We show O(NlogN) computational complexity of the heuristic algorithm proposing the introduction of the C 0 separators between the patches of elements, reducing the computational cost of the multi-frontal solver algorithm.