Title:	COMPARISON OF COMPUTATIONAL COSTS FOR TWO DIMENSIONAL ISOGEOMETRIC COLLOCATION AND FINITE ELEMENT METHODS FOR PARALLEL SHARED MEMORY MULTI-FRONTAL DIRECT SOLVER
Author(s):	Pawe? Lipski, Piotr Gurgu, Maciej Paszy?ski
ISBN:	978-989-8533-25-8
Editors:	Hans Weghorn
Year:	2014
Edition:	Single
Keywords:	Collocation method, finite element method, isogeometric analysis, multi-frontal solver, parallel computing
Type:	Full Paper
First Page:	93
Last Page:	100
Language:	English
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Paper Abstract:	In this paper we analyze the two dimensional algorithms for isogeometric collocation method and isogeometric finite element method. In particular we focus on interfacing with multi-frontal solver algorithm. This is done in the following steps. First we construct two dimensional patch of elements with basis functions defined as tensor products of one dimensional B-spline basis functions. Next, we generate element frontal matrices over the patch of element. Later, we analyze the multi-frontal algorithm that is merging patches of elements to obtain fully assembled rows and eliminate these rows that represent fully assembled basis functions. We estimate the computational cost of sequential and parallel multi-frontal solver algorithm and compare the theoretical results to numerical experiments. In particular, we show that the isogeometric collocation method outperforms the isogeometric finite element method. We also show that the isogeometric collocation method does not require the expensive integration algorithm. This is a big advantage of the isogeometric collocation method, since for higher order basis functions the integration is much expensive then the solution itself.
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