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OPEN SOURCE JAVA IMPLEMENTATION OF THE PARALLEL MULTI-THREAD ALTERNATING DIRECTION ISOGEOMETRIC L2 PROJECTIONS SOLVER FOR MATERIAL SCIENCE SIMULATIONS

GRZEGORZ GURGUL, MACIEJ WOŹNIAK, MARCIN ŁOŚ,DANUTA SZELIGA, MACIEJ PASZYŃSKI

Abstract: This paper describes multi-thread parallel open source JAVA implementation of alternating directions isogeometric L2 projections solver. The solver enables for fast numerical simulations of time-dependent problems. To apply our solver, the time-dependent problem must be discretized using isogeometric finite element method with B-spline basis functions in the spatial domain. The problem is solved using an explicit method with respect to time. The application of the explicit method with B-spline based spatial discretization results in a sequence of isogeometric L2 projections that can be solved using our fast solver. The computational cost of the solution of either 2D or 3D problem is linear O(N) in every time step. This cost is lower than the cost of traditional multi-frontal solvers, delivering O(N1.5) computational cost for 2D problems and O(N2) computational cost for 3D problems. This cost is also lower from any iterative solver, delivering O(Nk) computational cost, where k is the number of iterations, which depends on the particular iterative solver algorithm, and the k parameter is also a function of N, so cannot be ignored. Our algorithm is used for numerical solution of 3D elasticity problem.

Key words: Alternating directions solver, Isogeometric L2 projections, Material science eling