Tipo Seminário: Seminário MatApli
Palestrante(s): Maciej Paszynski , University of Science and Technology, Krakow - Polônia
Horário/Local: 14:00-15:00(Auditorio B)
In this talk, we focus on parallel multi-frontal direct solvers executed on distributed memory Linux clusters. We consider isogeometric finite element method (IGA-FEM) with higher-order B-spline basis functions. We first estimate the computation and communication complexities of the parallel multi-frontal direct solvers for IGA-FEM executed on the distributed memory Linux cluster.
From our estimates, it implies that both computational and communication costs are of the order of O(Np^2) (2D IGA-FEM) and O(N^(4/3)p^2) (3D IGA-FEM).
Next, we verify the obtained estimates by numerical experiments performed with MUMPS, PaSTiX and SuperLU over STAMPEDE Linux cluster from Texas Advanced Computing Center. For more details, we refer to.
Finally, we propose a methodology for reduction of the constants C_comp and C_comm from the computational and communication costs, namely C_comp*Np^2 and C_comm*Np^2 (2D) or C_comp*N^(4/3)p^2 and C_comm*N^(4/3)p^2 (3D). We call this methodology refined Isogeometric Analysis (rIGA).
This is done by introduction of some additional basis functions over the computational mesh, which make the global matrix larger, but also sparser, and the resulting computational cost is up to two orders of magnitude smaller.
The rIGA also reduces the communication cost, so the scalability of the parallel direct solver is better for rIGA-FEM than for the IGA-FEM, as it is shown in.