D. Garcia, D. Pardo, L. Dalcin, M. Paszyn ́ski, N. Collier, and V. Calo
Computer Methods in Applied Mechanics and Engineering, (In Press), (2016)
Isogeometric analysis (IGA); Finite element analysis (FEA); Refined isogeometric analysis (rIGA); Direct solvers; Multi-frontal solvers; k-refinement
We propose the use of highly continuous finite element spaces interconnected with low continuity hyperplanes to maximize the performance of direct solvers. Starting from a highly continuous Isogeometric Analysis (IGA) discretization, we introduce C0C0-separators to reduce the interconnection between degrees of freedom in the mesh. By doing so, both the solution time and best approximation errors are simultaneously improved. We call the resulting method “refined Isogeometric Analysis (rIGA)”. To illustrate the impact of the continuity reduction, we analyze the number of Floating Point Operations (FLOPs), computational times, and memory required to solve the linear system obtained by discretizing the Laplace problem with structured meshes and uniform polynomial orders. Theoretical estimates demonstrate that an optimal continuity reduction may decrease the total computational time by a factor between p2p2 and p3p3, with pp being the polynomial order of the discretization. Numerical results indicate that our proposed refined isogeometric analysis delivers a speed-up factor proportional to p2p2. In a 2D2D mesh with four million elements and p=5p=5, the linear system resulting from rIGA is solved 22 times faster than the one from highly continuous IGA. In a 3D3D mesh with one million elements and p=3p=3, the linear system is solved 15 times faster for the refined than the maximum continuity isogeometric analysis.