PARALLEL ADDITIVE SCHWARZ PRECONDITIONING FOR ISOGEOMETRIC ANALYSIS

We present a multi-level massively parallel additive Schwarz preconditioner for Isogeometric Analysis, a FEM-like numerical analysis for PDEs that permits exact geometry representation and high regularity basis functions. Two model problems are considered: the scalar elliptic equation and the advection-diffusion equation. Theoretical analysis proves that the adoption of a coarse correction grid is crucial in order to have the condition number of the preconditioned stiffness matrix independent from the number of subdomains, whenever the ratio between the coarse mesh size and the fine mesh size is kept fixed. Numerical tests for the scalar elliptic equation (in 2D and 3D on trivial and non-trivial domains) confirm the theory. The preconditioner is then applied to the advection-diffusion equation in 2D and 3D. Again, the numerical results shows that the condition number of the preconditioned linear system scales with the number of subdomains up to 8100 processors, eventually with SUPG stabilization. The tests are implemented in C programming language on the top of PETSc library.