Deflated PCG in problems of incompressible flows

• Date: 10. 4. 2025
• Time: 14:00 - 15:30
• Address:
  Sokolovská 83, Praha
• Room: K1
• Speaker: Jan Papež

When solving incompressible flow problems using the Balancing Domain Decomposition by Constraints (BDDC) method, one encounters a sequence of Poisson problems for the pressure. These problems share the same system matrix but have varying right-hand sides corresponding to different time steps. Each time step is typically solved using the preconditioned conjugate gradient (PCG) method, with BDDC serving as the preconditioner. It can be shown that the eigenvalues of the preconditioned system are greater or equal to one and typically remain bounded by $O(1)$. In this talk, we discuss the choice of stopping criteria for PCG and demonstrate that deflation can be effectively applied to this sequence of problems. In contrast to its usual application, we construct the deflation space to mitigate the influence of large, outlying eigenvalues. Numerical experiments confirm that this approach yields a significant reduction (up to 25%) in both the number of PCG iterations and the overall computation time.