PhD Thesis Proposal Exam - Gautam Luhana

Name: Gautam Luhana

Date: December 27

Time: 3PM

Location: ICCS X836

Supervisor: Chen Greif

Title: Truncated Domain Preconditioner for the implicit-in-time Immersed Boundary Method

Abstract:
The Immersed Boundary (IB) method is a widely used approach for simulating fluid-structure interactions. Explicit time-stepping in the IB method often requires very small time steps to ensure numerical stability, while implicit methods require solving a linear system at each time step, which is computationally expensive. We propose a novel block preconditioner for the implicit-in-time Immersed Boundary method that uses domain truncation for the nested Schur complement. This approach is particularly useful for applications where the structure occupies a small part of the fluid domain, as it enables faster construction and application of the preconditioner. The reduction in the degrees of freedom results in a speedup of each iteration of the outer Krylov solver while preserving the efficiency and robustness of the preconditioner.