Scalable smoothing strategies for a geometric multigrid method for the immersed boundary equations

Journal Article · Tue Dec 20 04:00:00 EST 2016 · arXiv.org Repository

OSTI ID:1398457

Bhalla, Amneet Pal Singh ^[1]; Knepley, Matthew G. ^[2]; Adams, Mark F. ^[3]; Guy, Robert D. ^[4]; Griffith, Boyce E. ^[1]

---

1. Univ. of North Carolina, Chapel Hill, NC (United States)
2. Rice Univ., Houston, TX (United States)
3. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
4. Univ. of California, Davis, CA (United States)

The immersed boundary (IB) method is a widely used approach to simulating fluid-structure interaction (FSI). Although explicit versions of the IB method can suffer from severe time step size restrictions, these methods remain popular because of their simplicity and generality. In prior work (Guy et al., Adv Comput Math, 2015), some of us developed a geometric multigrid preconditioner for a stable semi-implicit IB method under Stokes flow conditions; however, this solver methodology used a Vanka-type smoother that presented limited opportunities for parallelization. This work extends this Stokes-IB solver methodology by developing smoothing techniques that are suitable for parallel implementation. Specifically, we demonstrate that an additive version of the Vanka smoother can yield an effective multigrid preconditioner for the Stokes-IB equations, and we introduce an efficient Schur complement-based smoother that is also shown to be effective for the Stokes-IB equations. We investigate the performance of these solvers for a broad range of material stiffnesses, both for Stokes flows and flows at nonzero Reynolds numbers, and for thick and thin structural models. We show here that linear solver performance degrades with increasing Reynolds number and material stiffness, especially for thin interface cases. Nonetheless, the proposed approaches promise to yield effective solution algorithms, especially at lower Reynolds numbers and at modest-to-high elastic stiffnesses.

• Research Organization: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
• DOE Contract Number: AC02-05CH11231
• OSTI ID: 1398457
• Journal Information: arXiv.org Repository, Journal Name: arXiv.org Repository Vol. 2015; ISSN 9999-0017
• Publisher: Cornell University
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING