Scalable domain decomposition preconditioner for Navier–Stokes equations coupled with the heat equation

Abstract

In this article, we study the thermal instability that appears from time to time while printing using a 3D printer. To solve the semi-discretized problem at each time-step, we use a scalable parallel algorithm based on a two-level Optimized Restricted Additive Schwarz (ORAS) domain decomposition preconditioner for GMRES. Parallel scalability tests are conducted with comparison against the parallel direct solver MUMPS and the one-level Schwarz method, which show lack of robustness for larger number of processors. 2D numerical tests illustrate that the number of iterations to reach GMRES convergence depends on the state of the physical simulation during time, and that the second level of preconditioning is needed to achieve robustness.

Keywords:

• Parallel computation
• domain decomposition method
• preconditioner
• high-performance computing
• two-level method

2010 Mathematics Subject Classifications:

• Partial differential equations
• 65Y05

Disclosure statement

No potential conflict of interest was reported by the author(s).