McInnes, L. C. | Search NASA

DOE OSTI2012

First steps toward a multiphysics exemplars and benchmarks suite

A workshop report (Keyes et al., 2012) summarizes challenges and opporunities in multiphysics simulations from algorithmic and architectural perspectives, where "algorithmic" includes both mathematical analysis and computational complexity and "architectural" includes both software and hardware environments. The report discusses the significant and still remaining key needs for conducting the mathematical analysis and developing the corresponding flexible software necessary to ensure that coupling schemes are accurate, stable, robust, consistent, and are implemented correctly, as prerequisites for developing predictive multiphysics simulations. Such work is essential for exploiting emerging extreme-scale computing resources for scientific discovery.

Keyes, D. E.↗

NASA NTRS1998

Globalized Newton-Krylov-Schwarz Algorithms and Software for Parallel Implicit CFD

Implicit solution methods are important in applications modeled by PDEs with disparate temporal and spatial scales. Because such applications require high resolution with reasonable turnaround, "routine" parallelization is essential. The pseudo-transient matrix-free Newton-Krylov-Schwarz (Psi-NKS) algorithmic framework is presented as an answer. We show that, for the classical problem of three-dimensional transonic Euler flow about an M6 wing, Psi-NKS can simultaneously deliver: globalized, asymptotically rapid convergence through adaptive pseudo- transient continuation and Newton's method-, reasonable parallelizability for an implicit method through deferred synchronization and favorable communication-to-computation scaling in the Krylov linear solver; and high per- processor performance through attention to distributed memory and cache locality, especially through the Schwarz preconditioner. Two discouraging features of Psi-NKS methods are their sensitivity to the coding of the underlying PDE discretization and the large number of parameters that must be selected to govern convergence. We therefore distill several recommendations from our experience and from our reading of the literature on various algorithmic components of Psi-NKS, and we describe a freely available, MPI-based portable parallel software implementation of the solver employed here.

Gropp, W. D.↗