Wednesday, March 19, 2008
Class of '27 Lecture
Speaker: David E. Keyes (Columbia University) "A Nonlinearly Implicit Manifesto"
When: 4 p.m.
Where: Sage 3510

A reception will be held after this lecture, at 5 p.m. in the Amos Eaton fourth floor lounge.

Many simulations must be followed over time intervals that are long compared to the shortest timescales in the system, e.g., convective versus acoustic timescales in aerodynamics, ocean turnover versus gravity wave timescales in climate, plasma discharge versus Alfven timescales in tokamaks, piston travel versus fast reaction timescales in internal combustion. Often, the phenomena associated with the shortest timescales may be assumed to be in equilibrium relative to dynamics of interest; however, they control the computational timestep if an explicit method is used, with the result that even weak scaling cannot be achieved. Often, as well, one would ideally employ a high-order timestepping scheme and take relatively large timesteps for computational economy; however, if operator splitting techniques are used the lower order splitting error thwarts this objective. For these and other reasons, fully implicit methods are increasingly important for the nonlinear multiscale applications that pace large-scale simulations in energy, environment, and other complex systems. The good news is that advances in solution algorithms, globalization algorithms, and software that implements them (without necessarily demanding that the user constructs a full Jacobian) make implicit methods more inviting than ever. Moreover, we argue that computational challenges on the immediate horizon­ uncertainty quantification, inverse problems, multiphysics coupling, etc. ­ are most naturally tackled with fully nonlinearly implicit formulations well in hand. This talk illustrates the case for implicit methods with model problems and challenge problems arising from systems governed by partial differential equations.