On the Development of Implicit Solvers for Time-Dependent Systems
This presentation will describe some of our recent experiences in the development of efficient implicit solvers for systems of nonlinear time-dependent partial differential equations. These experiences are for different applications to weather and climate prediction, so the primary aim of the presentation is to stimulate discussion on some of the challenges and opportunities associated with the development of efficient implicit solvers. The main issues that will be addressed centre around the fast solution of the discrete algebraic systems arising at each time step: with a focus on multilevel solution methods and their parallel implementation. If time permits the further issues of adaptivity in time and space will also be considered.