Scalable solver software

Towards Optimal Petascale Simulations (TOPS) is a scalable solver software project based on domain decomposed parallelization to research, implement, and support in collaborations with users an open-source package for large-scale discretized PDE problems. Optimal complexity methods, such as multigrid/multilevel preconditioners, keep the time spent in dominant algebraic kernels close to linear in discrete problem size as the applications scale on massively parallel computers. Krylov accelerators and Jacobian-free variants of Newton's method, as appropriate, are wrapped around the multilevel methods to deliver robustness in multirate, multiscale coupled systems, which are solved either implicitly or in more traditional forms of operator splitting. The TOPS software framework is being extended beyond direct computational simulation to computational optimization, including design, control, and inverse problems. We outline and illustrate the philosophy of TOPS. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)