Teko: Block and Physics-Based Preconditioning

Introduction

Teko is a Trilinos package for the development and application of block and physics-based preconditioners. It provides tools to assemble and manipulate block linear operators, to decompose a fully coupled operator into its physical sub-blocks, and to build approximate inverses of those blocks using the full complement of Trilinos solvers and preconditioners (Ifpack2, MueLu, Amesos2, Belos, and others). On top of that infrastructure Teko ships a library of generic block preconditioners (block Jacobi, block Gauss-Seidel, LU 2x2) and physics-based preconditioners for the incompressible Navier-Stokes equations (SIMPLE, LSC, PCD).

User's Guide

The pages below document how to configure and use Teko, with a focus on the Teuchos::ParameterList / XML options that control every preconditioner:

• Overview and glossary
• Getting Started — core concepts and a minimal end-to-end example.
• Configuration Model — the three-layer configuration model and complete XML examples. Start here for options.
• The Inverse Library — named inverses and how they reference Ifpack2 / MueLu / Amesos2 / Belos.
• Block Preconditioner Reference — exhaustive parameter tables for every built-in block preconditioner.
• Navier-Stokes Preconditioners — SIMPLE, LSC, PCD.
• Examples — walkthroughs of the in-tree example drivers.
• Advanced Topics — the RequestHandler callback system, reordering, operator reuse, and writing your own factory.
• Cookbook — common blocking, solver-composition, reuse, and multiphysics patterns.

References

For the theory behind the Navier-Stokes methods, see Cyr, Shadid & Tuminaro, Stabilization and Scalable Block Preconditioning for the Navier-Stokes Equations, J. Comput. Phys. 2011.