The Solvers in PETSc/TAO

• Vectors and Parallel Data
  • Creating Vectors
  • Common vector functions and operations
  • Assembling (putting values in) vectors
  • Basic Vector Operations
  • Local/global vectors and communicating between vectors
  • Low-level Vector Communication
  • Application Orderings
• Matrices
  • Creating matrices
  • Low-level matrix creation routines
  • Assembling (putting values into) matrices
  • Basic Matrix Operations
  • Matrix-Free Matrices
  • Transposes of Matrices
  • Other Matrix Operations
  • Symbolic and Numeric Stages in Sparse Matrix Operations
  • Graph Operations
  • Partitioning
• KSP: Linear System Solvers
  • Using KSP
  • Solving Successive Linear Systems
  • Krylov Methods
  • Preconditioners
  • Solving Block Matrices with PCFIELDSPLIT
  • Solving Singular Systems
  • Using External Linear Solvers
  • Using PETSc’s MPI parallel linear solvers from a non-MPI program
• SNES: Nonlinear Solvers
  • Basic SNES Usage
  • The Nonlinear Solvers
  • General Options
  • Inexact Newton-like Methods
  • Matrix-Free Methods
  • Finite Difference Jacobian Approximations
  • Variational Inequalities
  • Nonlinear Preconditioning
• TS: Scalable ODE and DAE Solvers
  • Basic TS Options
  • DAE Formulations
  • Using Implicit-Explicit (IMEX) Methods
  • IMEX Methods for fast-slow systems
  • GLEE methods
  • Using fully implicit methods
  • Using the Explicit Runge-Kutta timestepper with variable timesteps
  • Special Cases
  • Monitoring and visualizing solutions
  • Error control via variable time-stepping
  • Handling of discontinuities
  • Explicit integrators with finite element mass matrices
  • Performing sensitivity analysis with the TS ODE Solvers
  • Using Sundials from PETSc
  • Using TChem from PETSc
• Solving Steady-State Problems with Pseudo-Timestepping
• TAO: Optimization Solvers
  • Getting Started: A Simple TAO Example
  • TAO Workflow
  • TAO Algorithms
  • Advanced Options
  • Adding a Solver