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SUNDIALS: Suite of nonlinear and differential/algebraic equation solvers
The current capabilities of the codes, along with some of the algorithms and heuristics used to achieve efficiency and robustness, are described.
VODE: a variable-coefficient ODE solver
VODE is a new initial value ODE solver for stiff and nonstiff systems that uses variable-coefficient Adams-Moulton and Backward Differentiation Formula methods in Nordsieck form, treating the Jacobian as full or banded.
Hybrid Krylov Methods for Nonlinear Systems of Equations
To improve the global convergence properties of these basic algorithms, hybrid methods based on Powell's dogleg strategy are proposed, as well as linesearch backtracking procedures.
Using Krylov Methods in the Solution of Large-Scale Differential-Algebraic Systems
In this paper, a new algorithm for the solution of large-scale systems of differential-algebraic equations is described. It is based on the integration methods in the solver DASSL, but instead of a…
GMRES On (Nearly) Singular Systems
Conditions under which the GMRES iterates safely to a least-squares solution or to the pseudoinverse solution are given, which apply to any residual minimizing Krylov subspace method that is mathematically equivalent to GMRES.
A Theoretical Comparison of the Arnoldi and GMRES Algorithms
- P. Brown
- Computer ScienceSIAM J. Sci. Comput.
- 2 January 1991
It is shown that there is a relationship between breakdowns in the two Krylov methods and it is suggested that if one of the methods performs poorly on a particular problem, then so will the other.
Convergence Theory of Nonlinear Newton-Krylov Algorithms
Some convergence theory for nonlinear Krylov subspace methods is presented, to analyze these methods when they are combined with global strategies such as linesearch techniques and model trust region algorithms.
Reduced storage matrix methods in stiff ODE systems
In the context of general nonlinear algebraic systems, this work provides some theoretical foundation for the combined Newton-Krylov method by giving convergence results that include errors due to the difference quotient approximation to the linear operator.
Semicoarsening Multigrid on Distributed Memory Machines
This paper presents the results of a scalability study for a three-dimensional semicoarsening multigrid solver on a distributed memory computer, and examines the scalability of the solver theoretically and experimentally.
Matrix-free methods for stiff systems of ODE's
We study here a matrix-free method for solving stiff systems of ordinary differential equations (ODE’s). In the numerical time integration of stiff ODE initial value problems by BDF methods, the…