Composing Scalable Nonlinear Algebraic Solvers

Composing Scalable Nonlinear Algebraic Solvers

Most efficient linear solvers use composable algorithmic components, with the most common model being the combination of a Krylov accelerator and one or more preconditioners. A similar set of concepts may be used for nonlinear algebraic systems, where nonlinear composition of different nonlinear solvers may significantly improve the time to solution. We describe the basic concepts of nonlinear ...

Composing Constraint Solvers

Comparing Solvers for Large Systems of Nonlinear Algebraic Equations

The solution of systems of nonlinear algebraic equations is a problem which complexity grows as the number of equations increases. The number of engineering problems, which led to these systems, is increasing each year. In this paper we compare the performance of four advanced solvers for systems of nonlinear algebraic equations which have been collected from Internet repositories. We are parti...

Multilevel Algebraic Elliptic Solvers

We survey some of the recent research in developing multilevel algebraic solvers for elliptic problems. A key concept is the design of a hierarchy of coarse spaces and related interpolation operators which together satisfy certain approximation and stability properties to ensure the rapid convergence of the resulting multigrid algorithms. We will discuss smoothed agglomeration methods, harmonic...

Algebraic attacks using SAT-solvers

Algebraic attacks lead to the task of solving polynomial systems over F2. We study recent suggestions of using SAT-solvers for this task. In particular, we develop several strategies for converting the polynomial system to a set of CNF clauses. This generalizes the approach in [4]. Moreover, we provide a novel way of transforming a system over F2e to a (larger) system over F2. Finally, the effi...