6. SLES: Linear Equations Solvers

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SLES is the heart of PETSc, because it provides uniform and efficient access to all of the package's linear system solvers, including parallel and sequential, direct and iterative. SLES is intended for solving nonsingular systems of the form

where A denotes the matrix representation of a linear operator, b is the right-hand-side vector, and x is the solution vector. SLES uses the same calling sequence for both direct and iterative solution of a linear system. In addition, particular solution techniques and their associated options can be selected at runtime.

The combination of a Krylov subspace method and a preconditioner is at the center of most modern numerical codes for the iterative solution of linear systems. See, for example, [7] for an overview of the theory of such methods. SLES creates a simplified interface to the lower-level KSP and PC modules within the PETSc package. The KSP component, discussed in Section Krylov Methods , provides many popular Krylov subspace iterative methods; the PC module, described in Section Preconditioners , includes a variety of preconditioners. Although both KSP and PC can be used directly, users should employ the interface of SLES.


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