# The Role of Multi-method Linear Solvers in PDE-based Simulations

## Abstract

The solution of large-scale, nonlinear PDE-based simulations typically depends on the performance of sparse linear solvers, which may be invoked at each nonlinear iteration. We present a framework for using multi-method solvers in such simulations to potentially improve the execution time and reliability of linear system solution. We consider *composite solvers*, which provide reliable linear solution by using a sequence of preconditioned iterative methods on a given system until convergence is achieved.We also consider *adaptive solvers*, where the solution method is selected dynamically to match the attributes of linear systems as they change during the course of the nonlinear iterations.We demonstrate how such multi-method composite and adaptive solvers can be developed using advanced software architectures such as PETSc, and we report on their performance in a computational fluid dynamics application.

## Keywords

Linear Solver Linear Solution Residual Norm Inexact Newton Method Drive Cavity## Preview

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