Architecture of iterative solvers for hp-adaptive finite element codes

Abstract

We present a layered architecture for iterative solvers of linear equations, designed to allow for easy integration with existing hp-adaptive FEM codes. We discuss interfaces between a solver and an external FEM code and requirements for the FEM code that must be met in order to work with the solver. Our solution is suited to work effectively with stationary as well as time-dependent problems. In this article, we provide an overview of the layered solver's structure and modules of each layer. In subsequent articles, we will present specific implementations of particular layers.