Dual-Order-PC

This repository contains the implementation of a preconditioner capable of handling both Full Order Models (FOM) and Reduced Order Models (ROM) using the appctx of the Firedrake solver infrastructure.

Contents

• dual_order_pc.py: Implements the dual-order preconditioner logic to handle FOM and ROM. This file contains the main functionality of the preconditioner.
• simple_mfe_FOM.py: Provides a Minimum Failing Example (MFE) to demonstrate the application of the FOM mode of the dual-order preconditioner in a minimal finite element setup. Currently, the FOM mode of the preconditioner is less performant compared to classic direct solvers with LU factorization and/or Firedrake's AssembledPC preconditioner.

Requirements

This project requires Firedrake. To use or modify the files, ensure you have:

• Firedrake: Installation guide
• Python 3.x

Usage

1. Clone the repository:

   git clone git@github.com:boutsitron/dual-order-pc.git
   cd dual-order-pc

2. Set up Firedrake following their installation guide and source it.

3. Run the MFE:

   # Sequential mode
   python simple_mfe_FOM.py
   
   # Parallel mode (8 processes)
   mpiexec -np 8 python simple_mfe_FOM.py

License

This project is licensed under the MIT License. See the LICENSE file for details.

Acknowledgments

Many thanks to the Firedrake project developers for their robust FEM framework, and special thanks to Julian Andrej, whose work inspired this preconditioner, for his valuable input.