Algebraic Multigrid for the Multi-Ion Transport and Reaction Model - A Physics-Aware Approach
Peter Thum
Cite this publication as
Peter Thum, Algebraic Multigrid for the Multi-Ion Transport and Reaction Model - A Physics-Aware Approach (2013), Logos Verlag, Berlin, ISBN: 9783832591519
Description / Abstract
The multi-ion transport and reaction model (MITReM) is used to simulate electrochemical processes. The governing partial differential equations (PDEs) are discretized in space by a combined finite element and residual-distribution scheme. The discrete system is linearized with Newton's method which results in a series of linear systems. The focus of this work is on the development of a stable and efficient point-based algebraic multigrid (PAMG) method for the solution of the linear systems which arise in the MITReM simulation.
Table of content
- BEGINN
- 1 Introduction
- 1.1 Context
- 1.2 Main Focus and Structure
- 2 The Multi-Ion Transport and Reaction Model (MITReM)
- 2.1 Electrochemical Background
- 2.2 Homogeneous Reactions
- 2.3 Basic System
- 2.4 Boundary Conditions
- 2.5 Existence and Uniqueness of Solutions
- 2.6 Discretization and Linearization
- 3 Algebraic Multigrid (AMG) for Convection-Dominated Flow Problems
- 3.1 AMG
- 3.2 PAMG
- 3.3 AMG for Convection-Dominated Flow Problems
- 4 The Reordering Framework
- 4.1 Terminology
- 4.2 State-of-the-Art Reordering in the Context of AMG
- 4.3 Basic Matrix
- 4.4 Reduction Techniques
- 4.5 Sorting Algorithms
- 4.6 Scalar Example
- 4.7 Reordering Framework for the MITReM
- 5 The Heuristic Peclet Number
- 5.1 Heuristic Peclet Number for Scalar Equations
- 5.2 Heuristic Peclet Number for Systems of PDEs
- 6 A Physics-Aware Point-Based AMG Approach (PAMG) for the Migration-Diffusion System
- 6.1 The Migration-Diffusion System
- 6.2 State-of-the-Art PAMG Approaches
- 6.3 The Physics-Aware Primary Matrix
- 6.4 PAMG for a Locally Violated Peclet Condition
- 6.5 The Final Physics-Aware PAMG Approach
- 7 A Physics-Aware PAMG Approach for the MITReM
- 7.1 The MITReM System
- 7.2 State-of-the-Art PAMG for the MITReM
- 7.3 Derivation of Efficient and Robust PAMG Approaches
- 7.4 PAMG for the MITReM
- 7.5 Conclusion
- 8 Conclusions and Future Work
- Bibliography
- List of Figures
- List of Tables