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

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