Algebraic multigrid for the multi-ion transport and reaction model : a physics-aware approach / Peter Thum.

Format:

Book

Author/Creator:

Thum, Peter, 1983- author.

Language:

English

Subjects (All):

Multigrid methods (Numerical analysis).

Physical Description:

1 online resource (232 pages)

Edition:

1st ed.

Place of Publication:

Berlin : Logos Verlag, [2012]

Summary:

Long description: 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.

Contents:

Intro

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.

Notes:

PublicationDate: 20130111

Includes bibliographical references.

Description based on print version record.

ISBN:

3-8325-9151-6

9783832591519

OCLC:

1112423177