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About this book

The main aim of this book is to discuss model order reduction (MOR) methods for differential-algebraic equations (DAEs) with linear coefficients that make use of splitting techniques before applying model order reduction. The splitting produces a system of ordinary differential equations (ODE) and a system of algebraic equations, which are then reduced separately. For the reduction of the ODE system, conventional MOR methods can be used, whereas for the reduction of the algebraic systems new methods are discussed. The discussion focuses on the index-aware model order reduction method (IMOR) and its variations, methods for which the so-called index of the original model is automatically preserved after reduction.

Table of Contents

Frontmatter

Chapter 1. Introduction

Abstract
The main aim of this book is to discuss model order reduction (MOR) methods for linear coefficients differential algebaric equations (DAEs).
N. Banagaaya, G. Alì, W. H. A. Schilders

Chapter 2. Differential-Algebraic Equations

Abstract
In this chapter, we introduce the differential algebraic equations which we abbreviate as DAEs. DAEs arise in a variety of applications such as modelling constrained multibody systems, electrical networks, aerospace engineering, chemical processes, computational fluid dynamics, gas transport networks, see [10–12, 35]. Therefore their analysis and numerical treatment plays an important role in modern mathematics.
N. Banagaaya, G. Alì, W. H. A. Schilders

Chapter 3. Decoupling of Linear Constant DAEs

Abstract
In this chapter, we discuss how to decouple DAEs using matrix, projector and basis chains. This approach is based on the projector and matrix chains introduced in [25].
N. Banagaaya, G. Alì, W. H. A. Schilders

Chapter 4. Index-aware Model Order Reduction

Abstract
In this chapter, we discuss the index-aware model order reduction (IMOR) and its invariant the implicit-IMOR(IIMOR) method. We use the decoupled systems (3.​2.​11) and (3.​7.​1) to derive the IMOR and IIMOR method respectively.
N. Banagaaya, G. Alì, W. H. A. Schilders

Chapter 5. Large Scale Problems

Abstract
In this chapter, we illustrate the robustness of the IMOR method on large scale problems from real-life applications.
N. Banagaaya, G. Alì, W. H. A. Schilders

Chapter 6. Conclusion

Abstract
In this book, two MOR methods for linear constant coefficient DAEs are discussed. These MOR methods are: the Index-aware MOR (IMOR) and Implicit IMOR (IIMOR) methods. They both reduce DAEs of any index by first decoupling it into differential and algebraic parts using projector, matrix and basis chain.
N. Banagaaya, G. Alì, W. H. A. Schilders

Backmatter

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