Koren B., Vuik K. (Editors) Advanced Computational Methods in Science and Engineering

Подождите немного. Документ загружается.

Lecture Notes

in Computational Science

and Engineering

Editors

Timothy J. Barth

Michael Griebel

David E. Keyes

Risto M. Nieminen

Dirk Roose

Tamar Schlick

ABC

•

Editors

Barry Koren Kees Vuik

Advanced Computational

With 109 Figures and 4 Tables

Methods in Science and

Engineering

Group Computing and Control

Barry Koren

Science Park 123

1098 XG Amsterdam

The Netherlands

Kees Vuik

Delft University of Technology

Institute of Applied Mathematics

Mekelweg 4

2628 CD Delft

The Netherlands

c.vuik@tudelft.nl

Centrum Wiskunde & Informatica

barry.koren@cwi.nl

Editors

Printed on acid-free paper

Springer is part of Springer Science+Business Media (www.springer.com)

This work is subject to copyright. All rights are reserved, whether the whole or part of the material

is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broad-

this publication or parts thereof is permitted only under the provisions of the German Copyright Law

of September 9, 1965, in its current version, and permission for use must always be obtained from

Springer. Violations are liable to prosecution under the German Copyright Law.

casting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of

The use of general descriptive names, registered names, trademarks, etc. in this publication does not

Springer Heidelberg Dordrecht London New York

imply, even in the absence of a specific statement, that such names are exempt from the relevant

protective laws and regulations and therefore free for general use.

Mathematics Subject Classification (2000): 65-XX, 70-XX, 74-XX, 76-XX, 78-XX

ISBN 978-3-642-03343-8 e-ISBN 978-3-642-03344-5

DOI 10.1007/978-3-642-03344-5

ISSN 1439-7358

Cover illustration: TU Delft, Delft Center for Computational Science and Engineering

Cover design: deblik, Berlin

Library of Congress Control Number: 2009932722

Foreword

James Clerk Maxwell wr ote in the introduction to his Treatise on E lec tricity

and Magnetism, in 1873:

“As I proceeded with the study of Faraday, I perceived that his method of

conceiving the phenomena was also a mathematical one, though not exhibited

in conventional form of mathematical symbols. I also found that these meth-

ods were capable of being expressed in the ordinary mathematical forms, and

thus compared with those of the professional mathematicians. For instance,

Faraday, in his minds eye, saw lines of force traversing all space where the

mathematicians saw centres of force attracting at a distance.” (sic!)

I consider this as a ﬁne ex ample how the model of the practitioner of s c ience

stimulates the mathematica l mind. This fruitful interaction was and still is

the objective of the Delft Centre for Computational Science and Engineering,

an interfaculty institution, founded in 2003 by Professor Piet Wesseling. In

its present form the centre acts as a forum for the computational aspec ts

of diﬀerent bra nches of s c ience and e ngineering, taught and studied at Delft

University of Technology. The centre proofs its value for the university in

a twofold way: scientists and e ngineers discuss their pro blems with mathe-

maticians, and mathematicians ﬁnd new applications for their theories and

methods . This is a clear case of cros s-fertilization. Certainly in a world with

growing interaction between diﬀerent disciplines, there is a growing need for a

common, albeit more complex, model representation. Mathematics fur nis hes

this framework b e c ause its language is commensura ble over the ﬁelds of ap-

plication.

The articles in this book are a ﬁne collection of examples that s how the

strength and progress of applied mathematics in the realm of technology.

Just like a museum director choos e s paintings with care to express to the

public the power of a certain art theme; the editors of this book have care-

fully chosen topics to demons trate the power of computational science and

engineering. I hope this book stimulates the reader to paint his/her own spec-

imen.

Jacob Fokkema

Rector Magniﬁcus

Delft University of Technology

Preface by the editors

Computational Science and Engineering (CSE) is of vital imp ortance to to-

day’s and tomorrow’s society. It enables the simulation of processes, phenom-

ena and systems that can not be studied by real exper iments because these

are too dangerous, too expensive, unethical, or just technically impossible.

Moreover, as oppose d to experiments, CSE allows for automatic design and

optimization. Every major discipline in science and eng ineer ing has its own

computational br anch now. E ngineers, medical doctors, policy makers, et

cetera rely more and more on CSE for decision support. With the longstand-

ing, c ontinuing growth in speed, memory and cost-eﬀectiveness of computers,

and with similar improvements in numerical algorithms, the ex isting and fu-

ture beneﬁts of CSE are enormous. CSE is and will be a crucial enabling

technolo gy.

Although CSE has spread over many diﬀerent disciplines, it is to be regarded

as a discipline in its own right, because of the specialized skills involved,

the long learning curve required, a nd the rapid pace of innovation, which is

impossible to keep track of by non-expe rts and casual users. The challenge

of CSE is the development and e xploitation o f ever more realistic computa-

tional models . Perfect realism by dire c t (brute-force) simulation is imposs ible

in most instances, and will remain to be so for a long time, if not forever.

With increasing realism, in general, multi-scalednes s and multi-disciplinarity

also increase, two fundamental inhibitor s for direct simulation. Signiﬁcant

disparity in scales motivates multi-sca le modeling instead. Although multi-

scale modeling has always been part and par c e l of science (think of replacing

a body by a p oint mass, or of the continuum approximation in ﬂuid dynam-

ics), CSE has led to a renewed interest in it, and has opened new perspec-

tives and challenges. Concerning multi-disciplinarity, this motivates more and

more the intelligent coupling of distinct, existing models: ﬂuid-dynamics plus

structural-mechanics models, thermal plus electrical models, et cetera.

Although CSE depends heavily on computer ar chitectures, numerical math-

ematics is at its heart. A challenge is to ensure that numerical methods

remain capable of optimally proﬁting from the growing speed and memory of

tomorrow’s computer architectures. With the incre asing realism and hence

complexity in CSE, numerical robustness and numerical eﬃciency are prop e r-

ties of growing importance . Baby-sitting a complex CSE simulation because

of the use of non-r obust numerical techniques in it, is unwanted. And so is

quick ﬁlling of fast and large computers by the use of ineﬃcient numerical

methods . Numerical robustness is to be obtained by developing and apply-

ing numerical methods that are stable and well-conditioned for the speciﬁc

problems a t hand. Numerical eﬃciency has to be striven for by extracting the

maximum amount of correct information from the minimum amount of grid

points, cells, and alike, and by aiming a t a linear proportionality between

the computing time required and the number of unknowns. Pr oblems with N

unknowns a re preferably to be solved in O(N) operations. With insuﬃcient

attention for the numerics, this may easily be O(N

) operations, implying

quick ﬁlling of the fastest and largest computers.

Numerical mathematics is found throughout the entire book, like oxygen

in the earth’s atmosphere; from low to high density, often imperceptible but

always indispensable.

CSE proﬁts from its strategic position along two a xes: the methodology axis

and the discipline axis. It ﬁnds its coherence and added value along the

methodology axis; in the numerical methods in common use by the vari-

ous disciplines. Along the discipline axis, CSE ﬁnds its research focus and

relevance. CSE is fruitful br e e ding gro und; its multi-methodological – multi-

disciplinary character allows for very many c ross-fertilizations.

In 2003, at TU Delft, the Delft Centre for Computational Science and

Engineering (www.cse.tudelft.nl) was founded. Computational groups from

various disciplines participate in the centre. In this book, we follow the dis-

cipline axis. Most of the disciplinary groups in the Delft Centre for CSE

contributed with a chapter on one or more of their own favorite resear ch top-

ics. The book is intended for readers, not necessarily numerical specialis ts,

who are involved in CSE somehow. Our aim is to provide the reader with an

impression of CSE’s challenge s and opportunities.

This book is the work of many people, whom we owe thank s. We thank Piet

Wesseling for his visionary work in founding the Delft Centre for Computa-

tional Science and Engineering. Rector Magniﬁcus Jaco b Fokkema is thanked

for his stimulus in preparing this book. Las t but not least, we thank the au-

thors for their eﬀorts put into the prepar ation of their chapters.

December 2008 Barry Koren and Kees Vuik

Preface by the editorsviii

Contents

A Model-Order Re ductio n Approach to Parametric

R.F. Remis and N.V. Budko

On Numerical Issues in Time Accurate Laminar Reacting

S. van Veldhuizen, C. Vuik, and C.R. Kleijn

Parallel Scientiﬁc Computing on Loosely Coupled

T.P. Collignon and M.B. van Gijzen

Data Assimilation Algorithms for Numerical Model

A.W. Heemink, R.G. Hanea, J. Sumihar, M. Roest, N. Velzen, and

M. Verlaan

Radial Basis Functions for Interface Interpolation and Mesh

A. de Boer, A.H. van Zuijlen, and H. Bijl

Least-Squares Spectral E lement Methods in Computational

M. Gerritsma and B. De Maerschalck

Finite-Volume Discretizations and Immersed Boundaries

Y. Hassen and B. Koren

Large Eddy Simulation of Turbulent Non-Premixed Jet

ith a High Order Numerical Metho

S. van der Hoeven, B.J. Boersma, and D.J.E.M. Roekaerts

E. Javierre, and A. van Keulen

A Suite of Mathematical Models for Bone Ingrowth, Bone

F.J. Vermolen, A. Andreykiv, E.M. van Aken, J.C. van der Linden,

Shifted-Laplacian Preconditi oners for Heterogeneo us

C.W. Oosterlee, C. Vuik, W.A. Mulder, and R.-E. Plessix

Helmholtz

Problems

107

Deformation

143

Fluid

Dynamics

179

229

Flames

w d

269

Fracture Healing and Intra-Osseous Wound Healing

2 98

Electromagnetic

Inversion

Gas

Flow

Solvers

Networks of Computers

Numerica

S.D.A. Hannot and D.J. Rixen

Simulation of Progressive Failure in Composite Laminates

F.P. van der Meer and L.J. Sluys

Numerical Modeling of Wave Propagation, Breaking and

G.S. Stelling and M. Zijlema

G. Abbate, B.J. Thijsse, and C.R. Kleijn

Multi-Scale PDE-Based Design of Hierarchically Structured

G. Wang, C.R. Kleijn, and M.-O. Coppens

S. Luding

Contents

l Mod e ling of the Electromechanical Interaction

315

343

Run-Up on a Beach

373

403

Porous Catalysts

437

Hybrid Navier-Stokes/DSMC Simulations of Gas Flows

with

Rarefied-Continuum Transitions

From M o l e c u l a r Dynamics and Part i c l e Simulations

towards Constitutive R e lations fo r Continuum theory

453

in MEM

A Model-Order Reduction Approach to

Parametric Electromagnetic Inversion

Rob F. Remis and Neil V. Budko

Abstract Inverse scattering is a systematic approach to nondestructive testing, geo-

physical prospecting, remote sensing, and medical imaging. Being both nonlinear

and ill-posed, inverse scattering problems are among the most challenging in com-

putational science. In this chapter we expose the intimate connection between these

problems and reduced-order modeling techniques, which allow signiﬁcant reduction

in computational complexity and efforts. Exploiting the natural symmetries of the

electromagnetic ﬁeld equations we develop and analyze reduced-order models for

the parametric inversion problems arising in effective medium theory, metamateri-

als, and photonics. These models are Pad

e approximations of the measured scattered

ﬁeld. The achieved signiﬁcant computational gain allows us to solve these large nu-

merical problems by simple inspection of a two-dimensional objective functional.

1 Introduction

In many applications we want to look inside an object without breaking it (non-

destructive testing), or digging it up (geophysical prospecting), or cutting it open

(medical imaging). Electromagnetic waves are often used for this purpose due to

their relatively large penetration depth. The basic idea is to illuminate the object and

to reconstruct its interior from the scattered ﬁeld measurements made somewhere

outside the object. This reconstruction problem is called an inverse scattering prob-

lem. The electromagnetic constitutive parameters one usually wants to reconstruct

are the permittivity ε and the conductivity σ . If the object is inhomogeneous these

parameters vary with position.

Rob F. Remis and Neil V. Budko

Faculty of Electrical Engineering, Mathematics and Computer Science, Laboratory of Electromag-

netic Research, Mekelweg 4, 2628 CD Delft, The Netherlands, e-mail: R.F.Remis@TUDelft.NL

and N.V.Budko@TUDelft.NL

Lecture Notes in Computational Science and Engineering 71,

DOI 10.1007/978-3-642-03344-5_1,

B. Koren and C. Vuik (eds.), Advanced Computational Methods in Science and Engineering,