Looking at it from some distance now, my scientific life consisted of three different periods: an introductory and exploratory phase, my successful flirt with finite differences and finally my long struggle with the unruly subject of finite elements. On this page I hope to describe each of these parts in a way that can be enjoyed by both the electromagnetic lay(wo)man and my former colleagues. Finally I will tell a few things about my life after science.
After graduating in Electrical
Engineering in 1970, I
got a job at the Delft University of Technology in Delft, the
Netherlands. Producing and teaching science that was within the realm
of interest of the electromagnetic theory group of this
faculty
would be my work.
For proving one is able to do
scientific work, a PhD thesis had to be written. Before writing my
thesis I first built a general picture of the field of interest and
did some work on various subjects that were hot topics at the time,
like holography and fibre optics. I also studied various
finite-difference techniques, with an application to hyperthermia in
mind. These tools were still too immature at the time and we did not
have enough computing power and memory available yet. My explorations
of the subject area finally led to compiling the thesis:
G. Mur, Computation of electromagnetic fields in inhomogeneous media: Scattering and Guiding properties, PhD Thesis, Delft, 24 May 1978.
This thesis, that consists of a number of papers I published in the 1970's, is still available. You can contact me about it by E-mail . The title of my thesis has accurately predicted the central theme of my scientific career, a subject that is usually referred to as computational electromagnetics, the research concerned with the question of how to efficiently, accurately and reliably compute electromagnetic fields in complex geometries. Because of the very fast development of computer power and memory capacity over the past decades this was a rapidly developing science over that period.
At the time I did my PhD it was customary in our research group to subsequently widen your view by spending a year doing research abroad. I found a place at the Department of Electrical and Electronic Engineering, University of Nottingham, United Kingdom, where I would work together with the then famous TLM (Transmission Line Modeling) advocate Dr. Peter Johns. I would work on FDTD (the Finite-Difference Time-Domain method, one of the work-horses of computational electromagnetics) and together we would analyze and compare TLM with FDTD. My stay in the UK was funded by a 12-month fellowship in the European Science Exchange Programme of the Royal Society. My work in the UK yielded the following two papers.
G. Mur, Absorbing Boundary Conditions for the finite-difference approximation of the time-domain electromagnetic-field equations, IEEE Transactions on Electromagnetic Compatibility, vol. 23, no. 4, pp. 377-382, 1981.
G. Mur, The modeling of singularities in the finite-difference approximation of the time-domain electromagnetic-field equations, IEEE Transactions on Microwave Theory and Techniques, vol. 29, no. 10, pp. 1073-1077, 1981.
The paper describing Absorbing
Boundary
Conditions (ABCs) proved to be a lasting success. The
terms first order Mur and second
order Mur
were coined by their users to indicate which one of the two methods
described in that paper they applied for solving their
problems.
Using those terms as search strings in Google proves that the methods
I developed almost 30 years ago now are still very popular, you may
even find exams on the subject. At a much later date I published an
inhomogeneous version of the ABC,
thus completing my work on this subject.
In 2007
the IEEE Transactions on Electromagnetic Compatibility
(EMC)
celebrated its 50th anniversary. On that occasion they republished
the paper on the ABCs because of it being the Second
Most-Referenced IEEE Transactions on EMC paper in the 50
years of
their existence.Click
this
line for the PDF of the relevant EMC Society Newsletter,
together
with the PDF of the paper.
Recently I
discovered that a lecture on a one-dimensional version of my ABCs,
given by professor Cynthia Furse of the Department of Electrical and
Computer Engineering, University of Utah, USA, can be found on
YouTube, among a number of more advanced lectures on the ABC's. So,
if you want to see the introductory lecture on the subject, click
YouTube
ABC lecture.
Meanwhile,
having returned to Delft, both my personal and my scientific life
(Delft was not quite ready yet for FDTD) were a mess. Fortunately my
personal problems came to a perfect solution and I could direct my
energy to reviving my scientific work again. An exciting scientific
excursion during this period, away from developing methods, was my
cooperation with Professor Jan Baan from the LUMC (Leiden University
Medical Center). We worked on a method to real-time measure the
(variations in time of) the volume of the left ventricle of the human
heart using an impedance catheter.
G. Mur and J. Baan, Computation of the input impedances of a catheter for cardiac volumetry, IEEE Transactions on Biomedical Engineering, vol. 31, pp. 448-453, 1984.
Another interesting activity
during the period
mentioned above was performing contract-research for firms interested
in our kind of expertise. This contract- research made us aware of
the state of the art in the Finite-Element Method (FEM) for
electromagnetics which, next to FDTD, is a very popular
computational tool. This brought me back to the subject of
computational electromagnetics. It struck us (=de
Hoop and me)
that everybody in the Finite-Element world was talking about
the
so-called edge elements that seemed to solve all
their
problems. Edge elements are a special kind of finite element that is
defined on simplices, i.e. on triangles
in 2D and tetrahedra in 3D (see the picture at the top or bottom of
this page). Those
edge elements then had, and possibly for many former colleagues still
have, very much of a panacea, but we did not see that then, we joined
the herd.
Professor Aad (A.T.) de Hoop and I
discussed edge elements at length, aiming at a more accurate and
efficient, a so-called fully consistent, version of them. After a few
weeks we both went home some day and independently designed new edge
elements. Comparing our results the next day our approaches proved to
be fundamentally different, this difference very much reflecting our
different approaches to mathematical science, but after analyzing the
final results we could show that we had designed exactly the same
fully consistent elements! Using them, a simple finite-element
programme was build by me to demonstrate our ideas and they were
published in the paper below.
G. Mur and A. T. de Hoop, A finite-element method for computing three-dimensional electromagnetic fields in inhomogeneous media, IEEE Transactions on Magnetics, vol. 21, no. 6, pp. 2188-2191, 1985.
When using our new elements for practical problems it became clear to us that, although being more efficient than the existing tools, they still were computationally rather expensive and that edge elements proved not to be entirely without problems. Successive improvements regarding both the choice of elements and the formulation of the finite-element method were reported in the following series of papers.
G. Mur, Optimum choice of finite elements for computing three-dimensional electromagnetic fields in inhomogeneous media, IEEE Transactions on Magnetics, vol. 24, no. 1, pp. 330-333, 1988.
G. Mur, Finite-element modeling of three-dimensional electromagnetic fields in inhomogeneous media, Radio Science, vol. 26, no. 1, pp. 275-280, 1991.
I. E. Lager and G. Mur, Compatibility relations for time-domain and static electromagnetic field problems, Applied Computational Electromagnetics Society Journal, vol. 9, no. 2, pp. 25-29, 1994. PDF.
G. Mur, Edge elements, their advantages and their disadvantages, IEEE Transactions on Magnetics, vol. 30, no. 5, pp. 3552-3557, 1994.PDF
In the above paper I summarized our findings until then. I continued my quest, from now on being skilfully supported by Hansi (I.E.) Lager who wrote his PhD thesis on the static and stationary version of the subject.
I. E. Lager and G. Mur, The finite element modeling of static and stationary electric and magnetic fields, IEEE Transactions on Magnetics, vol. 32, no. 3, pp. 631-634, 1996. PDF
I. E. Lager and G. Mur, Finite element method for stationary and static electromagnetic fields, Journal of Applied Physics, vol. 81, no. 8, pp. 4079-4081, 1997.
Our research led to mounting
evidence against
edge elements and at the 1997 COMPUMAG Conference on the Computation
of Electromagnetic Fields in Rio de Janeiro, Brazil, I presented the
final summary of our findings at an exciting Panel
Session on the subject of Edge Elements. A Power Point
version of
my presentation you can find here.
The analysis I presented at the Panel Session
was later published in print as:
G. Mur, The fallacy of edge elements, IEEE Transactions on Magnetics, vol. 34, no. 5, pp. 3244-3247, 1998. PDF
Obviously not everybody was
very pleased with
the critical conclusions I presented, but I was complimented by many,
envied by some and I was also warned by a concerned colleague
saying: "Dear Gerrit, Rio may be a dangerous city
but
from now on this conference room is even more dangerous for you."
After a nice 4 weeks holiday in various corners of Brazil, and where
we even met the legendary (in Holland), or infamous (in Germany),
Harm Dost in his very nice Pousada "Nova Holanda", about
13km. from Canguaretama, Rio Grande do Norte.
I
arrived home unharmed to continue my work on finite
elements. The
very explicit conclusions of this paper still remain unrefuted. We
continued our work with the intention to find solutions to the
fundamental reliability problems we had encountered.
I. E. Lager and G. Mur, Generalized Cartesian finite elements, IEEE Transactions on Magnetics, vol. 34, nr. 4, p. 2220-2227, 1998. PDF
G. Mur and I. E. Lager, A finite-element method for the modeling of electromagnetic fields using generalized Cartesian elements, IEEE Transactions on Magnetics, vol. 35, no. 3, pp. 1376-1379, 1999. PDF
G. Mur and I.E. Lager, A finite element package for electromagnetics using generalized Cartesian elements, Software for electrical Engineering. Analysis and Design IV, A. Konrad and C.A. Brebbia (editors), WITPRESS, Southampton, pp. 203-212, 1999.
Unfortunately our scientific
quest has
ended with the disappointing conclusion that the type of
finite-element method we had in mind, with or without edge elements,
could not be made fully reliable. Because of this the possibility of
obtaining, possibly undetected, erroneous results,
in this
context they are often kindly referred to as "spurious
solutions" or "spurious modes",
remains. This absence of reliability has far-reaching consequences
that many still prefer to, mostly silently but sometimes even
explicitly, ignore.
Some additional explicit
observations on the causes of spurious solutions were
presented
in:
G. Mur and I. E. Lager, On the causes of spurious solutions in electromagnetics, Electrotechnics, vol. 22, no. 4, pp. 357-367, 2002. PDF
To summarize my sad story about the
finite edge
elements it can be said that we rediscovered that it is very
unwise to impose 4 independent conditions on a vector having only 3
components, or alternatively to have more unknowns than independent
equations. But didn't we all learn that long ago?
New
formulations of a finite-element method for computational
electromagnetics that aim at avoiding the problems mentioned above
were proposed in:
I. E. Lager and G. Mur, Application of the Domain-Integrated Field Relations Method to the Solution of Large Scale Static and Stationary Magnetic Field Problems, IEEE Transactions on Magnetics, vol. 38, no. 2, pp. 465-468, 2002. PDF
I. E. Lager, E. Tonti, A. T. de Hoop, G. Mur, and M. Marrone, Finite Formulation and Domain-Integrated Field Relations in Electromagnetics—A Synthesis , IEEE Transactions on Magnetics, vol. 39, no. 3, pp. 1199-1202, 2003. PDF
I did not actively contribute to these last two papers, but the authors who did, expressed their appreciation for my work on the subject by making me their co-author. I wish to use this opportunity to thank them for this honor.
From early 2001 I was unable to continue my work
because of a heavy fatigue that forced me to stay at home almost
permanently. It turned out to be a new symptom of the Primary
Progressive version of Multiple Sclerosis that I
was diagnosed
with the year before. For overcoming this fatigue a companion
in distress advised my to start biking, which fortunately is, and
always was, my type of sport. I followed his advise and started
biking, twice a week, in summer on the roads around Delft, in winter
in the gym. In the beginning biking a small distance of about 3 or 4
kilometers were a major mental and physical effort. I went on,
improving slowly, and two years later I had progressed to biking 100
or sometimes even 160 kilometers a day, still doing this twice
a
week. Not counting my efforts in the gym, I biked a total distance of
about 10,000km over that period. Although the fatigue has not left me
completely I can cope with it now and I am still very happy with the
excellent advice I got.
After my retirement in 2002
I first started modeling in clay and wax and subsequently I
started sculpting in stone, first in relatively soft materials like
alabaster and serpentine and nowadays mainly in harder materials like
the beautiful black Noir de Mazy (Belgian marble) and often in
marble. Sculpting is a very physical outdoors (because of the dust)
activity that keeps me physically fit, without needing to bike all
day. It requires about the same set of skills as my scientific work
did, i.e. a good spatial insight, a lot of stamina and finally also
some creativity. Now that you have come this far, do also have a look
at these more recent results of my efforts, I hope you like some of
them, and please don't hesitate to comment using E-mail. Below you
can choose between a Dutch and an English version of the presentation
of my sculptures.
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Gert Mur