A selection from the list of publications of Gerrit Mur,


The story of my scientific life

   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. I also have a link to some new ideas about finite elements for electromagnetics. Finally I will tell a few things about my life after science.

1. My PhD

   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:

1.      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.

  2. FDTD

   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.

2.      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.

3.      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.

4.      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.

3. FEM

    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.

5.      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.

6.      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.

7.      G. Mur, Finite-element modeling of three-dimensional electromagnetic fields in inhomogeneous media, Radio Science, vol. 26, no. 1, pp. 275-280, 1991.

8.      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.  

9.      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. 

10.  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

11.  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:

12.  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, during which 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.

13.  I. E. Lager and G. Mur, Generalized Cartesian finite elements, IEEE Transactions on Magnetics, vol. 34, nr. 4, p. 2220-2227, 1998. PDF

14.  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

15.  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:

16.  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:

17.  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

18.  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.

   NEW: Some of my recent thoughts about the finite-element modeling of electromagnetic fields can be found here. Do have a look there if you are familiar with edge elements.

4. My second life as a sculptor

   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 was 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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