Postdoc mathematical analysis and scientific computing in wave equations

The faculty of Electrical Engineering, Mathematics and Computer Science from the University of Twente educates, and conducts research with approximately 2000 students including 300 PhD-students. The faculty is also responsible for a large volume of service education for programmes of other faculties. The faculty has approximately 300 permanent staff.

The faculty of EEMCS conducts BSc-programmes in Electrical Engineering, Applied Mathematics, Computer Science and Business Information Systems and MSc-programmes in Electrical Engineering, Mechatronics, Applied Mathematics, Business Information Technology, Computer Science, Telematics, Human Media Interaction en Embedded Systems and is partner in various programmes of other faculties.

Postdoc mathematical analysis and scientific computing in wave equations

Within the chair Applied Analysis and Mathematical Physics of the Faculty of Electrical Engineering, Mathematics and Computer Science, there is vacancy for a postdoc. He or she will be part of the project “Wave propagation and reflection seismology” of Dr. C.C. Stolk, which is funded by NWO via a VIDI subsidy. The postdoc is to work on innovative methods for the wave equation, using ideas from analysis to develop fast numerical schemes. Seismic applications can be part of this work.

Research topic

Reflection seismology is a technique used in industry and in academia to study the properties of the inside of the earth using acoustic waves that are generated and observed at the surface. The most important application is in the exploration for oil and gas, but it is also used to study fundamental geophysical questions about the Earth, and in engineering applications. The problem of converting the measured data into reliable images of the Earth leads to much interesting mathematics. For example regarding seismic imaging and migration, inverse problems and computational methods for wave equations. This last aspect is important since the problem is usually computationally very intensive and computation of solutions to the wave equation in practice takes up most computational time. Not only is this an interesting problem for applying mathematical ideas by mathematicians, but also mathematicians can learn from the methods that geophysicists have come up with over time. Often this involves a combination of ideas about physical wave propagation and reflection, analysis and geometry and computational aspects.

We propose the postdoc to work on recent, new techniques for wave equations. Some references are given below. Different techniques are used to obtain an improvement in speed or accuracy. For example special basis functions, or special ways to approximate operators, using careful decompositions and near-sparsity. Or explicit propagation by translating over the rays of geometrical optics (so far only in 1-D). This is based on high-frequency, ray theory. In these ways the expensive small time step requirement (CFL condition) for finite difference or finite element schemes can be circumvented. Such approaches combine analytical and numerical ideas, and require further research.

References:

E. Candes, L. Demanet, and L. Ying, “Fast computation of fourier integral operators”, Technical report, Stanford University, 2006, see http://math.stanford.edu/~laurent/html/publications.html.

C. C. Stolk, “A fast method for linear waves based on geometrical optics”, preprint 2007.

G. Beylkin and K. Sandberg, “Wave propagation using bases for bandlimited functions”, Wave Motion, 41(3):263–291, 2005.

Group

There is quite a large number of people interested in simulation and numerical analysis of such differential equations from physics, coming from two chairs. These are Applied Analysis and Mathematical Physics (AAMP, www.math.utwente.nl/aamp), and Numerical Analysis and Computation Mechanics (NACM, www.math.utwente.nl/nacm). Together these groups consist of about 15 permanent staff and approximately the same number of PhD students and postdocs.

Candidates

The Postdoc should have excellent academic achievements in mathematics or applied mathematics. He or she has a strong background in mathematical analysis and/or numerical analysis, and a good knowledge of PDEs. Some experience with programming numerical codes will be beneficial.

Employment

We offer a fulltime position (38 hrs/week), with a maximum duration of 2 years. The gross salary will start from approximately EUR 2740 per month, depending on experience and background.

Contact

For further information, contact

Dr. C.C. (Chris) Stolk
University of Twente
Dept. of Applied Mathematics
POBox 217, 7500 AE Enschede, The Netherlands
Phone: +31 53 4893460, email: c.c.stolk@ewi.utwente.nl

Application

Letters of applicants (preferably by email) should be sent to the address given above and should contain a CV including references, full academic record and a letter of motivation.

Reactions are expected before January 24, 2008.

http://www.utwente.nl/vacatures/vacatures_externe_werving/07-172-eng.doc/