Wave Propagation and Scattering, Inverse Problems, and ...

Workshop on
Wave Propagation and Scattering,
Inverse Problems, and Applications in
Energy and the Environment
November 21-25, 2011
as part of the
Radon Special Semester 2011 on
Multiscale Simulation & Analysis in Energy and the Environment

The efficient computation of wave propagation and scattering is a core problem in numerical mathematics,
which is currently of great research interest and is central to many applications in energy and the environment.
Two generic applications which resonate strongly with the central aims of this special semester
are forward wave propagation in heterogeneous media and seismic inversion for subsurface imaging. As
an example of the first application, modelling of absorption and scattering of radiation by clouds, aerosol
and precipitation is used as a tool for interpretation of (e.g.) solar, infrared and radar measurements,
and as a component in larger weather/climate prediction models in numerical weather forecasting. One
key numerical component in this modelling is the prediction of the total optical properties and the full
scattering matrix from an ensemble of irregular particles. The underlying mathematical problem is that
of accurately computing high frequency wave propagation in a highly heterogeneous medium. As an
example of the second application, inverse problems in wave propagation in heterogeneous media arise
in the problem of imaging the subsurface below land or marine deposits. Solutions to this problem have
a number of environmental uses, for example in the location of hydrocarbon-bearing rocks, in the monitoring
of pollution in groundwater or in earthquake modelling. A seismic source is directed into the
ground and the material properties of the subsurface are inferred by analysing the observed scattered
field, recorded by sensors. The inversion process (a large scale optimisation problem) is complicated by
the presence of multiple reflections and the fact that the scales involved in the exploration of sub-marine,
sub-basalt or sub-salt oil reservoirs can be many kilometres in extent, leading to a challenging multi-scale
problem. Current iterative methods for solving the inverse problem involve repeated solution of the forward
problem (the computational kernel), which is typically a frequency-domain reduction of the elastic
(or scalar) wave equation with high frequency and typically highly spatially varying wave speed. If the
inversion is to be competitive, the key underlying problem to be overcome is the design of robust and
scalable solvers for the large highly indefinite linear systems arising from these problems.
The workshop will bring together key numerical mathematicians whose interest is in the analysis and
computation of wave propagation and scattering problems, and in inverse problems, together with practitioners
from engineering and industry whose interest is in the applications of these core problems.
Particular problems to be considered will be (i) The design of accurate methods for solving frequency
domain problems; (ii) The use of wave enriched and other hybrid approximation strategies in the solution
of high-frequency problems; (iii) Fast linear algebra solvers for frequency domain problems in heterogeneous
media; (iv) advanced inverse problem approaches for wave problems such as reverse time migration
which move away from traditional ray-based approaches in the high frequency case.
Workshop Organizers
Ivan G. Graham, University of Bath, UK
Ulrich Langer, Johann Radon Institute & University of Linz, Austria
Jens Markus Melenk, Vienna University of Technology, Austria
Mourad Sini, Johann Radon Institute, Austria
cover picture of tsunami simulation in Indian Ocean:
courtesy of Jörn Behrens (KlimaCampus, Universität Hamburg) and Widodo S. Pranovo (Indonesia).

Welcome
to Linz and thank you very much for participating in the sixth RICAM Special Semester on Multiscale
Simulation & Analysis in Energy and the Environment, hosted by the Johann Radon Insitute for
Computational and Applied Mathematics (RICAM) from October 3 to December 16, 2011.
Technological advances have greatly improved our quality of life. However, they bring with them a
huge surge in energy requirements which in turn puts at risk our entire bio-sphere. It is of paramount
importance to predict these risks and to develop better solutions for the future. One of the central tasks
is the accurate simulation of multiphase flow above and under ground. The risk analysis and uncertainty
quantification, as well as the assimilation of data require statistical tools and efficient solvers for stochastic
and deterministic PDEs as well as for the associated inverse problems. The key features that make it
extremely hard to predict these physical phenomena accurately are the multiple time and length scales
that arise, as well as the lack of and uncertainty in data. Because of the highly varying scales involved, the
resolution of all scales is currently impossible even on the largest supercomputers. While there is a fairly
long history of empirically successful robust computational techniques for certain multiscale problems,
the rigorous (numerical) analysis of such methods is of extremely high current interest.
The goal of the special semester is to provide a stimulating environment for civil engineers, hydrologists,
meteorologists and other environmental scientists to address together with mathematicians working at
the cutting edge of rigorous numerical analysis for multiscale (direct and inverse) problems the emerging
challenges in the quantitative assessment of the risks and uncertainties of atmospheric and subsurface
flow, focusing in particular on
• Simulation of Flow in Porous Media and Applications in Waste Management and CO2 Sequestration
• Large-Scale Inverse Problems and Applications in the Earth Sciences
• Data Assimilation and Multiscale Simulation in Atmospheric Flow
• Wave Propagation and Scattering, Direct and Inverse Problems and Applications in Energy and
the Environment
• Multiscale Numerical Methods and their Analysis and Applications in Energy and the Environment
• Stochastic Modelling of Uncertainty and Numerical Methods for Stochastic PDEs
Specific activities planned for the Special Semester are
• 4 thematic workshops addressing some of the key topics of the Special Semester;
• Special Lecture Series on ”Multilevel Methods for Multiscale Problems”;
• Graduate Seminar on ”Multiscale Discretization Techniques”;
• Wednesday Research Kitchen;
• Public Lecture by Prof. Jörn Behrens (KlimaCampus, Universität Hamburg) on
“Tsunami Früh-Warnung: Mathematik und Wissenschaftliches Rechnen im Dienste der Sicherheit”.
We sincerely hope that you enjoy your stay in Linz!
Local Organizing Committee Program Committee
Robert Scheichl, Bath & RICAM (Chair) Peter Bastian, University of Heidelberg, Germany
Jörg Willems, RICAM (Coordinator) Mike Cullen, Met Office, Exeter, UK
Johannes Kraus, RICAM (Co-Coordinator) Heinz Engl, RICAM & University of Vienna, Austria
Erwin Karer, RICAM (Co-Coordinator) Melina Freitag, University of Bath, UK
Ivan G. Graham, University of Bath, UK
Ulrich Langer, RICAM & University of Linz, Austria
Markus Melenk, TU Vienna, Austria
Robert Scheichl, University of Bath, UK (Chair)
Mary F. Wheeler, University of Texas at Austin, USA

Contents
Information 2
Workshop Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Social Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Restaurants and Cafes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
General Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Program 5
Posters 7
Abstracts 8
Abstracts for Posters 17
List of Participants 20
1

Information
Workshop Information
Registration. The workshop registration will be on November 21st, 2011 from 9:00 - 9:40 am next to the
seminar room SP2 416 on the 4th floor of the Science Park Building 2 (see floor plan). Participants
that arrive later in the week can register at the special semester office SP2 456.
Registration Fee. Non-invited participants are kindly asked to pay the registration fee in cash upon
registration.
Campus plan and overview map as well as a floor plan of the 4th floor of the workshop venue (Science
Park Building 2) are located on the next pages.
Seminar room. The workshop will take place in seminar room SP2 416 on the 4th floor of the Science
Park Building 2 (see floor plan).
Program. A time schedule for the workshop is located on the backside of this booklet.
Coffee breaks. The coffee breaks will be in the corridor of the 4th floor of the Science Park Building 2.
Internet access. There will be an extra information sheet regarding internet access available at registration.
Social Events
Welcome Reception & Poster Session. Monday, November 21st, 2011, 5:15 pm, on the 4th floor of
the Science Park Building 2.
Conference Dinner. Thursday, November 24th, 2011, 7:00 pm, at the restaurant “Kepler’s”, situated
in the Mensa building
Restaurants and Cafes
• Mensa Markt (lunch time only) - Main canteen of the University (see campus plan)
• KHG Mensa (lunch time only) - Smaller canteen - good traditional food (see overview map: “KHG
Linz”)
• Pizzeria “Bella Casa” - Italian and Greek restaurant (located next to the tram stop)
• Chinese restaurant “Jadegarten” - (located close by the tram stop, adjacent to “Bella Casa”)
• Asia restaurant “A2” - (located behind the Science Park on Altenbergerstrasse)
• “Chat” cafe - coffee, drinks and sandwiches (located in the “Hörsaaltrakt” - see overview map)
• Cafe “Sassi” - coffee, drinks and small snacks (located in the building “Johannes Kepler Universität”
- see overview map)
• Bakery “Kandur” - bakery and small cafe (located opposite the tram stop)
General Information
Accommodation. The arranged accomodation for invited participants is the “Sommerhaus” hotel. You
can find its location in the overview map on page 4.
Special Semester Office: Room SP2 456. The special semester administrator is Susanne Dujardin.
Audiovisual & Computer Support. Room SP2 458, Wolfgang Forsthuber or Florian Tischler.
2

Orientation/ Local Transport. From the railway station you have to take tram number 1 or 2 in
direction “Universität”. It takes about 25 minutes to reach the desired end stop “Universität”.
In order to get to the city center of Linz (“Hauptplatz”) and back you have to take again tram
number 1 or 2 (about 20 minutes). For more information see www.ricam.oeaw.ac.at/location/.
Taxi Numbers.
+43 732 6969 Oberösterreichische Taxigenossenschaft
+43 732 2244 2244 Linzer Taxi
+43 732 781463 Enzendorfer Taxi & Transport
+43 732 2214 Linzer Taxi
+43 732 660217 LINTAX TaxibetriebsgesmbH
Further important phone numbers.
+43 (0)732 2468 5222 RICAM & Special Semester Office (Susanne Dujardin)
+43 (0)732 2468 5250/5255 RICAM IT Support (Florian Tischler/ Wolfgang Forsthuber)
+43 (0)732 2457-0 Reception of Hotel Sommerhaus
133 General emergency number for the police
144 General emergency number for the ambulance
More information about RICAM can be found at www.ricam.oeaw.ac.at. See also the Special
Semester webpage www.ricam.oeaw.ac.at/specsem/specsem2011/ for additional information.
Figure 1: 4th floor of Science Park Building 2.
Figure 2: Campus plan
3

Figure 3: Overview map
4

Program
Monday, November 21st
00:00 - 09:40 Registration
09:40 - 09:50 Opening
09:50 - 10:40 Ralf Hiptmair (ETH Zürich)
10:40 - 11:10 Coffee Break
“Convergence of truncated T-matrix approximation”
11:10 - 12:00 Timo Betcke (University College London)
12:00 - 14:00 Lunch Break
“Modulated plane wave methods for Helmholtz problems in heterogeneous media”
14:00 - 14:50 Susan Minkoff (University of Maryland, Baltimore County)
14:50 - 15:20 Coffee Break
“Two scale wave equation modeling”
15:20 - 16:10 Paul Childs (Schlumberger Cambridge Research)
“Numerics of waveform inversion for seismic data”
16:10 - 17:00 Chris Stolk (University of Amsterdam)
“Seismic inverse scattering by reverse time migration”
17:15 Poster Session & Welcome Reception
Tuesday, November 22nd
09:00 - 09:50 Martin Gander (University of Geneva)
“Are absorbing boundary conditions and perfectly matched layers really so different?”
09:50 - 10:40 Lothar Nannen (Vienna University of Technology)
10:40 - 11:10 Coffee Break
“Hardy space infinite elements for exterior Maxwell problems”
11:10 - 12:00 Habib Ammari ( École Normale Supérieure)
11:30 - 14:00 Lunch Break
“Electromagnetic invisibility and super-resolution”
14:00 - 14:50 Marcus Grote (University of Basel)
14:50 - 15:20 Coffee Break
“Discontinuous Galerkin methods and local time stepping for transient wave propagation”
15:20 - 16:10 Joachim Schöberl (Vienna University of Technology)
16:10 - 17:00 Break
“Hybrid discontinuous Galerkin finite element methods for the Helmholtz equation”
17:15 - 18:00 Radon colloquium by Martin Gander (University of Geneva)
“From Euler, Schwarz, Ritz and Galerkin to Modern Computing”
5

Wednesday, November 23rd
09:00 - 09:50 Ronny Ramlau (University of Linz)
“Inverse problems in adaptive optics”
09:50 - 10:40 Frédéric Nataf (Université Paris 6, Laboratoire J.L. Lions)
10:40 - 11:10 Coffee Break
“Time reversed absorbing condition in the partial aperture case”
11:10 - 12:00 Olaf Steinbach (Graz University of Technology)
“Boundary element methods for acoustic and electromagnetic scattering problems”
free afternoon (please feel free to make use of the seminar room and the Special
Semester offices)
Thursday, November 24th
09:00 - 09:50 Roland Potthast (Deutscher Wetterdienst & University of Reading)
“Approaches to dynamical inverse scattering problems”
09:50 - 10:40 Thanh Nguyen (RICAM)
10:40 - 11:10 Coffee Break
“Inverse obstacle scattering problems using multifrequency measurements”
11:10 - 12:00 Guanghui Hu (WIAS Berlin)
12:00 - 14:00 Lunch Break
“Direct and inverse scattering of elastic waves by diffraction gratings”
14:00 - 14:50 Jari Toivanen (University of Jyväskylä)
14:50 - 15:20 Coffee Break
“Domain decomposition and multigrid preconditioners for the Helmholtz equation
in layered and heterogeneous media”
15:20 - 16:10 Radek Tezaur (Stanford University)
“The discontinuous enrichment method and its domain decomposition solver for
the Helmholtz equation”
16:10 - 17:00 Ira Livshits (Ball State University)
“Algebraic multigrid algorithm for solving Helmholtz equations with large wave
numbers”
19:00 Conference dinner
6

Friday, November 25th
09:00 - 09:50 Manfred Kaltenbacher (University of Klagenfurt)
“Spectral finite elements for a mixed formulation in computational acoustics taking
flow effects into acount”
09:50 - 10:40 Euan Spence (University of Bath)
10:40 - 11:10 Coffee Break
“Stability and conditioning of boundary integral methods for high frequency scattering”
11:10 - 12:00 Simon Chandler-Wilde (University of Reading)
12:00 Closing
Posters
“Numerical-Asymptotic Integral Equation Methods for High Frequency Scattering”
The poster session will take place on the 4th floor of the 2nd Science Park Building. It will start
at 5:15 pm on Monday, November 21st.
Carlos Borges (Worcester Polytechnic Institute)
“Numerical solution of the high frequency 2D direct scattering problem for convex objects using nonuniform
B-splines”
Victor A. Kovtunenko (University of Graz)
“Variational methods for the identification of objects”
Marie Kray (Université Paris 6)
“Time reversed absorbing conditions: discrimination between one single inclusion and two close inclusions
in a non-homogeneous medium”
Jens Markus Melenk (Vienna University of Technology)
“Wavenumber-explicit convergence analysis for the Helmholtz equation: hp-FEM and hp-BEM”
Andrea Moiola (ETH Zürich)
“Trefftz-discontinuous Galerkin methods for time-harmonic Maxwell’s equations”
Imbo Sim (University of Klagenfurt)
“Stable absorbing layer for convective wave propagation”
7

Abstracts
“Electromagnetic invisibility and super-resolution”
Habib Ammari
École Normale Supérieure
Abstract
The aim of this talk is threefold: - to give a mathematical justification of cloaking due to anomalous
localized resonance; - to provide an original method for enhancing near cloaking; - to achieve resolved
inclusion imaging.
“Modulated plane wave methods for Helmholtz problems in heterogeneous media”
Timo Betcke
Department of Mathematics
University College London
Gower Street, London, WC1E 6BT, UK
Abstract
A major challenge in seismic imaging is full waveform inversion in the frequency domain. If an
acoustic model is assumed the underlying problem formulation is a Helmholtz equation of the form
� �2 ω
−∆u − u = f,
c(x)
where c(x) is the varying speed of sound in the heterogeneous medium. Typically, in seismic applications
the solution u has many wavelengths across the computational domain, leading to very
large linear systems after discretisation with standard finite element methods. Much progress has
been achieved in recent years by the development of better preconditioners for the iterative solution
of these linear systems. But the fundamental problem of requiring many degrees of freedom per
wavelength for the discretisation remains.
For problems in homogeneous media, that is c is constant, plane wave finite element methods have
gained significant attention. The idea is that instead of polynomials on each element we use a linear
combination of plane waves of the form e i ω c d j ·x , where the dj are direction vectors of unit length.
These basis functions already oscillate with the right wavelength, leading to a significant reduction in
the required number of unknowns. However, higher-order convergence is only achieved for problems
with constant or piecewise constant media.
In this talk we discuss the use of modulated plane waves of the form p(x)e i ω ¯c d j ·x for problems in
heterogeneous media, where p is a polynomial of low degree (typically 2 or 3) and ¯c is a constant
approximation to the speed of sound in an element. The idea is that high-order convergence in a
varying medium is recovered due to the polynomial modulation of the plane waves. Wave directions
are chosen based on information from raytracing or other fast solvers for the eikonal equation. This
approach is related to the Amplitude FEM originally proposed by Giladi and Keller in 2001. However,
for the assembly of the systems we will use a discontinuous Galerkin method, which allows a simple
way of incorporating multiple phase information in one element. We will discuss the dependence of
the element sizes on the wavelenth and the accuracy of the phase information, and present several
examples that demonstrate the properties of modulated plane wave methods for heterogeneous media
problems.
“Numerical-asymptotic integral equation methods for high frequency scattering”
Simon Chandler-Wilde
Department of Mathematics and Statistics
University of Reading
Reading RG6 6AX, UK
Abstract
Conventional discretisation methods for wave propagation and scattering (finite elements, finite
difference, boundary element, ...) have costs which increase rapidly as the frequency increases because
of the need for large numbers of degrees of freedom to resolve the oscillatory solution. In particular,
this is an issue in boundary element calculations for time harmonic problems, where in 3D the degrees
of freedom need to increase in proportion to k 2 , where k is the wave number, in order to maintain a
fixed number of degrees of freedom per wavelength, required to maintain accuracy. High frequency
asymptotic methods, in the other hand, based on ray tracing/solving eikonal/transport equations,
8

have a cost which is fixed as k increases, but have unacceptably low accuracy for many problems,
except at very high k.
In this talk, we overview progress in developing numerical methods for high frequency problems
which try to combine standard numerical and asymptotic approaches. In particular, we focus on
boundary integral equation based methods, describing progress in generating numerical schemes which
deliver an arbitrarily high requested accuracy with a number of degrees of freedom which provably
(through numerical analysis theorems and numerical experiments) needs only grow logarithmically
as k increases.
The methodology is to obtain knowledge of the phase structure of the solution, by rather elementary
high frequency ray analysis, and to build this phase structure into the basis functions used to
approximate the solution. This idea, in a simple form, dates back at least to [1], but the methodology
has seen a wealth of new ideas in the last 5-10 years, see [1–6] and the references therein, which we
review.
[1] T. Abboud, J.C. Nédélec, B. Zhou, Méthode des équations intégrales pour les hautes fréquencies,
C.R. Acad. Sci. Paris., 318 Série I (1994), 165-170.
[2] O.P. Bruno, F. Reitich, High Order Methods for High-Frequency Scattering Applications, In:
Modeling and Computations in Electromagnetics, H. Ammari (Ed.), Springer, 2007, pp. 129–164.
[3] S.N. Chandler-Wilde, I.G. Graham, Boundary Integral Methods in High Frequency Scattering, In:
Highly Oscillatory Problems, B. Engquist, T. Fokas, E. Hairer, A. Iserles (Eds.), Cambridge University
Press, 2009, pp. 154–193.
[4] M. Ganesh, S.C. Hawkins, A Fully Discrete Galerkin Method for High Frequency Exterior Acoustic
Scattering in Three Dimensions, J. Comp. Phys. 230, (2011), 104–125.
[5] A. Spence, S.N. Chandler-Wilde, I.G. Graham, V.P. Smyshlyaev, A New Frequency-Uniform Coercive
Boundary Integral Equation for Acoustic Scattering, Comm. Pure Appl. Math., 64, (2011),
1384-1415.
[6] S.N. Chandler-Wilde, I.G. Graham, S. Langdon, E. Spence, Numerical-asymptotic boundary integral
methods in high frequency acoustic scattering, to appear in Acta Numerica.
“Numerics of waveform inversion for seismic data”
Paul Childs
Schlumberger Cambridge Research
Abstract
Depth imaging and inversion of seismic data is becoming commonplace within the seismic exploration
industry. However, the inversion procedures used today often fail to find the global minimum,
and careful multiscale data processing must be included in the workflow. Although developed by
Tarantola et al in the 1980s, there are still numerous mathematical challenges remaining relating to
non-uniqueness, size of the null space of the inversion operator, and the sheer computational size
of industrial datasets. In this talk, we will review some approaches to improving the robustness
of the full waveform inversion method, which today is regarded as a highly interpretive procedure.
Because the PDE-constrained inversion procedure used in industry can be very expensive due to the
large number of PDE solves required, we will review and address some of the numerical challenges
in this area. The talk will serve as an introduction to the subject and will concentrate mainly on
computational developments. Illustrations will be given with industrial examples from full waveform
inversion of seismic data.
“Are absorbing boundary conditions and
perfectly matched layers really so different?”
Martin J. Gander
Section of Mathematics
University of Geneva
2-4 Rue du Lièvre, CH–1211 Genève 4
Abstract
In order to truncate infinite computational domains, there are two major competitors: absorbing
boundary conditions and perfectly matched layers. The former use approximations of the Dirichlet
to Neumann map, and the latter adds a layer outside the truncated domain, in which a modified
equation is solved, which absorbs outgoing parts of the solution.
Using the concept of the pole condition, we show for a model problem that these two seemingly
very different techniques are in fact related. For the particular case of an absorbing boundary
condition given by a Pade approximation of the Dirichlet to Neumann map, we show that a natural
implementation leads to a layer structure corresponding to a perfectly matched layer with an
exponentially scaled outer problem.
9

“From Euler, Schwarz, Ritz, and Galerkin to modern computing”
Martin J. Gander
Section of Mathematics, University of Geneva, 2-4 Rue du Lièvre, CH–1211 Genève 4
Abstract
The origins of modern computing are dispersed over centuries, often in the work of pure mathematicians,
who invented methods in order to understand mathematical objects and prove theorems.
A typical example is the famous Schwarz method for parallel computing, whose origins lie in a problem
in Riemann’s audacious proof of the Riemann mapping theorem. Another example is the finite
element method, which has its origins in the variational calculus of Euler-Lagrange and in the thesis
of Walther Ritz, who died just over 100 years ago at the age of 31 from tuberculosis. We will see
in this talk that the path leading to modern computational methods and theory was a long struggle
over three centuries requiring the efforts of many great mathematicians.
“Discontinuous Galerkin methods and local time stepping for transient wave propagation”
Marcus J. Grote
Mathematisches Institut
Rheinsprung 21, CH–4051 Basel
Abstract
The accurate and reliable simulation of transient wave phenomena is of fundamental importance
in a wide range of engineering applications such as fiber optics, wireless communication, seismic
imaging, and non-invasive testing. Finite element methods are probably the most flexible approach
for computational wave propagation in heterogeneous media or complex geometry. When combined
with explicit time integrators, standard conforming finite element methods lead to efficient and highly
parallel methods, if mass-lumping techniques are used. Alternatively, discontinuous Galerkin methods
easily accommodate irregular non-matching grids and hp-refinement, while they inherently lead to
block-diagonal mass matrices. Hence, they also lead to efficient and highly parallel methods when
combined with explicit time-stepping schemes. Nonetheless, both suffer from the severe stability
(CFL) condition imposed on the time step by the smallest elements in the mesh. To circumvent that
CFL condition, we propose high-order explicit local time-stepping schemes, which allow smaller time
steps precisely where the smallest elements in the mesh are located.
This is joint work with J. Diaz (INRIA), T. Mitkova (Basel) and D. Schoetzau (UBC).
“Direct and inverse scattering of elastic waves by diffraction gratings”
Guanghui Hu
WIAS Berlin
Mohrenstr. 39
D–10117 Berlin
Abstract
This talk is concerned with the scattering of a time-harmonic plane elastic wave by an unbounded
periodic structure. Such structures are also called diffraction gratings and have many important
applications in diffractive optics, radar imaging, non-destructive testing, etc.
The talk is arranged into three sections. (i) Variational approach to scattering of plane elastic
waves by an impenetrable two-dimensional periodic structure. Using a variational formulation in a
bounded periodic cell involving a non-local boundary operator, uniqueness and existence of quasiperiodic
solutions are presented under the first (Dirichlet), second (Neumann), third and fourth kind
boundary conditions. (ii) Uniqueness for the inverse problem in determining a polygonal diffraction
grating from near-field measurements under the third or fourth kind boundary conditions. We determine
and classify all the unidentifiable grating profiles corresponding to one given incident pressure or
shear wave, relying on the reflection principle of the Navier equation. (iii) An optimization method for
the inverse problem in recovering an unknown grating profile from scattered elastic waves measured
above the structure. Based on the Kirsch-Kress optimization scheme, we apply a two-step algorithm
to both smooth and piecewise linear gratings for the Dirichlet boundary value problem of the Navier
equation. Numerical reconstructions from exact and noisy data will be shown.
Some results for bi-periodic structures will also be mentioned. This is joint work with Dr. J.
Elschner under the DFG Project: ”Direct and inverse scattering problems for elastic waves”
10

“Convergence of truncated T-matrix approximation”
Ralf Hiptmair
Seminar for Applied Mathematics
ETH Zürich
Abstract
The T-matrix encodes the scattering properties of an obstacle independently of the incident and
receiver directions. It boils down to a basis representation of the operator mapping incident fields
to the far field pattern with respect to (spherical) harmonics. Discretization can be achieved by
truncating the T-matrix, which amounts to using a finite number of basis functions. The truncated
T-matrix can be computed by solving several large forward scattering problems during a preparatory
offline stage. Then, the scattering response to an incident field of any direction or source position
can be computed very fast (online stage).
My presentation is concerned with the a priori analysis of the effect of truncating the T-matrix for
acoustic scattering. Detailed error estimates and predictions of the rates of exponential convergence
are derived for both point-source and plane-wave incident waves. Errors in solving the forward
problem are also taken into account.
This is joint work with M. Ganesh (Colorado School of Mines) and S.C. Hawkins (Macquarie
University, Sydney).
References.
M. Ganesh, S. Hawkins, and R. Hiptmair, Convergence analysis with parameter estimates
for a reduced basis acoustic scattering T-matrix method, Report 2011-04, SAM, ETH Zürich, Zürich,
Switzerland, 2011. To appear in IMA J. Numer. Anal.
“Spectral finite elements for a mixed formulation in computational acoustics taking flow effects into account”
Manfred Kaltenbacher
Applied Mechatronics
University of Klagenfurt
Austria
Abstract
Formulations which include effects of a mean flow on the acoustic wave propagation are mostly
based on a splitting of the unknowns velocity �u, pressure p and density ρ into mean (denoted by an
overline) and fluctuating (denoted by the superscript a) parts. Such an ansatz results, e.g., in the
acoustic perturbation equations as used in computational aeroacoustics [1]
∂p a
∂t + c2 ρ ∇ · �u a + �u · ∇p a = qc ; ρ ∂�ua
∂t + ρ(�u · ∇)�u a + ∇p a = �qm
with c the speed of sound and qc, �qm acoustic source terms. Its variational formulation is then given as
follows (for simplification we use homogeneous Dirichlet boundary conditions): Find (�u , p ′ ) ∈ V × W
such that
�
∂
∂t
p a ϕ, dx − c 2 �
ρ �u
Ω
a �
· ∇ϕ dx + �u · ∇p
Ω
a �
dx = qcϕ dx (1)
ρ
Ω
∂
�
∂t
�v a · � �
ψ dx + ∇p a · � �
ψ dx + ρ (�u · ∇)�u a �
dx = �qm · � ψ dx (2)
Ω
for all ( � ψ , ϕ) ∈ V × W .
Following [2] we apply a mixed formulation and use spectral elements with the following discrete
spaces
Wh = � ϕh ∈ H 1 �
�
�
0 ϕh|Kj ◦ Fj ∈ PN ,
�
Vh = �φh ∈ [L 2 ] d � � |Jj|J −1
j
� φ|Kj ◦ Fj ∈ [PN ] d�
In order to stabilize our formulation, we use similar techniques as for DG-approaches and reformulate
the third term in (2) as a special flux term (upwinding) and furthermore add a jump-term in the
acoustic particle velocity �u a along common element interfaces.
This topic is a joint work with A. Hüppe (University of Klagenfurt), G. Cohen and S. Imperial (IN-
RIA, Paris) and B. Wohlmuth (TU Munich).
[1] R. Ewert and W. Schröder. Acoustic perturbation equations based on flow decomposition via
source filtering. Journal of Comp. Phys., 188:365398, 2003.
[2] G. Cohen and S. Fauqueux. Mixed finite elements with mass-lumping for the transient wave
equation. Journal of Comp. Acoustics, 8:171188, 2000.
Ω
11
Ω
.

“Algebraic multigrid algorithm for solving Helmholtz equations with large wave numbers”
Ira Livshits
Department of Mathematical Sciences
Ball State University
USA
Abstract
In this talk we introduce a new adaptive algebraic multigrid approach for solving indefinite
Helmholtz equations. The proposed approach is an interplay between the idea of multiple smooth
representations of oscillatory kernel components of the Helmholtz operator on coarse grids, as in the
geometric multigrid wave-ray algorithm, and a flexibility of a more recent least-squares Bootstrap
AMG approach, which has demonstrated its potential in different types of applications. We present
preliminary results in two dimensions and discuss future directions.
“Two Scale Wave Equation Modeling”
Susan E. Minkoff
Department of Mathematics and Statistics
University of Maryland, Baltimore County
1000 Hilltop Circle
Baltimore, MD 21250, USA
Email: sminkoff@umbc.edu
Abstract
Imaging the Earth’s subsurface requires determination of the “important information” inherent in
data that ranges over multiple scales. While numerical upscaling is a common approach for speeding
up solution of the fluid flow equations, simulation of waves through the same Earth is generally
accomplished using single scale finite differences. We describe a two-scale finite-element based wave
simulator and the associated adjoint problem. Operator-based upscaling decomposes the solution
into coarse and subgrid components. The subgrid solution lives at the fine nodes inside each coarse
cell. Fine-scale solution information is incorporated in the coarse solution. After adapting operatorbased
upscaling to the acoustic and elastic wave equations in 2 and 3D, we give a matrix analysis of
this two-stage process that produces the first explanation of the underlying physical equations being
solved by this technique. We see that the coarse grid solution involves solving a matrix problem
with entries that are averages of the original parameter field on coarse grid boundaries. Calculation
of the adjoint for the upscaled wave equation simulator is straight-forward if differentiation of the
continuous pde model is accomplished before discretization. The result is that the adjoint problem
can be solved by the same upscaling method as the standard acoustic wave equation.
“Hardy space infinite elements for exterior Maxwell problems”
Lothar Nannen
Institute for Analysis and Scientific Computing
Vienna University of Technology
Austria
Abstract
In this talk we present an infinite element method for solving electromagnetic scattering and
resonance problems posed on unbounded domains. As our motivation is to solve Maxwell’s equations
we take care that these infinite elements fit into the discrete de Rham diagram, i.e. they span discrete
spaces, which together with the exterior derivative form an exact sequence.
The theoretical framework of the method is the so called pole condition, which characterizes
radiating solutions via the poles or singularities of the Laplace transformed solutions: The Laplace
transform in radial direction of an outgoing wave belongs to a certain Hardy space of holomorphic
functions, while the Laplace transform of an incoming wave does not. Hence, the Hardy space infinite
elements are constructed using tensor products of Hardy space basis functions with standard finite
element surface basis functions.
Numerical tests indicate super-algebraic convergence in the number of additional unknowns per
degree of freedom on the coupling boundary.
12

“Time reversed absorbing condition in the partial aperture case”
Frédéric Nataf
Laboratoire J.L. Lions and CNRS UMR7598
University Pierre & Marie Curie
Paris, France
Abstract
The time-reversed absorbing conditions (TRAC) method introduced in Time Reversed Absorbing
Condition: Application to Inverse Problems, Assous, Kray and Nataf (Inverse Problems, 2011) enables
one to “recreate the past” without knowing the source which has emitted the signals that are backpropagated.
It has been applied to inverse problems for the reduction of the computational domain
size and for the determination, from boundary measurements, of the location and volume of an
unknown inclusion. The method does not rely on any a priori knowledge of the physical properties
of the inclusion. We present the extension of the TRAC method to the partial aperture configuration
and to discrete receivers with various spacing. In particular the TRAC method is applied to the
differentiation between a single inclusion and a two close inclusion case. Subwavelength resolution
can be achieved even with more than 20% noise in the data.
“Inverse obstacle scattering problems using multifrequency measurements”
Trung Thành Nguyen
RICAM
Altenbergerstrasse 69, A-4040 Linz
Abstract
In this talk, we consider the problem of reconstructing the shapes of sound-soft acoustic obstacles
using far field measurements associated with only one or a few incident directions but at multiple
frequencies. The motivation for using multifrequency data is explained as follows. On the one hand,
we know that the reconstruction problem is uniquely solvable at low frequencies, but its stability is
poor (only of log-type). That means, at low frequencies, it is difficult to reconstruct small details
of the obstacle. On the other hand, at high frequencies, this inverse problem may not be uniquely
solvable but it is more stable. To take the advantages of both low and high frequencies, we use the following
approach. We first reconstruct a rough approximation of the obstacles at the lowest frequency
using the least-squares approach. This reconstruction is then refined by using recursive optimization
methods at higher frequencies. This approach enables us to obtain an accurate reconstruction of the
parts of the obstacles’ boundary illuminated by the incident waves without requiring a good initial
guess. The analysis of this approach is divided into three steps.
In the first step, we derive a quantitative estimate of the set of local convexity of the objective
functional at a fixed frequency. Our analysis shows that, the size of this set is inversely proportional
to the used frequency. As a consequence, if the obstacles are expected to be contained in a known
domain, the lowest frequency should be chosen small enough so that the set of convexity of the
objective functional contains this domain and any shape in this domain can be used as an initial
guess.
The appropriate choice of the lowest frequency avoids the need of a good initial guess to obtain
an approximation of the true shapes. However, due to the lack of good stability at low frequencies,
we can only expect a rough approximation. To enhance the accuracy, our idea is then to use this
rough approximation as an initial guess for minimizing the objective functional at higher frequencies.
For this purpose, we make use of recursive optimization methods. The second step is devoted to the
convergence of the recursive optimization algorithms.
To analyze the reconstruction accuracy, in the third step, we discuss the stability at high frequencies.
We justify a conditional asymptotic Lipschitz stability estimate of the so-called support function
on the parts of the obstacles’ boundary illuminated by the incident wave. This result explains why
we can reconstruct small details of the illuminated parts at high frequencies.
The results presented are joint work with Mourad Sini (RICAM).
“Approaches to dynamical inverse scattering problems”
Roland Potthast
Deutscher Wetterdienst, University of Reading, University of Göttingen
Abstract
We discuss several different approaches to dynamics inverse scattering problems. Dynamical
problems are widely spread in nature. Dynamics can refer to the dynamics to the scattered field,
i.e. when we have time-dependent fields. In this case several new methods have been developed
13

over the past years and we will describe dynamical approaches like the time-domain probe method
and orthogonality sampling. When the scatterers under consideration are time-dependent, we need
additional techniques from the area of data assimilation. We will provide a survey for the case where
scale separation can be employed for the time-scales of the scatterer and the waves.
“Inverse problems in adaptive optics”
Ronny Ramlau
Institute for Industrial Mathematics
Johannes Kepler University Linz
Austria
Abstract
Most of the large earthbound astronomical telescopes use Adaptive Optics technology (AO) in order
to enhance the image quality. The degradation of the measured images is caused by atmospheric
turbulences. The correction is achieved by the use of deformable mirrors, where the deformation is
obtained from the measurements of the light of a bright natural star or artificial stars (laser guide
stars). We consider Inverse Problems that arise form Single Conjugate Adaptive Optics (SCAO) and
Multi Conjugate Adaptive Optics (MCAO). In order to measure the incoming wavefront, different
types of sensors are used. We consider the so called Shack - Hartmann sensor which measures an
average of the gradient of the wavefront. For SCAO, the Inverse Problem is now the reconstruction
of the wavefront from the (noisy) sensor measurements. Besides the reconstruction quality the
reconstruction time is most important, as the reconstructions have to be carried out in real time.
The presented reconstruction algorithms for SCAO are also an ingredient for the computation of the
mirror deformation for MCAO, which is based on a tomography of the atmosphere. The analytical
results are illustrated by numerical experiments.
“Hybrid discontinuous Galerkin finite element methods for the Helmholtz equation”
Joachim Schöberl
Institute for Analysis and Scientific Computing
Vienna University of Technology
Abstract
In this paper we present Hybrid Discontinuous Galerkin (HDG) Methods to discretize the Helmholtz
equation. In constrast to elliptic equations, we introduce two hybrid variables, one for the Dirichlet
and one for Neumann data. Thanks to this choice, the element equations can be formulated using
impedance traces.
We present computational results for iterative solvers with BDDC–type domain decomposition
preconditioners.
This talk contains joint work with A. Pechstein, P. Monk, M. Huber, A. Hannukainen, and G.
Kitzler.
“Stability and conditioning of boundary integral methods for high frequency scattering”
Euan A. Spence
Department of Mathematical Sciences
University of Bath
Bath, BA2 7AY, UK
Abstract
Boundary integral equations are a classical tool for solving acoustic scattering problems modelled
by the Helmholtz equation.
This talk will discuss the following two questions:
1. How do the condition numbers of the integral operators depend on the wavenumber k (in
particular for k large)?
2. Can one give a k-explicit error analysis, (a) for methods using conventional piecewise polynomial
basis functions (which require the number of degrees of freedom to grow as k increases to
preserve accuracy), and (b) for methods using novel k-dependent basis functions (which have
the potential to give almost uniform accuracy independent of k – see the next talk by Simon
Chandler-Wilde)?
14

Both these questions are interesting because the standard analysis of boundary integral equations
for the Helmholtz equation does not yield k-explicit results.
This talk will give an overview of some recent developments in answering these questions and will
discuss joint work with Timo Betcke (University College London), Simon Chandler-Wilde (Reading),
Ivan Graham (Bath), and Valery Smyshlyaev (University College London), as well as independent
work by Markus Melenk (Vienna).
“Boundary element methods for acoustic and electromagnetic scattering problems”
Olaf Steinbach
Institut für Numerische Mathematik
TU Graz
Steyrergasse 30
8010 Graz
Austria
Abstract
For the numerical solution of acoustic and electromagnetic scattering problems we discuss stabilized
boundary integral formulations and related boundary element methods. For problems with
piecewise local wave numbers we apply a tearing and interconnecting domain decomposition approach
which is based on modified Robin interface conditions to ensure unique solvability.
The talk is based on joint work with Sarah Engleder and Markus Windisch.
“Seismic inverse scattering by reverse time migration”
Chris Stolk
University of Amsterdam
Korteweg-de Vries Institute for Mathematics
Science Park 904
1098 XH, Amsterdam
The Netherlands
Abstract
We will consider the linearized inverse scattering problem from seismic imaging. While the first
reverse time migration algorithms were developed some thirty years ago, they have only recently become
popular for practical applications. We will analyze a modification of the reverse time migration
algorithm that turns it into a method for linearized inversion, in the sense of a parametrix. This is
proven using tools from microlocal analysis. We will also discuss the limitations of the method and
show some numerical results.
“The discontinuous enrichment method and its domain decomposition solver for the Helmholtz equation”
Radek Tezaur
Stanford University
Aeronautics and Astronautics
496 Lomita Mall
Stanford, CA 94305-4035, USA
Abstract
The Discontinuous Enrichment Method (DEM) is a discretization method designed for an efficient
solution of multi-scale problems. It is based on a hybrid variational formulation with Lagrange
multipliers. In addition to an optional polynomial field, it employs free-space solutions of the governing
differential equation for approximating large gradients or highly oscillatory components of the
solution. It relies on Lagrange multipliers to enforce a weak form of the inter-element continuity
of the solution. Recent developments and applications of DEM are discussed. These include the
solution of acoustic scattering and structural dynamics problems in the medium frequency regime,
and advection-diffusion problems with high Peclet numbers. Comparisons to other method are shown
and variable coefficient ideas are discussed.
Then, a nonoverlapping domain decomposition method is presented for the solution of Helmholtz/structural
dynamics problems discretized by DEM with and without the optional polynomial field. In this domain
decomposition method, the primal subdomain degrees of freedom are eliminated by local static
condensations to obtain an algebraic system of equations formulated in terms of the interface Lagrange
multipliers only. As in the FETI-H and FETI-DPH domain decomposition methods for continuous
15

Galerkin discretizations, this system of Lagrange multipliers is iteratively solved by a Krylov method
equipped with both a local preconditioner based on subdomain data, and a global one using a coarse
space. Numerical experiments performed for two- and three-dimensional acoustic problems demonstrate
the scalability of the method with respect to the size of the global problem and the number of
subdomains.
The principal co-authors of this talk are Charbel Farhat and Jari Toivanen. Other co-authors will
be acknowledged during the talk.
“Domain decomposition and multigrid preconditioners for the Helmholtz equation in layered and heterogeneous
media”
Jari Toivanen
Department of Mathematical Information Technology, University of Jyväskylä
FI-40100 Jyväskylä
Finland
Abstract
We consider the efficient numerical solution of time-harmonic acoustic scattering problems.
For layered media, we propose a domain decomposition preconditioner which is based on domain
embedding subdomain preconditioners and a fast direct solver. The iterations can be carried out on
small subspaces associated to the interfaces between layers/subdomains. The numerical experiments
demonstrate the capability to solve very large scale two-dimensional and three-dimensional problems
with up to billions of unknowns. The number of iterations seems to behave roughly logarithmically
with respect to the frequency.
For heterogeneous media, we consider a multigrid preconditioner which is based on an algebraic
multigrid method and a physically damped operator. Numerical experiments show this approach to
lead to efficient solution procedure for low and medium frequency problems. The number of iterations
grows roughly linearly with respect to the frequency.
This is joint work with Tuomas Airaksinen (University of Jyväskylä) and Kazufumi Ito (North
Carolina State University, Raleigh, NC).
16

Abstracts for Posters
“Numerical solution of the high frequency 2D direct scattering problem for convex objects using nonuniform
B-splines”
Carlos Borges
Worcester Polytechnic Institute
100 Institute Rd
Worcester, MA
USA
Abstract
We present a method for the numerical solution of the acoustic two dimensional direct scattering
problem for non penetrable convex scatterers for high frequencies. The method takes advantage of the
fact that, for the integral formulation considered for the problem, the solution to the integral equation
is a physical quantity and thereby can be written as the product of a known highly oscillatory function
and a unknown slow oscillatory function. We solve the problem for the slow oscillatory function using
a collocation method and we approximate the solution by a linear combination of non-uniform Bsplines,
where the density of control points corresponding will be higher where more resolution is
needed. To perform the integrations, we use ideas of the method of stationary phase, techniques
of integration of high oscillatory functions and singular kernels. Numerical results of the proposed
method are presented.
“Variational methods for the identification of objects”
Victor A. Kovtunenko
Institute for Mathematics and Scientific Computing
KF-University of Graz
Heinrichstr.36, A-8010 Graz
Lavrent’ev Institute of Hydrodynamics
630090 Novosibirsk, Russia,
e-mail: victor.kovtunenko@uni-graz.at
Abstract
Topology optimization problems for identification and reconstruction of small geometric objects of
arbitrary shapes and unknown boundary conditions are addressed. By arbitrary shapes we mean the
most general, i.e., the least restrictive, geometric assumptions which are commonly used in variational
formulations. We refer to singular geometric objects such as thin obstacles, cracks, multi-dimensional
junks, and alike. For unknown boundary conditions we consider Robin type boundary conditions
described by unknown parameters, which are discrete or distributed. Thus, the boundary conditions
are determined a-posteriori, i.e., after solving the optimization problem.
From a mathematical point of view, identification of unknown objects is an inverse problem, which
belongs to the field of shape and topology optimization and parameter estimation. Our approach
to the identification problems is based on variational methods supported with generalized methods
of singular perturbations. The key ingredients of the optimization approach are as follows. Firstly,
we consider the identification problem as a state-constrained optimization problem and apply proper
duality principles providing us with optimality conditions in the weak setting, thus accounting for
the features above. Second, we employ asymptotic methods of singular perturbation theory to obtain
approximate, geometry-dependent models. While the the first-order terms are somewhat known in
the literature as the topological derivative, we get the second-order terms to determine the boundary
conditions. Third, from multi-parametric optimization we get semi-analytical solution strategies.
We consider an example of inverse scattering problem. Some numerical aspects of the topology
optimization will be discussed.
17

“Time reversed absorbing conditions:
discrimination between one single inclusion and two close inclusions in a non-homogeneous medium”
Marie Kray
Jacques-Louis Lions Laboratory, Pierre et Marie Curie University
Paris, France
kray@ann.jussieu.fr
Abstract
We introduce the time-reversed absorbing conditions (TRAC) in time-reversal methods. They
enable one to “recreate the past” without knowing the source which has emitted the signals that
are back-propagated. We present two applications in inverse problems: the reduction of the size of
the computational domain and the determination, from boundary measurements, of the location and
volume of an unknown inclusion. The method does not rely on any a priori knowledge of the physical
properties of the inclusion. Numerical tests with the wave equation illustrate the efficiency of the
method. Moreover the TRAC method is fairly insensitive with respect to the magnitude of noise on
the recorded data.
In order to be closer to realistic cases as in geophysics, mine detection, medical imaging, ..., we
consider non homogeneous media (random or layered media). The application we propose is to investigate
the ability of the TRAC method to discriminate a unique inclusion from two distinct close
inclusions in a non-homogeneous medium. This test is inspired by a more realistic setting. Our intent
is to detect one or two iron or plastic mines in a background medium that can be random or layered.
The physical equation we use is a scalar wave equation derived from the Maxwell equations.
Joint work with Franck Assous (Bar-Ilan University & Ariel University Center, Israel,
franckassous@netscape.et) and Frédéric Nataf (Université Paris 6, nataf@ann.jussieu.fr)
Publications:
• F. Assous, M. Kray, F. Nataf, Time Reversed Absorbing Condition in the Partial Aperture Case,
http://hal.archives-ouvertes.fr/hal-00581291/fr/
• F. Assous, M. Kray, F. Nataf, E. Turkel, Time Reversed Absorbing Condition: Application to
inverse problem, Inverse Problems (2011), Vol. 27, no 6, pp 065003.
• F. Assous, M. Kray, F. Nataf, E. Turkel, Time Reversed Absorbing Conditions, Comptes Rendus
Mathmatiques, Serie I (2010), Vol. 348, no 19-20, pp 1063-1067, doi:10.1016/j.crma.2010.09.014
.
“Wavenumber-explicit convergence analysis for the Helmholtz equation: hp-FEM and hp-BEM”
J.M. Melenk
Vienna University of Technology
Abstract
We consider boundary value problems for the Helmholtz equation at large wave numbers k. In
order to understand how the wave number k affects the convergence properties of discretizations of
such problems, we develop a regularity theory for the Helmholtz equation that is explicit in k. At
the heart of our analysis is the decomposition of solutions into two components: the first component
is an analytic, but highly oscillatory function and the second one has finite regularity but features
wavenumber-independent bounds.
This understanding of the solution structure opens the door to the analysis of discretizations of the
Helmholtz equation that are explicit in their dependence on the wavenumber k. As a first example,
we show for a conforming high order finite element method that quasi-optimality is guaranteed if
(a) the approximation order p is selected as p = O(logk) and (b) the mesh size h is such that kh/p
is small. As a second example, we consider combined field boundary integral equation arising in
acoustic scattering. Also for this example, the same scale resolution conditions as in the high order
finite element case suffice to ensure quasi-optimality of the Galekrin discretization.
This work presented is joint work with Stefan Sauter (Zürich) and Maike Löhndorf (Vienna).
18

“Trefftz-discontinuous Galerkin methods for time-harmonic Maxwell’s equations”
Andrea Moiola
Seminar for Applied Mathematics
ETH Zürich
Rämistrasse 101, CH–8092 Zürich
moiola@sam.math.ethz.ch
Abstract
The propagation and the interaction of time-harmonic electric waves are described by the Maxwell
equations ∇ × (∇ × E) − ω 2 E = 0. The need of resolving oscillating solutions and the so-called
pollution effect make their numerical discretization through standard finite element schemes extremely
expensive for high frequencies. The Trefftz methods offer a way to tackle this problem: the trial and
the test functions are solution of the PDE inside each element, thus they are oscillating functions
and we can expect to be able to approximate the solution with smaller discrete spaces. The basis
functions are often chosen as vector plane waves.
We formulate a class of Trefftz-discontinuous Galerkin (TDG) methods that includes the wellknown
ultra weak variational formulation (UWVF) of Cessenat and Després, and we study the
convergence of their p-version (spectral version) for an impedance boundary value problem. Wellposedness
and quasi-optimality in a mesh skeleton norm follow from the coercivity of the bilinear
form defining the method on the Trefftz function space. A novel vector Rellich-type identity allows to
prove new (wavenumber-independent) stability and regularity estimates for the considered boundary
value problem in star-shaped polyhedral domains; these estimates, in turn, are used in a duality
argument to prove error bounds in a mesh-independent norm.
The abstract convergence analysis is carried out for any Trefftz trial space. In the case of vector
plane or spherical waves, concrete error bounds are obtained by using best approximation estimates
for general Maxwell solutions that are proved from the analogous scalar (Helmholtz) results. The
convergence is algebraic both in the dimension of the local trial space and in the meshwidth and all
the bounds are explicit in the wavenumber.
This work is part of my PhD thesis, carried out under the supervision of Ralf Hiptmair (ETH
Zürich) and Ilaria Perugia (Università di Pavia).
“Stable absorbing layer for convective wave propagation”
Imbo Sim
University of Klagenfurt
Abstract
In a multi-model approachfor computational aeroacoustics (CAA) one often uses within the acoustic
source region some kind of acoustic perturbation equations and then in the ambient region the
convective wave equation. Thereby, an efficient approach to model free field radiation conditions are
required for the convective wave equation. The perfectly matched layer (PML) approach has proved
a flexible and accurate method, which consists in surrounding the computational domain by an absorbing
layer. However, most PML formulations require wave equations stated in their standard
second-order form to be reformulated as first-order hyperbolic systems, thereby introducing many
additional unknowns. Here, we propose instead a simple stable PML formulation directly for the
second-order convective wave equation both in two and in three space dimensions.
The work presented is joint work with Manfred Kaltenbacher (Klagenfurt).
19

List of Participants
Akindeinde Saheed Ojo RICAM saheed.akindeinde@oeaw.ac.at
Alyaev Sergey University of Bergen cobxo3bot@gmail.com
Ammari Habib École Normale Supérieure habib.ammari@ens.fr
Arnold Thomas WIAS Berlin Thomas.Arnold@wias-berlin.de
Betcke Timo University College London t.betcke@reading.ac.uk
Borges Carlos Worcester Polytechnic Institute ceduardo@wpi.edu
Buck Marco Fraunhofer Institute for
Industrial Mathematics
marco.buck@itwm.fraunhofer.de
Buckwar Evelyn Johannes Kepler Universität
Linz
Evelyn.Buckwar@jku.at
Challa Durga Prasad RICAM durga.challa@oeaw.ac.at
Chandler-Wilde Simon University of Reading s.n.chandler-wilde@reading.ac.uk
Childs Paul Schlumberger Cambridge
Research
CHILDS4@slb.com
Engl Heinz RICAM & University of Vienna heinz.engl@oeaw.ac.at
Ernst Oliver TU Bergakademie Freiberg ernst@math.tu-freiberg.de
Freitag Melina University of Bath m.freitag@maths.bath.ac.uk
Gander Martin University of Geneva Martin.Gander@unige.ch
Georgiev Ivan RICAM ivan.georgiev@oeaw.ac.at
Gessese Alelign University of Canterbury alelign.gessese@pg.canterbury.ac.nz.
Graham Ivan University of Bath i.g.graham@bath.ac.uk
Grote Marcus University of Basel Marcus.Grote@unibas.ch
Hegedüs Gabor RICAM gabor.hegedues@oeaw.ac.at
Helin Tapio RICAM tapio.helin@oeaw.ac.at
Hiptmair Ralf ETH Zürich hiptmair@sam.math.ethz.ch
Hoang Viet Ha NTU, Singapore vhhoang@ntu.edu.sg
Hrtus Rostislav Institute of Geonics of the AS
CR, v.v.i., Ostrava, CZ
hrtus@ugn.cas.cz
Hu Guanghui WIAS Berlin Guanghui.Hu@wias-berlin.de
Kaltenbacher Barbara University of Klagenfurt barbara.kaltenbacher@uni-graz.at
Kaltenbacher Manfred University of Klagenfurt manfred.kaltenbacher@uni-graz.at
Kar Manas RICAM manas.kar@oeaw.ac.at
Karer Erwin RICAM erwin.karer@oeaw.ac.at
Kollmann Markus Doctoral Program
Computational Mathematics,
Johannes Kepler University
markus.kollmann@dk-compmath.jku.at
Kolmbauer Michael Institute of Computational
Mathematics
kolmbauer@numa.uni-linz.ac.at
Kovtunenko Victor KF-University Graz; Lavrent’ev
Institute of Hydrodynamics
victor.kovtunenko@uni-graz.at
Kraus Johannes RICAM johannes.kraus@oeaw.ac.at
Kray Marie Laboratoire J-L Lions, UPMC kray@ann.jussieu.fr
Langer Ulrich University of Linz ulanger@numa.uni-linz.ac.at
Leindl Mario Montanuniversität Leoben,
Institut für Mechanik
mario.leindl@unileoben.ac.at
Livshits Irene Ball State University ilivshits@bsu.edu
Melenk Jens Markus TU Wien melenk@tuwien.ac.at
Migliorati Giovanni Department of Mathematics,
Politecnico di Milano
giovanni.migliorati@gmail.com
Minkoff Susan Dept. of Mathematics and
Statistics, University of
Maryland Baltimore County
sminkoff@umbc.edu
20

Mitrovic Darko University of Bergen Darko.Mitrovic@math.uib.no
Mohamed Menad University of Chlef
Moiola Andrea SAM - ETH Zürich andrea.moiola@sam.math.ethz.ch
Motamed Mohammad KAUST mohammad.motamed@nullkaust.edu.sa
Nannen Lothar TU Vienna lothar.nannen@tuwien.ac.at
Nataf Frédéric Laboratoire J.L Lions and
CNRS
nataf@ann.jussieu.fr
Naumova Valeriya RICAM valeriya.naumova@oeaw.ac.at
Nayak Sridhara Indian Institute of Technology
Kharagpur
sridharanayakiitkgp@gmail.com
Nguyen Trung Thanh RICAM trung-thanh.nguyen@oeaw.ac.at
Nordbotten Jan Martin University of Bergen jan.nordbotten@math.uib.no
Pechstein Clemens Institute of Computational
Mathematics, Johannes Kepler
University Linz
clemens.pechstein@numa.uni-linz.ac.at
Polydorides Nick Cyprus Institute nickpld@cyi.ac.cy
Potthast Roland Deutscher Wetterdienst, Univ.
of Reading, Uni Göttingen
r.w.e.potthast@reading.ac.uk
Ramlau Ronny Industrial Mathematics
Institute, Kepler University
Linz, Austria
ronny.ramlau@jku.at
Rieder Andreas Department of Mathematics,
Karlsruhe Institute of
Technology
andreas.rieder@kit.edu
Sarkis Marcus Mathematical Sciences
Dept./Worcester Polytechnic
Institute
msarkis@wpi.edu
Scheichl Robert University of Bath r.scheichl@bath.ac.uk
Schicho Josef RICAM josef.schicho@oeaw.ac.at
Schöberl Joachim Vienna UT joachim.schoeberl@tuwien.ac.at
Shanks Douglas University of Bath J.D.Shanks@bath.ac.uk
Sim Imbo University of Klagenfurt imbo.sim@uni-klu.ac.at
Sini Mourad RICAM mourad.sini@oeaw.ac.at
Sokol Vojtěch Institute of Geonics of the AS
CR, v.v.i., Ostrava, CZ
sokol.vojtech@gmail.com
Spence Euan University of Bath e.a.spence@bath.ac.uk
Spillane Nicole Laboratoire Jacques Louis Lions
(Paris) - Michelin
spillane@ann.jussieu.fr
Steinbach Olaf TU Graz o.steinbach@tugraz.at
Stolk Chris University of Amsterdam C.C.Stolk@uva.nl
Talagrand Olivier Laboratoire de Météorologie
Dynamique, École Normale
Supérieure, Paris, France
talagrand@lmd.ens.fr
Teckentrup Aretha University of Bath, Department
of Mathematical Sciences
A.L.Teckentrup@bath.ac.uk
Tezaur Radek Stanford University rtezaur@stanford.edu
Toivanen Jari Stanford University toivanen@stanford.edu
Tomar Satyendra RICAM satyendra.tomar@ricam.oeaw.ac.at
Wachsmuth Daniel RICAM daniel.wachsmuth@oeaw.ac.at
Willems Jörg RICAM joerg.willems@ricam.oeaw.ac.at
Wohlmuth Barbara Technische Universität
München
wohlmuth@ma.tum.de
Wolfmayr Monika Institute of Computational
Mathematics, University of Linz
monika.kowalska@numa.uni-linz.ac.at
Yang Huidong RICAM huidong.yang@oeaw.ac.at
Zikatanov Ludmil The Pennsylvania State
University
ltz@math.psu.edu
Zulehner Walter Johannes Kepler University
Linz
zulehner@numa.uni-linz.ac.at
21

Monday Tuesday Wednesday Thursday Friday
Registration (9:00-9:40) Martin Gander Ronny Ramlau Roland Potthast Manfred Kaltenbacher
9:00-9:50
Spectral finite elements for a
mixed formulation in
Are absorbing boundary
Approaches to dynamical inverse
scattering problems
Inverse problems in adaptive
optics
conditions and perfectly matched
layers really so different?
Opening (9:40-9:50)
computational acoustics taking
flow effects into acount
Ralf Hiptmair Lothar Nannen Frédéric Nataf Thanh Nguyen Euan Spence
9:50-10:40
Stability and conditioning of
boundary integral methods for
Inverse obstacle scattering
problems using multifrequency
Time reversed absorbing
condition in the partial aperture
case
Hardy space infinite elements for
exterior Maxwell problems
Convergence of truncated
T-matrix approximation
high frequency scattering
measurements
Coffee Coffee Coffee Coffee Coffee
Timo Betcke Habib Ammari Olaf Steinbach Guanghui Hu Simon Chandler-Wilde
11:10-12:00
Modulated plane wave methods
Boundary element methods for Direct and inverse scattering of Numerical-asymptotic integral
Electromagnetic invisibility and
for Helmholtz problems in
acoustic and electromagnetic elastic waves by diffraction
equation methods for high
super-resolution
heterogeneous media
scattering problems
gratings
frequency scattering
Lunch Lunch Lunch Lunch Closing
Susan Minkoff Marcus Grote free afternoon Jari Toivanen
14:00-14:50
Domain decomposition and
multigrid preconditioners for the
Helmholtz equation in layered
(please feel free to make use of
the seminar room and the Special
Discontinuous Galerkin methods
and local time stepping for
Two scale wave equation
modeling
Semester offices)
transient wave propagation
and heterogeneous media
Coffee Coffee Coffee
Paul Childs Joachim Schöberl Radek Tezaur
15:20-16:10
The discontinuous enrichment
method and its domain
Hybrid discontinuous Galerkin
finite element methods for the
decomposition solver for the
Numerics of waveform inversion
for seismic data
Helmholtz equation
Helmholtz equation
Chris Stolk Ira Livshits
16:10-17:00
Algebraic multigrid algorithm for
solving Helmholtz equations with
Seismic inverse scattering by
reverse time migration
large wave numbers
Radon Colloquium
Martin Gander
17:15
Posters & Reception
Conference Dinner
(19:00)
From Euler, Schwarz, Ritz and
Galerkin to modern computing
Each talk is 40 minutes long. After the end of each talk, there are 10 minutes for discussion.