Wave equation

Friday, June 30, 2017 - 9:00am - 9:50am
Jay Gopalakrishnan (Portland State University)
Tent-shaped spacetime regions appear to be natural for solving hyperbolic equations. By constraining the height of the tent pole, one can ensure causality. The subject of this talk is a technique to advance the numerical solution of a hyperbolic problem by progressively meshing a spacetime domain by tent shaped objects. Such tent pitching schemes have the ability to naturally advance in time by different amounts at different spatial locations. Local time stepping without losing high order accuracy in space and time is thus possible.
Tuesday, November 2, 2010 - 3:00pm - 3:45pm
Bjorn Engquist (The University of Texas at Austin)
We will give a brief overview of multiscale modeling for wave equation
problems and then focus on two techniques. One is an energy conserving
DG method for time domain and the other is a new a new sweeping
preconditioner for frequency domain simulation. The latter is resulting
in a computational procedure that essentially scales linearly even in
the high frequency regime.
Monday, November 1, 2010 - 3:45pm - 4:30pm
This presentation is devoted to plane wave methods for approximating the time-harmonic wave equation paying particular attention to the Ultra Weak Variational Formulation (UWVF). This method is essentially an upwind Discontinuous Galerkin (DG) method in which the approximating basis functions are special traces of solutions of the underlying wave equation. In the classical UWVF, due to Cessenat and Després, sums of plane wave solutions are used element by element to approximate the global solution.
Monday, March 23, 2009 - 11:00am - 11:45am
Chiu-Yen Kao (University of Minnesota, Twin Cities)
The Kadomtsev-Petviashvili (KP) equation is a two-dimensional dispersive
wave equation
which was proposed to study the stability of one soliton solution of the
KdV equation
under the influence of weak transversal perturbations. It is well know
that some closed-form
solutions can be obtained by function which have a Wronskian determinant
It is of interest to study KP with an arbitrary initial condition and see
whether the
solution converges to any closed-form solution asymptotically. To reveal
Wednesday, March 4, 2009 - 3:20pm - 3:50pm
Enrique Zuazua (Basque Center for Applied Mathematics)
In this lecture we shall present a survey of recent work on several topics related with numerical approximation of waves.

Control Theory is by now and old subject, ubiquitous in many areas of Science and Technology. There is a quite well-established finite-dimensional theory and many progresses have been done also in the context of PDE (Partial Differential Equations). But gluing these two pieces together is often a hard task from a mathematical point of view.
Friday, October 21, 2005 - 9:00am - 9:50am
Wim Mulder (The Shell Group)
Joint with R.-E. Plessix.

The goal of seismic surveying is the determination of the structure and properties of the subsurface. Oil and gas exploration is
restricted to the upper 5 to 10 kilometers. Seismic data are usually recorded at the earth's surface as a function of time. Creating a
subsurface image from these data is called migration.

Seismic data are band-limited with frequencies in the range from about 10 to 60 Hz. As a result, they are mainly generated by short-range
Friday, October 21, 2005 - 3:50pm - 4:40pm
Maarten De Hoop (Purdue University)
in collaboration with Gunther Uhlmann and Hart Smith

In reflection seismology one places sources and receivers on the
Earth's surface. The source generates waves in the subsurface that are
reflected where the medium properties vary discontinuously; these
reflections are observed in all the receivers. The data thus obtained
are commonly modeled by a scattering operator in a single scattering
approximation: the linearization is carried out about a smooth
background medium, while the scattering operator maps the (singular)
Friday, October 21, 2005 - 10:20am - 11:10am
Patrick Lailly (Institut Français du Pétrole)
Joint work with Florence Delprat-Jannaud.

Geophysicists are quite aware of the important troubles that can be met when
the seismic data are contaminated by multiple reflections. The situation
they have in mind is the one where multiple reflections are generated by
isolated interfaces associated with high impedance contrasts. We here study
a more insidious effect of multiple scattering, namely the one associated
with fine scale heterogeneity.
Our numerical experiments show that the effect of such multiple scattering
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