# 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.

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

form.

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

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

form.

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.

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

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)

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

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