Bilateral German-Greek ProjectNew Mathematical and Numerical Techniques
|
Bilateral German-Greek ProjectNew Mathematical and Numerical Techniques
|
The main goal of the present project is to derive and analyze new numerical schemes for one-way wave equations preserving important features of the continuous model, such as conservation of the acoustic energy. These models are of Schrödinger-type and arise from the ``parabolic'' equation (PE), which has been widely used for one-directional wave propagation problems in various application areas (acoustics, optics, seismology, radio frequency technology and plasma physics). In underwater acoustics they appear as wide angle approximations to the Helmholtz equation in cylindrical coordinates and they are called wide angle parabolic equations (WAPE).
Another important topic of this project is the analysis of a hybrid model that couples a scalar wave equation (``fluid'' model) for the ocean to an elastic wave equation for the sea bottom. The main emphasis will again be on a conservative formulation which yields a basis for stable numerical schemes.
Finally we will investigate in the third subproject the kinetic reformulation of the Schrödinger-type one-way wave equations using the Wigner transform.
German team:
Greek team: German institutions:
Greek institutions:
ehrhardt@math.tu-berlin.de
