Numeerisen analyysin ja laskennallisen
tieteen seminaari
30.1.2006 klo
14.15
U356
Kenrick Bingham TKK, Matematiikan laitos
Inverse problem
for the wave equation and focusing waves
The inverse problem of the wave equation is to determine the spatially
varying wave speed and potential functions, when Cauchy data on the
boundary of the domain of different solutions of the equation are
known. A strategy for solving such an inverse problem uses the
Blagoveshchenskii identity for calculating inner products of
appropriate solutions inside the domain, using the known boundary data.
This tool allows one to construct waves that focus at a particular time
into a small neighbourhood of a point. This gives information about the
local behaviour of the solutions, which can be used for solving the
inverse problem. Questions about the numerical implementation are
discussed.