Michigan
Technological University
Department of Mathematical Sciences
Department of Mathematical Sciences
|
Michigan
Technological University
Department of Mathematical Sciences |
Mark Gockenbach
Center for Applied Mathematics
Recent research activities include preparing version 1.0 of the Hilbert
Class Library (HCL) for public release. HCL is a software package for
large-scale optimization and inverse problems; it uses object-oriented
programming techniques to implement optimization algorithms, allowing a
scientist to use the algorithms with the data structures and interfaces
that are natural to his or her problem.
Gockenbach has also been studying the degree to which it is possible to recover
the elastic parameters of a heterogeneous membrane from an experiment in
which the stretching of the membrane is observed. This is an example of
an "elliptic" inverse problem, that is, an inverse problem in which the
governing mathematical model is an elliptic partial differential equation.
He is also involved in studying computational procedures for determining
the acoustic velocity of the subsurface of the earth from a standard
seismic experiment. This is an inverse problem of interest in petroleum
exploration and other areas of seismology; the acoustic velocity is needed
to construct an accurate map of the subsurface from seismic data gathered
at the surface of the earth.