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Year 4

Tackle a challenging application problem that uses all the tools
of the MathBus. Here we give an example of the kind of problem that
might be suitable. The electrical impedance tomography (EIT) problem
may be stated as follows. An electrical field is induced on a domain;
it is known that the electrical potential u obeys the law
. Here, c is a scalar field that denotes
conductivity. However, neither c nor u is known a priori.
Instead, what is known is a sequence of Neumann/Dirichlet boundary
data specifications. The problem is to reconstruct c from this
data. This problem, which has been the subject of a fair amount of
recent interest (see the 7/94 issue of SIAM News and
[98]), arises in medical
imaging. The medical imaging application is to determine the internal
structure of organs using electrical field measurements. EIT is a
very inexpensive way to carry out medical imaging, but is currently
far less precise than more expensive imaging technology such as CAT
scans and MRI scans. The lack of precision is partly due to the need
for better numerical algorithms.
To design algorithms for the EIT problem, one must have finite element solvers, mesh generators that can specify and handle internal boundaries, and sophisticated optimization tools. Furthermore, to develop algorithms, one must be able to rewrite parts of the various packages and specifications ``on the fly'' as algorithmic ideas are refined. Our plan is to have by Year 4 an environment sufficiently powerful to make the design of these algorithms much easier than the current environments.

Generation of parallel code for sparse matrix applications.
We will generate parallel implementations of direct methods for
solving large, sparse systems of equations. In particular, we will
produce code for multifrontal, supernodal sparse Cholesky
factorization, as well as multifrontal sparse QR factorization,
starting from the corresponding dense matrix programs. Combined with
the iterative solvers produced by Year 2, this will give us a large
arsenal of sparse parallel solvers. The Bernoulli project will be the
consumer of this technology, and it will drive the development of
the technology.
Next: Year 5 Up: Milestones Previous: Year 3
nuprl project
Tue Nov 21 08:50:14 EST 1995