Silver Professor of Mathematics and Computer Science
Throughout his career, Olof Widlund has focused on numerical algorithms for partial differential equations. His primary concern has been new algorithms and mathematical tools for their analysis. For two decades, with students and other associates, he has concentrated his efforts on domain decomposition algorithms for the large linear systems of algebraic equations that arise in many computational continuum mechanics problems, for example in fluid dynamics and elasticity. These algorithms use a preconditioned conjugate gradient approach and they are designed for parallel and distributed computers. A main challenge is to overcome the potential computational bottleneck arising because the solutions of the linear systems depend on the data everywhere in the region. A research monograph, ``Domain Decomposition Methods - Algorithms and Theory'', coauthored with Andrea Toselli, was published by the Springer Verlag in 2005. In February 2006, it received the Award for Excellence in Professional and Scholarly Publications of the Association of American Publisher, in the category Mathematics and Statistics. The book contains many results developed by the seventeen doctoral students, who have completed doctoral dissertations at the Courant Institute in this field of research since 1989.
These algorithms are increasingly being accepted by the user community and their usefulness on loosely-coupled computer systems and the very largest parallel computers has been demonstrated in a substantial number of experimental studies, some of them using the PETSc system developed at the Mathematics and Computer Science Division of the Argonne National Laboratory .
In recent years, the Courant Institute research group has focused its work on FETI-DP and BDDC algorithms for elliptic systems, including those of saddle point type and on domain decomposition methods for electro-magnetics. The group has also actively developed new, hybrid domain decomposition algorithms, which combine features of iterative substructuring methods and two-level overlapping Schwarz methods; the principal applications so far has been to almost incompressible elasticity. Very recently, work on domain decomposition algorithms for isogeomtric analysis has also begun.
A large number of his former students, and many other friends and coworkers, participated in a meeting held at the Courant Institute on January 23-24, 1998, on the occasion of his sixtieth birthday.
He is also a regular participant in the
on Domain Decomposition in Science and Engineering and has helped
edit a number of the proceedings of these conference. The sixteenth,
and one of the largest in the series, was held at the Courant Institute on
January 11-15, 2005. On the day just before the twentieth conference
in the series, held at UCSD February 7-11, 2011,
he offered a full day tutorial ;
see also a four page introduction to
this set of slides.