Great Lakes Section Holds Third Forum

July 17, 2000

Brian McCartin, Kevin TeBeest, Frank Massey, Joan Remski, and Jennifer Zhao

There was no fooling around when three dozen members of the Great Lakes Section of SIAM converged on the University of Michigan-Dearborn on the afternoon of Saturday, April 1, for the 3rd Forum on Numerics and Modeling for Partial Differential Equations (NUMPDES 2000). Previous forums had been held at Kettering University (1998) and Bowling Green State University (1999). This year's participants were treated to presentations cutting a broad swath across the landscape of applied and computational mathematics.

Invited speaker Gang Bao of Michigan State University described work performed with his colleagues on scattering by diffractive structures. Using a variational formulation coupled with a least-squares finite-element method, he discussed optical applications ranging from computer monitor displays to military visors. This and other work will be included in a forthcoming volume in the SIAM Frontiers in Applied Mathematics series.

S.I. (Hari) Hariharan of the University of Akron followed with an invited presentation on the comparison of phase-field and sharp-interface models in directional solidification. Hariharan described joint work with G.W. Young that uses asymptotic solutions of a prototypical problem to determine which of the several available phase-field models best compares to the sharp-interface model. This asymptotic analysis also leads to improvements in the predicted location of the moving interface.

Also included in the program were four contributed presentations. Brian McCartin (with Sydney Forrester) of Kettering University described work on the numerical simulation of the self-purification of heavily polluted rivers. Sally Shao (with Percy Yip) presented a new adaptive stochastic approximation algorithm with applications in system identification and signal processing. Mark Gockenbach (with Daniel Reynolds, William Symes, and Chaoming Zhang) of Michigan Technological University introduced a simplified derivation of the adjoint state method for inverse and control problems that greatly alleviates the burden of implementation. Finally, Wen Zhang (with Meir "Fiki" Shillor) of Oakland University detailed a viscoelastic model of two beams joined at a gap and demonstrated its ability to predict the transmission of vibrations across the joint.

The forum was held in the School of Management building, the newest addition to the beautiful UM-Dearborn campus, adjacent to the sprawling estate of the Ford family. As in previous years, the presenters' illustrations will be collected in a proceedings and distributed to participants.

Brian McCartin and Kevin TeBeest are members of the faculty at Kettering University. Frank Massey, Joan Remski, and Jennifer Zhao are from the University of Michigan-Dearborn.

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