Thursday, July 17

3:15 PM-5:15 PM
Law School, Room 190

Adaptive Method of Lines (Part I of III)

The method of lines (MOL) has evolved in recent years as an effective numerical algorithm for the solution of all major classes of partial differentials equations (PDEs), i.e., nonlinear elliptic, parabolic, hyperbolic PDEs in one, two and three dimensions and time. The basic idea is to replace the spatial (boundary value) derivatives with an algebraic approximation over a spatial grid. The resulting system of initial-value ordinary differential equations (ODEs) is then integrated numerically, typically by an established ODE code.

If the PDE solution includes sharp spatial variations and/or a sharp moving front, then the spatial resolution of the solution may not be adequate on a fixed spatial grid. Rather, an adaptive grid must be used which automatically tracks the regions of sharp spatial variation. Thus, this extension is termed "adaptive MOL."

In this minisymposium, a series of papers will cover the theoretical aspects of adaptive MOL, and applications to challenging PDE problems which require adaptive grid methods. Our intention is to provide a forum for the latest developments in adaptive MOL, and to provide enough coverage that attendees will have a clear indication of the current status of adaptive MOL. Also, the availability of transportable, adaptive MOL codes will be stressed.

Organizers: A. Vande Wouwer and P. Saucez, Faculte Polytechnique de Mons, Belgium; and William E. Schiesser, Lehigh University

3:15 Adaptive Method of Lines Solution of Parabolic Systems with Applications to Ceramic Composites
S. Adjerid, M. Aiffa, Joseph E. Flaherty, John Hudson, T. Ohsumi, and M. S. Shephard, Rensselaer Polytechnic Institute
3:45 An Adaptive MOL Approach for Tracking Optimal Solutions of Variational Problems
M. J. Baines, University of Reading, United Kingdom
4:15 SPRINT2D an Adaptive MOL Solver for Convective PDES in Two Space Dimensions
Roger Fairlie, Martin Berzins, and S. V. Pennington, University of Leeds, United Kingdom
4:45 Highly Effective Spatial Grids for Nonlinear Evolution Problems
J. Lang, Konrad-Zuse-Zentrum fuer Informationstechnik, Germany

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MMD, 3/31/97
tjf, 5/29/97
MMD, 6/3/97