Browsing by Author "Kearsley, A.J."

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    Fictitious Domain Methods for Viscous Flow Simulation
    (1995-05) Glowinski, R.; Kearsley, A.J.; Pan, T.W.; Periaux, J.
    We discuss the fictitious domain solution of the Navier-Stokes equations modeling unsteady incompressible viscous flow. The method is based on a Lagrange multiplier treatment of the boundary conditions to be satisfied and is particularly well suited to the treatment of no-slip boundary conditions. This approach allows the use of structured meshes and fast specialized solvers for problems on complicated geometries. Another interesting feature of the fictitious domain approach is that it allows the solution of optimal shape problems without regridding. The resulting methodology is applied to the solution of flow problems including external viscous flow past oscillating rigid body and vortex dynamics of two-dimensional flow modeled by the incompressible Navier-Stokes equations and then to an optimal shape problem for Stokes and Navier-Stokes flows.
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    The Solution of the Metric STRESS and SSTRESS Problems in Multidimensional Scaling Using Newton's Method
    (1994-12) Kearsley, A.J.; Tapia, R.A.; Trosset, M.W.
    This paper considers numerical algorithms for finding local minimizers of metric multidimensional scaling problems. The two most common optimality criteria (STRESS and SSTRESS) are considered, the leading algorithms for each are carefully explicated, and a new algorithm is proposed. The new algorithm is based on Newton's method and relies on a parameterization that has not previously been used in multidimensional scaling algorithms. In contrast to previous algorithms, a very pleasant feature of the new algorithm is that it can be used with either the STRESS or the SSTRESS criterion. Numerical results are presented for the metric STRESSS problem. These results are quite satisfying and, among other things, suggest that the well-known SMACOF-I algorithm tends to stop prematurely.