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The immersed interface method: a numerical approach for partial differential equations with interfaces
This thesis describes the Immersed Interface Method (IIM) for interface problems, in which the partial differential equations have discontinuities and singularities in the coefficients and the solutions. A typical example of such problems is heat conduction in different materials (discontinuous heat conductivity), or fluid ...
Reproducing color images with custom inks
This dissertation investigates the general problem of reproducing color images on an off-set printing press using custom inks in any combination and number. Many mathematical and algorithmic challenges arise when printing with inks other than the standard process colors (cyan, magenta, yellow, and black), particularly as the ...
A splitting algorithm for multistage stochastic programming with application to hydropower scheduling
With water in short supply and utility deregulation imminent, the problem of long-term scheduling on a hydroelectric power system has become increasingly important.Many of the algorithms developed for this large-scale multistage stochastic problem have relied on the dynamic programming algorithm; and so have suffered from the ...
An adaptive multilevel method for boundary layer meteorology
This thesis presents a new adaptive multilevel numerical model for incompressible flows and applies such a model for the first time to the simulation of atmospheric boundary layers capped by shallow cumulus and stratocumulus clouds. One needs to simulate a large domain, while locally having enough resolution to resolve the ...