This report consists of a dissertation submitted to the faculty of the Department of Electrical and Computer Engineering, in partial fulfillment of the requirements for the degree of Doctor of Philosophy, Graduate College, The University of Arizona, 2008.
Spatio-temporal systems with heterogeneity in their structure and behavior have two major problems associated with them. The first one is that such complex real world systems extend over very large spatial and temporal domains and consume so many computational resources to simulate that they are infeasible to study with current computational platforms. The second one is that the data available for understanding such systems is limited because they are spread over space and time making it hard to obtain micro and macro measurements. This also makes it difficult to get the data for validation of their constituent processes while simultaneously considering their global behavior. For example, the valley fever fungus considered in this dissertation is spread over a large spatial grid in the arid Southwest and typically needs to be simulated over several decades of time to obtain useful information. It is also hard to get the temperature and moisture data (which are two critical factors on which the survival of the valley fever fungus depends) at every grid point of the spatial domain over the region of study. In order to address the first problem, we develop a method based on the discrete event system specification which exploits the heterogeneity in the activity of the spatio-temporal system and which has been shown to be effective in solving relatively simple partial differential equation systems. The benefit of addressing the first problem is that it now makes it feasible to address the second problem. We address the second problem by making use of a multilevel methodology based on modeling and simulation and systems theory. This methodology helps us in the construction of models with different resolutions (base and lumped models). This allows us to refine an initially constructed lumped model with detailed physics-based process models and assess whether they improve on the original lumped models. For that assessment, we use the concept of experimental frame to delimit where the improvement is needed. This allows us to work with the available data, improve the component models in their own experimental frame and then move them to the overall frame. In this dissertation, we develop a multilevel methodology and apply it to a valley fever model. Moreover, we study the model's behavior in a particular experimental frame of interest, namely the formation of new sporing sites.
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Multilevel Methodology for Simulation of Spatio-Temporal Systems with Heterogeneous Activity; Application to Spread of Valley Fever Fungus