KDI: Structure Preserving Algorithms and Model Reduction in the Natural Sciences

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Structure Preserving Algorithms and Model Reduction in the Natural SciencesProject SummaryNew theoretical and computational techniques will be developed that combine research in mathematics, computer science, and the geophysical sciences. Understanding and controlling modern physical systems typically requires numerical simulations of multiscale dynamics that occur over a wide range of time and space scales. It is generally prohibitively expensive (e.g., a great deal of computational time) to simulate all of the scales involved in many naturally occurring phenomena. Scales outside the computable range must be described by a reduced model that conscientiously represent the effects of the unresolved degrees of freedom on the resolved scales. These models may also have constraints that provide reduced descriptions of the interactions with other systems. The goal of this study will be to develop both the model reduction techniques and new algorithms to address these problems.