Geometric Multigrid for Unstructured Finite Elements: Implementation and Applications
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In the realm of computational science, a fundamental interest lies in our ability to construct models of complex phenomenon and probe them in order to gain understanding and make predictions about the systems at hand. Yet for these predictions to hold value, we must assert confidence in them and perform them with maximum efficiency so that we can provide timely analysis. This CDSE dissertation addresses the above consideration directly by designing a project which composes and investigates such complex simulations, evolves them forward in time, and strives to control the error in the results. A large expense of this project is due to the computationally cumbersome nature of the simulation and its design and analysis. Due to these concerns, the implementation focuses on high speed, reusable, and modular components which allow for the framework to later be adapted to a variety of other problems. Specifically, we discuss the application of these principles to simulations pertaining to nonlinear elasticity and thermally coupled flows; problems which serve as perfect examples of experiments which while difficult and expensive to perform and analyze in physical experiments are, although computationally nuanced, manageable from a numerical simulation standpoint.