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Full-Text Articles in Applied Mathematics
Homogenization In Perforated Domains And With Soft Inclusions, Brandon C. Russell
Homogenization In Perforated Domains And With Soft Inclusions, Brandon C. Russell
Theses and Dissertations--Mathematics
In this dissertation, we first provide a short introduction to qualitative homogenization of elliptic equations and systems. We collect relevant and known results regarding elliptic equations and systems with rapidly oscillating, periodic coefficients, which is the classical setting in homogenization of elliptic equations and systems. We extend several classical results to the so called case of perforated domains and consider materials reinforced with soft inclusions. We establish quantitative H1-convergence rates in both settings, and as a result deduce large-scale Lipschitz estimates and Liouville-type estimates for solutions to elliptic systems with rapidly oscillating periodic bounded and measurable coefficients. Finally, …
High Accuracy Multiscale Multigrid Computation For Partial Differential Equations, Yin Wang
High Accuracy Multiscale Multigrid Computation For Partial Differential Equations, Yin Wang
University of Kentucky Doctoral Dissertations
Scientific computing and computer simulation play an increasingly important role in scientific investigation and engineering designs, supplementing traditional experiments, such as in automotive crash studies, global climate change, ocean modeling, medical imaging, and nuclear weapons. The numerical simulation is much cheaper than experimentation for these application areas and it can be used as the third way of science discovery beyond the experimental and theoretical analysis. However, the increasing demand of high resolution solutions of the Partial Differential Equations (PDEs) with less computational time has increased the importance for researchers and engineers to come up with efficient and scalable computational techniques …