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Geometric Partial Differential Equations - Part 2, Volume 22, includes basic ideas, analyses and applications of state-of-the-art, fundamental algorithms surrounding the approximation of geometric PDEs, along with their impact in a variety of fields within mathematics, science and engineering. Chapters in this latest release include Optimal control of geometric partial differential equations, Shape optimization, Total variation minimization, Numerical relativity, Numerical Simulation and Bench- marking of Drops and Bubbles, Optimal Transport, Gradient flows, Isogeometric Analysis, Liquid Crystals, and more. Includes sections on Optimal control of geometric partial differential equations, Shape optimization, Total variation minimization, Numerical relativity, and moreProvides a comprehensive description of algorithms and their analysis for a specific geometric PDE class, starting from basic concepts and concluding with interesting applicationsAuthored by world leaders in their field of expertise and skillful writers