Intro; Preface; Contents; Homogenization in Magnetic-Shape-Memory Polymer Composites; 1 Introduction; 2 The Model; 3 Analytical Homogenization; 4 Numerical Study of the Cell Problem; 5 Conclusions and Outlook; References; Homogenization of Stochastic Parabolic Equationsin Varying Domains; 1 Introduction; 2 Homogenization of Semilinear Stochastic Parabolic Equations in a Domain with Fine Grained Boundaries; 2.1 Our Notion of Solution and Its Existence; 2.2 Probability Measures Generated by the Sequence ( W( s) ,u( s) ) and Their Tightness; 2.3 Cell Problem

2 Problem Formulation: NMPC and MHE3 Decomposition of the MHE Problem; 4 Decomposition of the NMPC Problem; 5 Multilevel Iterations; 5.1 Establishing the Reduced Problems; 5.2 Iteration on the Level A; 5.3 Iteration on the Level B; 5.4 Iteration on the Level C; 6 Numerical Results; 7 Conclusions; References; Some Recent Developments in Optimal Control of Multiphase Flows; 1 Introduction; 1.1 Notation; 2 Existence of Solutions of the Cahn-Hilliard-Navier-Stokes System; 2.1 The Semi-Discrete CHNS System; 2.2 Existence of Solutions; 3 The Optimal Control Problem; 4 Stationarity Conditions

4.1 Boundary Control5 Numerical Solution Methods; 5.1 Adaptive Mesh Refinement Techniques; 5.2 Numerical Results; 6 Future Directions; References; Localized Model Reduction in PDE Constrained Optimization; 1 Introduction; 2 Weak Formulation for the Parameterized Multiscale Problem and Non-conforming Reference Approximation; 3 A General Non-conforming Weak Formulation for Numerical Multiscale Methods; 4 A General Framework for Localized Model Reduction Based on Numerical Multiscale Methods with Oversampling; 5 The Reduced Basis Heterogeneous Multiscale Method (RB-HMM)