Part I: Fundamentals and mathematical background

• Motivation of reduced order modeling (many-query, real-time, high-dimensional scenarios)
• Traditional engineering approaches: static condensation, modal decomposition
• Foundations of parametrized partial differential equations
• Proper orthogonal decomposition, snapshots, offline/online strategies
• Reduced basis methods, Galerkin projection and orthonormalization, sampling strategies

Part II: Model order reduction in computational solid mechanics

• Computational homogenization of heterogeneous materials
• Generalized multiscale finite element methods

Part III: Advanced topics

• Stability, system conditioning, empirical interpolation methods