Colloquium January 30
Date: Friday, January 30
Time: 16:00 to 17:00
Place: 455 McBryde (Commons Room)
Speaker: John Singler of Missouri Univ of Science and Technology
Title: New POD-Based Algorithms for Model Reduction and Control of PDEs
Abstract: Model reduction and control problems for partial differential equations (PDEs) are important for many applications. For linear PDE systems, the solutions to such problems are known to exist, however they can be challenging to compute. We present new efficient and accurate algorithms for two fundamental problems in feedback control design and model reduction: approximating solutions of operator Lyapunov equations and constructing balanced reduced models of linear infinite dimensional systems. Our approach is based on proper orthogonal decomposition (POD), an optimal data reconstruction technique. We use POD systematically to provide convergence theory and error bounds for the algorithms. We also introduce the new group POD method for model reduction of certain types of time dependent nonlinear PDEs. We demonstrate on a model PDE that simulating the group POD reduced model is much more efficient than simulating a standard Galerkin POD-based reduced model.
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