Projection Based Model Reduction for Optimal Design of the Time-dependent Stokes System

摘要: The optimal design of structures and systems described by partial differential equations (PDEs) often gives rise to large-scale optimization problems, in particular if the underlying system PDEs represents a multi-scale, multi-physics problem. Therefore, reduced order modeling techniques such as balanced truncation model reduction, proper orthogonal decomposition, or basis methods are used significantly decrease computational complexity while maintaining desired accuracy approximation. In particular, we interested shape problems where issue is restricted relatively small portion domain. this case, it appears be natural rely on full only that specific part domain use elsewhere. A convenient methodology realize idea consists suitable combination decomposition reduction. We will consider an approach for associated with time-dependent Stokes derive explicit error bounds error. As application life sciences, concerned capillary barriers network microchannels reservoirs microfluidic biochips clinical diagnostics, pharmacology, forensics high-throughput screening hybridization genomics protein profiling proteomics.