A Unified Krylov Projection Framework for Structure-Preserving Model Reduction

Physical systems often have certain characteristics that are critical in determining the system behavior. Often these characteristics appear in the form of system matrices that are naturally blocked with each sub-block having its own physical relevance. for example, the system matrices from linearizing a second order dynamical system admit a natural 2-by-2 block partitioning. General purpose subspace projection techniques for model order reduction usually destroy any block structure and thus the reduced systems may not be of the same type as the original system. For similar reasons we would like to preserve the block structure and hence some of the important characteristics so that the reduced systems are much like the original system but only at a much smaller scale.

The remainder of this chapter is organized as follows. In Section 2, we discuss a unified Krylov subspace projection formulation for model order reduction with properties of structure-preserving and moment-matching, and present a generic algorithm for constructing structure-preserving projection matrices. The inherent structural properties of Krylov subspaces for certain block matrices are presented in Section 3. Section 4 examines structure-preserving model order reduction of RCL and RCS equations including the objective to develop synthesized RCL and RCS equations.