Model order reduction for strictly passive and causal distributed systems

ABSTRACT

This paper presents a class of algorithms suitable for model reduction of distributed systems. Distributed systems are not suitable for treatment by standard model-reduction algorithms such as PRIMA, PVL, and the Arnoldi schemes because they generate matrices that are dependent on frequency (or other parameters) and cannot be put in a lumped or state-space form. Our algorithms build on well-known projection-based reduction techniques, and so require only matrix-vector product operations and are thus suitable for operation in conjunction with electromagnetic analysis codes that use iterative solution methods and fast-multipole acceleration techniques. Under the condition that the starting systems satisfy system-theoretic properties required of physical systems, the reduced systems can be guaranteed to be passive. For distributed systems, we argue that causality of the underlying representation is as important a consideration.

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INDEX TERMS

Primary Classification:
  B. Hardware
  B.7 INTEGRATED CIRCUITS
      B.7.2 Design Aids
          Subjects: Simulation

Additional Classification:
  B. Hardware
  B.8 Performance and Reliability
      B.8.2 Performance Analysis and Design Aids

  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.1 Interpolation
      G.1.2 Approximation

  I. Computing Methodologies
  I.6 SIMULATION AND MODELING

General Terms:
Algorithms, Design, Performance

Keywords:
distributed systems, passive reduced order modeling