A parallel Hamiltonian eigensolver for passivity characterization and enforcement of large interconnect macromodels

The passivity characterization and enforcement of linear interconnect macromodels has received much attention in the recent literature. It is now widely recognized that the Hamiltonian eigensolution is a very reliable technique for such characterization. However, most available algorithms for the determination of the required Hamiltonian eigenvalues still require excessive comoputational resources for large-size macromodels with thousands of states. This work intends to break this complexity by introducing the first parallel implementation of a specialized Hamiltonian eigensolver, designed and optimized for shared memory multicore architectures. Our starting point is a multi-shift restarted and deflated Arnoldi process. Excellent parallel efficiency is obtained by running different Arnoldi iterations concurrently on different threads. The numerical results show that macromodels with several thousands states are characterized in few seconds on a 16-core machine, with close to ideal speedup factors.