Efficient Linear System Solution Techniques in the Simulation of Large Dense Mutually Inductive Circuits

The verification of integrated Circuits (ICs) in deep
submicron technologies requires that all mutual inductive effects
are taken into account to properly validate the performance and
reliable operation of the chip. However, the inclusion of all mutual
inductive couplings results in a fully dense inductance matrix that
renders the circuit simulation computationally intractable. In this
paper we present efficient techniques for the solution of the linear
systems arising in transient analysis of large mutually inductive
circuits. These involve the compression of the dense inductance
matrix block by low-rank products in hierarchical matrix format,
as well as the development of a Schur-complement preconditioner
for the iterative solution of the transient linear system (which
comprises sparse blocks alongside the dense inductance block).
Experimental results indicate that substantial compression rates
of the inductance matrix can be achieved without compromising
accuracy, along with considerable reduction in iteration count
and execution time of iterative solution methods.