Journal of Parallel and Distributed Computing
Provably Good Partitioning and Load Balancing Algorithms for Parallel Adaptive N-Body Simulation
SIAM Journal on Scientific Computing
Parallel Hierarchical Solvers and Preconditioners for Boundary Element Methods
SIAM Journal on Scientific Computing
A solenoidal basis method for efficient inductance extraction
Proceedings of the 39th annual Design Automation Conference
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
A Provably Optimal, Distribution-Independent Parallel Fast Multipole Method
IPDPS '00 Proceedings of the 14th International Symposium on Parallel and Distributed Processing
Parallel iterative methods for dense linear systems in inductance extraction
Parallel Computing - Parallel matrix algorithms and applications (PMAA '02)
Parallel Software for Inductance Extraction
ICPP '04 Proceedings of the 2004 International Conference on Parallel Processing
Parallel performance of hierarchical multipole algorithms for inductance extraction
HiPC'04 Proceedings of the 11th international conference on High Performance Computing
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Inductance extraction involves estimating the mutual inductance in a VLSI circuit. Due to increasing clock speed and diminishing feature sizes of modern VLSI circuits, the effects of inductance are increasingly felt during the testing and verification stages. Hence, there is a need for fast and accurate inductance extraction software. A generalized approach for inductance extraction requires the solution of a dense complex symmetric linear system that models mutual inductive effects among circuit elements. Iterative methods are used to solve the system without explicit computation of the matrix itself. Fast hierarchical techniques are used to compute approximate matrix-vector products with the dense system matrix. This work presents an overview of a new parallel software package for inductance extraction of large VLSI circuits. The technique uses a combination of the solenoidal basis method and effective preconditioning schemes to solve the linear system. Fast Multipole Method (FMM) is used to compute approximate matrix-vector products with the inductance matrix. By formulating the preconditioner as a dense matrix similar to the coefficient matrix, we are able to use FMM for the preconditioning step as well. A two-tier parallelization scheme allows an efficient parallel implementation using both OpenMP and MPI directives simultaneously. The experiments conducted on various multiprocessor machines demonstrate the portability and parallel performance of the software.