The role of elimination trees in sparse factorization
SIAM Journal on Matrix Analysis and Applications
Parallel algorithms for forward and back substitution in direct solution of sparse linear systems
Supercomputing '95 Proceedings of the 1995 ACM/IEEE conference on Supercomputing
Matrix computations (3rd ed.)
Efficient large-scale power grid analysis based on preconditioned krylov-subspace iterative methods
Proceedings of the 38th annual Design Automation Conference
Reducing the bandwidth of sparse symmetric matrices
ACM '69 Proceedings of the 1969 24th national conference
Nested Dissection: A Survey
Parallel domain decomposition for simulation of large-scale power grids
Proceedings of the 2007 IEEE/ACM international conference on Computer-aided design
Power grid analysis benchmarks
Proceedings of the 2008 Asia and South Pacific Design Automation Conference
Stochastic Preconditioning for Diagonally Dominant Matrices
SIAM Journal on Scientific Computing
Circuit Simulation
PowerRush: a linear simulator for power grid
Proceedings of the International Conference on Computer-Aided Design
Fast static analysis of power grids: algorithms and implementations
Proceedings of the International Conference on Computer-Aided Design
On the preconditioner of conjugate gradient method: a power grid simulation perspective
Proceedings of the International Conference on Computer-Aided Design
Power grid analysis with hierarchical support graphs
Proceedings of the International Conference on Computer-Aided Design
A hierarchical matrix inversion algorithm for vectorless power grid verification
Proceedings of the International Conference on Computer-Aided Design
Hierarchical analysis of power distribution networks
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
A multigrid-like technique for power grid analysis
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Power grid analysis using random walks
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Deterministic random walk preconditioning for power grid analysis
Proceedings of the International Conference on Computer-Aided Design
2012 TAU power grid simulation contest: benchmark suite and results
Proceedings of the International Conference on Computer-Aided Design
PGT_SOLVER: an efficient solver for power grid transient analysis
Proceedings of the International Conference on Computer-Aided Design
PowerRush: efficient transient simulation for power grid analysis
Proceedings of the International Conference on Computer-Aided Design
2012 TAU power grid simulation contest: benchmark suite and results
Proceedings of the International Conference on Computer-Aided Design
Benchmarking for research in power delivery networks of three-dimensional integrated circuits
Proceedings of the 2013 ACM international symposium on International symposium on physical design
Scalable power grid transient analysis via MOR-assisted time-domain simulations
Proceedings of the International Conference on Computer-Aided Design
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Parallelizing power grid simulation with factorization-based direct or preconditioned iterative methods is a challenging task due to the data dependency among forward and back substitution. In this paper, we propose two approaches to parallelize forward and back substitution. The first approach exploits the parallelism by computing independent variables in parallel; the second approach resolves the data dependency by leveraging a node ordering produced by nested dissection. According to the requirements of TAU 2012 power grid simulation contest, a parallel power grid transient simulator is developed and tested with IBM power grid benchmarks. Results show that the second approach with the nested-dissection-based node ordering is more efficient.