A Supernodal Approach to Sparse Partial Pivoting
SIAM Journal on Matrix Analysis and Applications
The Design and Use of Algorithms for Permuting Large Entries to the Diagonal of Sparse Matrices
SIAM Journal on Matrix Analysis and Applications
An Asynchronous Parallel Supernodal Algorithm for Sparse Gaussian Elimination
SIAM Journal on Matrix Analysis and Applications
Solving Unsymmetric Sparse Systems of Linear Equations with PARDISO
ICCS '02 Proceedings of the International Conference on Computational Science-Part II
SuperLU_DIST: A scalable distributed-memory sparse direct solver for unsymmetric linear systems
ACM Transactions on Mathematical Software (TOMS)
Algorithm 837: AMD, an approximate minimum degree ordering algorithm
ACM Transactions on Mathematical Software (TOMS)
Fast circuit simulation on graphics processing units
Proceedings of the 2009 Asia and South Pacific Design Automation Conference
Towards dense linear algebra for hybrid GPU accelerated manycore systems
Parallel Computing
Algorithm 907: KLU, A Direct Sparse Solver for Circuit Simulation Problems
ACM Transactions on Mathematical Software (TOMS)
The university of Florida sparse matrix collection
ACM Transactions on Mathematical Software (TOMS)
TinySPICE: a parallel SPICE simulator on GPU for massively repeated small circuit simulations
Proceedings of the 50th Annual Design Automation Conference
IA^3 '13 Proceedings of the 3rd Workshop on Irregular Applications: Architectures and Algorithms
Parallel power grid analysis using preconditioned GMRES solver on CPU-GPU platforms
Proceedings of the International Conference on Computer-Aided Design
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Sparse solver has become the bottleneck of SPICE simulators. There has been few work on GPU-based sparse solver because of the high data-dependency. The strong data-dependency determines that parallel sparse LU factorization runs efficiently on shared-memory computing devices. But the number of CPU cores sharing the same memory is often limited. The state of the art Graphic Processing Units (GPU) naturally have numerous cores sharing the device memory, and provide a possible solution to the problem. In this paper, we propose a GPU-based sparse LU solver for circuit simulation. We optimize the work partitioning, the number of active thread groups, and the memory access pattern, based on GPU architecture. On matrices whose factorization involves many floating-point operations, our GPU-based sparse LU factorization achieves 7.90x speedup over 1-core CPU and 1.49x speedup over 8-core CPU. We also analyze the scalability of parallel sparse LU factorization and investigate the specifications on CPUs and GPUs that most influence the performance.