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## MATEX: A Distributed Framework for Transient Simulation of Power Distribution Networks

### Citations

2277 |
Iterative Methods for Sparse Linear Systems
- Saad
- 1996
(Show Context)
Citation Context .... However, at each time step, these methods have to solve a linear system, which is sparse and often ill-conditioned. Due to the requirement of a robust solution, compared to iterative matrix solvers =-=[12]-=-, direct matrix solvers [5] are often favored for VLSI circuit simulation, and thus adopted by state-of-the-art power grid (PG) solvers in TAU PG simulation contest [18–20]. During transient simulatio... |

191 |
Direct methods for sparse linear systems,
- Davis
- 2006
(Show Context)
Citation Context ..., these methods have to solve a linear system, which is sparse and often ill-conditioned. Due to the requirement of a robust solution, compared to iterative matrix solvers [12], direct matrix solvers =-=[5]-=- are often favored for VLSI circuit simulation, and thus adopted by state-of-the-art power grid (PG) solvers in TAU PG simulation contest [18–20]. During transient simulation, these solvers require on... |

134 | Analysis of some Krylov subspace approximations to the matrix exponential operator
- Saad
- 1992
(Show Context)
Citation Context ...ed exponential time differencing (ETD) has been embraced by MEXP [15]. The major complexity of ETD is caused by matrix exponential computations. MEXP utilizes standard Krylov subspace method based on =-=[11]-=- to approximate matrix exponential and vector product. MEXP can solve the DAEs with high polynomial approximations [11, 15] than traditional ones. Another merit of using MEXP-like SPICE simulation for... |

128 |
et al., “A view of cloud computing
- Armbrust, Fox, et al.
- 2010
(Show Context)
Citation Context ...uits have been always favored. Nowadays, the emerging multi-core, many-core platforms bring powerful computing resource and opportunities for parallel computing. Even more, cloud computing techniques =-=[1]-=- drive distributed systems scaling to thousands of computing nodes [6], etc. Such Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without... |

94 | Hierarchical analysis of power distribution networks.
- Zhao, Panda, et al.
- 2002
(Show Context)
Citation Context ...eavily on the analysis of power distribution network (PDN) to estimate power supply noises. PDN is often modeled as a large-scale linear circuit with voltage supplies and time-varying current sources =-=[8, 21]-=-. Such circuit is extremely large, which makes the corresponding transient simulation very time-consuming. Therefore, scalable and theoretically elegant algorithms for the transient simulation of line... |

24 |
den Eshof and M. Hochbruck, Preconditioning Lanczos approximations to the matrix exponential
- van
(Show Context)
Citation Context ...ximation in MEXP [15] is not computationally efficient for stiff circuit. The reason is that Hessenberg matrix Hm of standard Krylov subspace tends to approximate the large magnitude eigenvalues of A =-=[13]-=-. Due to the exponential decay of higher order terms in Taylor’s expansion, such components are not the crux of circuit system’s behavior [2, 13]. Dealing with stiff circuit, therefore, needs to gathe... |

22 |
et al. Mesos: A platform for fine-grained resource sharing in the data center
- Hindman
- 2011
(Show Context)
Citation Context ...-core platforms bring powerful computing resource and opportunities for parallel computing. Even more, cloud computing techniques [1] drive distributed systems scaling to thousands of computing nodes =-=[6]-=-, etc. Such Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or co... |

18 | Power grid analysis benchmarks.
- Nassif
- 2008
(Show Context)
Citation Context ...x. x(t) is the vector of time-varying node voltages and branch currents. u(t) is the vector of supply voltage and current sources. In PDN, such current sources are often characterized as pulse inputs =-=[8, 10]-=-. To solve Eq. (1) numerically, it is, commonly, discretized with time step h and transformed to a linear algebraic system. Given an initial condition x(0) from DC analysis, or previous time step x(t)... |

17 |
Kronecker's Canonical Form and the QZ Algorithm
- Wilkinson
- 1979
(Show Context)
Citation Context ...rings extra computational overhead when the case is large. Actually, it is not necessary if we can obtain the generalized eigenvalues and corresponding eigenvectors for matrix pencil (−G,C). Based on =-=[17]-=-, we derive the following lemma, Lemma 1. Considering a homogeneous system Cẋ = −Gx, u and λ are the eigenvector and eigenvalue of matrix pencil (−G,C), then x = etλu is a solution of this system. An... |

10 |
Circuit Simulation.
- Najm
- 2010
(Show Context)
Citation Context ...tes to deal with these scenarios. 4.2 Adaptive Time Stepping Comparisons IBM power grid benchmarks [10] are used to investigate the performance of adaptive stepping TR (adpt) based on LTE controlling =-=[9, 15]-=- as well as the performance of I-MATEX and R-MATEX. Experiment is carried out on a single computing node. In Table 2, the speedups of I-MATEX is not as large as R-MATEX because I-MATEX with a large sp... |

5 |
P.: Computer aided analysis of electric circuits: algorithms and computational techniques, rst edn
- Chua, Lin
- 1975
(Show Context)
Citation Context ...is an efficient framework and adopted by the top PG solvers in 2012 TAU PG simulation contest [8, 18–20]. 2.2 Exponential Time Differencing Method The solution of Eq. (1) can be obtained analytically =-=[4]-=-. For simple illustration, we convert Eq. (1) into ẋ(t) = Ax(t) + b(t), (3) when C is not singular, A = −C−1G and b(t) = C−1Bu(t). Given the solution at time t and a time step h, the solution at t+ h... |

4 |
Parallel forward and back substitution for efficient power grid simulation
- Xiong, Wang
- 2012
(Show Context)
Citation Context ...ansient computation, at each fixed time step, needs only a pair of forward and backward substitutions, which achieves better efficiency over adaptive stepping methods by reusing the factorized matrix =-=[8, 18,20]-=-. Beyond traditional methods, a new class of methods called exponential time differencing (ETD) has been embraced by MEXP [15]. The major complexity of ETD is caused by matrix exponential computations... |

4 | Powerrush: Efficient transient simulation for power grid analysis - Yang, Li, et al. - 2012 |

3 | A short guide to exponential Krylov subspace time integration for Maxwell’s equations
- Botchev
- 2012
(Show Context)
Citation Context ...tends to approximate the large magnitude eigenvalues of A [13]. Due to the exponential decay of higher order terms in Taylor’s expansion, such components are not the crux of circuit system’s behavior =-=[2, 13]-=-. Dealing with stiff circuit, therefore, needs to gather more vectors into subspace basis and increase the size of Hm to fetch more useful components, which results to both memory overhead and computa... |

3 |
2012 tau power grid simulation contest: benchmark suite and results
- Li, Balasubramanian, et al.
- 2012
(Show Context)
Citation Context ...eavily on the analysis of power distribution network (PDN) to estimate power supply noises. PDN is often modeled as a large-scale linear circuit with voltage supplies and time-varying current sources =-=[8, 21]-=-. Such circuit is extremely large, which makes the corresponding transient simulation very time-consuming. Therefore, scalable and theoretically elegant algorithms for the transient simulation of line... |

3 |
Time-domain analysis of large-scale circuits by matrix exponential method with adaptive control.
- Weng, Chen, et al.
- 2012
(Show Context)
Citation Context ...ncy over adaptive stepping methods by reusing the factorized matrix [8, 18,20]. Beyond traditional methods, a new class of methods called exponential time differencing (ETD) has been embraced by MEXP =-=[15]-=-. The major complexity of ETD is caused by matrix exponential computations. MEXP utilizes standard Krylov subspace method based on [11] to approximate matrix exponential and vector product. MEXP can s... |

3 | Circuit simulation via matrix exponential method for stiffness handling and parallel processing - Weng, Chen, et al. |

3 |
Pgt solver: an efficient solver for power grid transient analysis
- Yu, Wong
- 2012
(Show Context)
Citation Context ...ansient computation, at each fixed time step, needs only a pair of forward and backward substitutions, which achieves better efficiency over adaptive stepping methods by reusing the factorized matrix =-=[8, 18,20]-=-. Beyond traditional methods, a new class of methods called exponential time differencing (ETD) has been embraced by MEXP [15]. The major complexity of ETD is caused by matrix exponential computations... |

2 |
A practical regularization technique for modified nodal analysis in largescale time-domain circuit simulation
- Chen, Weng, et al.
- 2012
(Show Context)
Citation Context ...1 and Alg. 2 with input matrices X1 = (C + γG) for the LU decomposition, and X2 = C. 3.3.3 Regularization-Free Matrix Exponential Method When dealing singular C, MEXP needs the regularization process =-=[3]-=- to remove the singularity of DAE in Eq. (1). It is because MEXP is required to factorize C in Alg. 1. This brings extra computational overhead when the case is large. Actually, it is not necessary if... |

1 | Parallel circuit simulation: A historical perspective and recent developments - Li |

1 | Scalable power grid transient analysis via mor-assisted time-domain simulations - Wang, Xiong - 2013 |

1 | Power grid simulation using matrix exponential method with rational krylov subspaces
- Zhuang, Weng, et al.
- 2013
(Show Context)
Citation Context ... very sensitive to γ, once it is set to around the order near time steps used in transient simulation. The similar idea has been applied to simple power grid simulation with matrix exponential method =-=[22]-=-. Here, we generalize this technique and integrate into MATEX. The Arnoldi process constructs Vm and Hm, and the relationship is given by (I−γA)−1Vm = VmH̃m+ h̃m+1,mvm+1eTm, we can project the eA onto... |