An approach to construct pre-conditioning matrices for block iteration of linear equations

Wang, Z.-Y.; Wu, Kechih; Dutton, R.W.

doi:10.1109/43.177397

Cited by 6 publications

(4 citation statements)

References 13 publications

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“…Therefore, we can expect that the degree of coupling of the off-diagonal blocks has been reduced to some extent This decoupling operator was proposed by Bank et al 27 as the Alternate-Block Factorization (ABF) procedure and is subject to further analysis in other works 28,29 . The ABF operator was successfully applied by Klie 13 for two-phase flow problems where Properties 1-5 from above were shown to be strongly satisfied under mild conditions (e.g., if blocks ps A and sp A satisfy the M-matrix condition).…”

Section: Decoupling Operatorsmentioning

confidence: 96%

Algebraic Multigrid Methods (AMG) for the Efficient Solution of Fully Implicit Formulations in Reservoir Simulation

Stueben

Clees

Klíe

et al. 2007

SPE Reservoir Simulation Symposium

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fax 01-972-952-9435. AbstractA primary challenge for a new generation of reservoir simulators is the accurate description of multiphase flow in highly heterogeneous media and very complex geometries. However, many initiatives in this direction have encountered difficulties in that current solver technology is still insufficient to account for the increasing complexity of coupled linear systems arising in fully implicit formulations. In this respect, a few works have made particular progress in partially exploiting the physics of the problem in the form of two-stage preconditioners.

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Section: Decoupling Operatorsmentioning

confidence: 96%

Algebraic Multigrid Methods (AMG) for the Efficient Solution of Fully Implicit Formulations in Reservoir Simulation

Stueben

Clees

Klíe

et al. 2007

SPE Reservoir Simulation Symposium

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“…Many workers have observed that a superior preconditioner can boost performance by an order of magnitude [5], [40], while a better acceleration technique may only improve the performance by 10-30%. In [5] and [34], various new developments in iterative methods for device simulation have been summarized.…”

mentioning

confidence: 98%

“…If the Jacobian equations are ordered so that all the electric potential equations are grouped first, followed by the electron conservation equations, and then the hole conservation equations, and the unknowns are ordered so that all the electric potentials are first, then the electron concentrations, and finally the hole concentrations, then the Jacobian matrix can be partitioned as where Dij is the diagonal matrix of Jij. More recently, the approximate block elimination (ABE) has been proposed which uses an incomplete 3 x 3 block factorization of the original block structured Jacobian [40].…”

mentioning

confidence: 99%

Performance Issues for Iterative Solvers in Device Simulation

Qing¹,

McMacken²,

Tang³

1996

SIAM J. Sci. Comput.

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Due to memory limitations, iterative methods have become the method of choice for large scale semiconductor device simulation. However, it is well known that these methods suffer from reliability problems. The linear systems that appear in numerical simulation of semiconductor devices are notoriously ill conditioned. In order to produce robust algorithms for practical problems, careful attention must be given to many implementation issues. This paper concentrates on strategies for developing robust preconditioners. In addition, effective data structures and convergence check issues are also discussed. These algorithms are compared with a standard direct sparse matrix solver on a variety of problems.

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“…Nevertheless, this formulation is instructive in the sense that besides approximating the main diagonal A , which is dictated by the requirement for simplicity, the coupling matrix A, is also approximated by its diagonal Dan,,,. The significance of this approximation become dear when it is realized that a scheme using A instead of DQnv had been tried in [6] …”

Section: Discussionmentioning

confidence: 98%

Further improvements in decoupled methods for semiconductor device modeling

Obrecht

Heasell

Elmasry

et al.

Proceedings of International Workshop on Numerical Modeling of Processes and Devices for Integrated Circuits: NUPAD V

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Two complementary techniques for accelerating the Gummel iterations are successfully combined to yield an efficient and robust. decoupled nonlinear solution method for semiconductar device simulation. The reasons for this success are explored. The effectiveness of the new method under high level injection, and its robustness in the presence of large time or bias steps should pave the way to its widespread application in multidimensional semiconductor device simulation.

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An approach to construct pre-conditioning matrices for block iteration of linear equations

Cited by 6 publications

References 13 publications

Algebraic Multigrid Methods (AMG) for the Efficient Solution of Fully Implicit Formulations in Reservoir Simulation

Algebraic Multigrid Methods (AMG) for the Efficient Solution of Fully Implicit Formulations in Reservoir Simulation

Performance Issues for Iterative Solvers in Device Simulation

Further improvements in decoupled methods for semiconductor device modeling

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