A Parallel Block Iterative Method for the Hydrodynamic Device Model

Carl L. Gardner; Donald J. Rose; Paul J. Lanzkron

doi:10.1109/43.85765

A Parallel Block Iterative Method for the Hydrodynamic Device Model

Carl L. Gardner, Donald J. Rose, Paul J. Lanzkron

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

Abstract

Block iterative methods are applied to hydrodynamic simulations of a one-dimensional (1-D) submicrometer semiconductor device. We show that block successive under-relaxation (SUR) converges with a fixed relaxation factor ω = 0.13 for simulations at 300 K and ω = 0.04 at 77 K. To demonstrate the robustness of the block iterative method, we present numerical simulations of a steady-state electron shock wave in Si at 300 K for a 0.1-μm channel and at 77 K for a 1.0-μm channel. The block SUR method is parallelizable if each diagonal block solve can be done efficiently in parallel. Using chaotic relaxation and the preconditioned conjugate gradient method for the parallel diagonal block solves, we obtain a parallel speed up of approximately 2.5 on 10 processors of a Butterfly GP-1000. The 1-D simulations serve as a numerical laboratory for developing methods that will be essential for computational efficiency in two-dimensional (2-D) problems.

Original language	English (US)
Pages (from-to)	1187-1192
Number of pages	6
Journal	IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Volume	10
Issue number	9
DOIs	https://doi.org/10.1109/43.85765
State	Published - Sep 1991
Externally published	Yes

ASJC Scopus subject areas

Software
Computer Graphics and Computer-Aided Design
Electrical and Electronic Engineering

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title = "A Parallel Block Iterative Method for the Hydrodynamic Device Model",

abstract = "Block iterative methods are applied to hydrodynamic simulations of a one-dimensional (1-D) submicrometer semiconductor device. We show that block successive under-relaxation (SUR) converges with a fixed relaxation factor ω = 0.13 for simulations at 300 K and ω = 0.04 at 77 K. To demonstrate the robustness of the block iterative method, we present numerical simulations of a steady-state electron shock wave in Si at 300 K for a 0.1-μm channel and at 77 K for a 1.0-μm channel. The block SUR method is parallelizable if each diagonal block solve can be done efficiently in parallel. Using chaotic relaxation and the preconditioned conjugate gradient method for the parallel diagonal block solves, we obtain a parallel speed up of approximately 2.5 on 10 processors of a Butterfly GP-1000. The 1-D simulations serve as a numerical laboratory for developing methods that will be essential for computational efficiency in two-dimensional (2-D) problems.",

author = "Gardner, {Carl L.} and Rose, {Donald J.} and Lanzkron, {Paul J.}",

note = "Funding Information: Manuscript received July 3, 1990. The work of C. L. Gardner was supported in part by the National Science Foundation under Grant DMS-8905872. The work of D. J. Rose was supported in part by the Office of Naval Research under Contract N00014-85-K-0487. This paper was recommended by Guest Editor M. Law.",

year = "1991",

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doi = "10.1109/43.85765",

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AU - Gardner, Carl L.

AU - Rose, Donald J.

AU - Lanzkron, Paul J.

N1 - Funding Information: Manuscript received July 3, 1990. The work of C. L. Gardner was supported in part by the National Science Foundation under Grant DMS-8905872. The work of D. J. Rose was supported in part by the Office of Naval Research under Contract N00014-85-K-0487. This paper was recommended by Guest Editor M. Law.

PY - 1991/9

Y1 - 1991/9

N2 - Block iterative methods are applied to hydrodynamic simulations of a one-dimensional (1-D) submicrometer semiconductor device. We show that block successive under-relaxation (SUR) converges with a fixed relaxation factor ω = 0.13 for simulations at 300 K and ω = 0.04 at 77 K. To demonstrate the robustness of the block iterative method, we present numerical simulations of a steady-state electron shock wave in Si at 300 K for a 0.1-μm channel and at 77 K for a 1.0-μm channel. The block SUR method is parallelizable if each diagonal block solve can be done efficiently in parallel. Using chaotic relaxation and the preconditioned conjugate gradient method for the parallel diagonal block solves, we obtain a parallel speed up of approximately 2.5 on 10 processors of a Butterfly GP-1000. The 1-D simulations serve as a numerical laboratory for developing methods that will be essential for computational efficiency in two-dimensional (2-D) problems.

AB - Block iterative methods are applied to hydrodynamic simulations of a one-dimensional (1-D) submicrometer semiconductor device. We show that block successive under-relaxation (SUR) converges with a fixed relaxation factor ω = 0.13 for simulations at 300 K and ω = 0.04 at 77 K. To demonstrate the robustness of the block iterative method, we present numerical simulations of a steady-state electron shock wave in Si at 300 K for a 0.1-μm channel and at 77 K for a 1.0-μm channel. The block SUR method is parallelizable if each diagonal block solve can be done efficiently in parallel. Using chaotic relaxation and the preconditioned conjugate gradient method for the parallel diagonal block solves, we obtain a parallel speed up of approximately 2.5 on 10 processors of a Butterfly GP-1000. The 1-D simulations serve as a numerical laboratory for developing methods that will be essential for computational efficiency in two-dimensional (2-D) problems.

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A Parallel Block Iterative Method for the Hydrodynamic Device Model

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