Multigrid Methods for Process Simulation
It was about 1985 when both of the authors started their work using multigrid methods for process simulation problems. This happened in dependent from each other, with a completely different background and different intentions in mind. At this time, some important monographs appeared or have been i...
| Main Authors: | , |
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| Format: | eBook |
| Language: | English |
| Published: |
Vienna
Springer Vienna
1993, 1993
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| Edition: | 1st ed. 1993 |
| Series: | Computational Microelectronics
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 5.4 Local Grid-Decomposition Algorithmic Strategy for Simulation of Multiparticle Evolution Processes
- 5.5 Simulation of Critical Process Simulation Steps of BiCMOS Technology—Case Study
- References
- 1 Introduction
- 2 A Practical Guide to Standard Multigrid Methods
- 2.1 Continuous and Discrete Model Problems
- 2.2 The Multigrid Principle
- 2.3 The Components of the Algorithm
- 2.4 Multigrid Strategies for Model Problems—Complete Algorithms
- 2.5 The Full Approximation Scheme
- 2.6 Full Multigrid
- 2.7 Multigrid Methods for Refined Grids
- 2.8 Parabolic Initial Boundary Value Problems
- 2.9 Systems of Partial Differential Equations
- 2.10 Tools to Estimate Multigrid Convergence
- 2.11 Multigrid on Parallel Computers
- 2.12 Standard Multigrid for Semiconductor Device Simulation
- 3 Adaptive Multilevel Grid Selection Strategies for Process Simulation Evolution Problems
- 3.1 Adaptive Multilevel Discrete Approximation
- 3.2 Discretization Errors and Their Properties
- 3.3 Evaluation of the Discretization Errors by Two-Level Extrapolation Techniques
- 3.4 Local Refinement Criteria Based on Discretization Errors
- 3.5 Two-Level Time Stepping Schemes Based on Extrapolation Techniques
- 4 Tayloring Multigrid Components for a Diffusion Model Problem
- 4.1 The Physical Problem and the Mathematical Representation
- 4.2 The Discretization
- 4.3 Relaxation Methods
- 4.4 Results of the Smoothing Analysis with Respect to Time-Step Size
- 4.5 Experiments with the Crank-Nicolson Scheme and with the Fully Implicit Scheme
- 4.6 The Prolongation of Grid Functions
- 4.7 The Restriction of Approximations and of Residuais
- 4.8 Technical Aspects of Time-Dependent Refinements
- 4.9 Numerical Results for the Model Problem
- 5 Procedures for Adaptive Multigrid Simulation of Evolution Processes
- 5.1 Practical Algorithmic and Programming Techniques for Multilevel Local Grid Refinement
- 5.2 The Adaptive Construction of an Initial State Discrete Approximation
- 5.3 Basic Procedures for theAdaptive Transient Simulation of Evolution Problems