Contents
Home
Abstract
Kurzfassung
Acknowledgement
List of Figures
List of Tables
List of Abbreviations
1 Introduction and Motivation
1.1 Research Goals
1.2 Research Setting
1.3 Thesis Outline
2 Theory and Background
2.1 Graphs
2.1.1 Graph Coloring
2.1.2 Solving the Graph Coloring Problem
2.1.3 Solution Quality
2.2 Meshes
2.2.1 Mesh Quality
2.2.2 Mesh Adaptation
2.2.2.1 Refinement
2.2.2.2 Swapping
2.2.2.3 Coarsening
2.2.2.4 Smoothing
2.3 Parallel Computers
2.3.1 Basic Computer Architecture
2.3.1.1 Multi-Core Processor
2.3.1.2 Multi-Threaded Processor
2.3.2 Parallel Programming
2.3.2.1 Shared-Memory Systems
2.3.2.2 Distributed-Memory Systems
2.3.2.3 Hybrid Systems
2.3.2.4 Accelerators
2.3.2.5 Basics of Parallelization
2.4 Benchmarking Platforms
3 Approximative Shared-Memory Graph Coloring Algorithms
3.1 Related Work
3.1.1 Exact Algorithms
3.1.2 Approximative Algorithms
3.1.3 Shared-Memory Parallel Algorithms
3.2 Evaluation
3.2.1 Benchmark Platforms and Setup
3.2.2 Test Graphs
3.2.3 Coloring Quality
3.2.4 Performance Analysis
3.3 Summary and Conclusion
4 Coarse-Grained Shared-Memory Parallel Mesh Adaptation
4.1 Related Work
4.1.1 Distributed-Memory Methods
4.1.2 Shared-Memory Parallel Methods
4.1.3 Hybrid Methods
4.2 Software Tools
4.3 Coarse-Grained Parallel Mesh Adaptation Framework
4.3.1 Partitioning and Coloring
4.3.2 Mesh Adaptation and Mesh Healing
4.4 Evaluation
4.4.1 Test Geometries and Benchmark Setup
4.4.2 Partition Coloring
4.4.3 Strong Scalability
4.4.4 Mesh Quality
4.5 Summary and Conclusion
5 Material Interface-Aware Surface Mesh Partitioning for Process TCAD
5.1 Related Work
5.2 Dual-Damascene Process
5.3 Multi-Material Representation
5.4 Multi-Material Interface-Aware Iterative Partitioning
5.5 Evaluation
5.5.1 Simulation Setup
5.5.2 Performance and Accuracy
5.5.3 Variation of Thresholds
5.5.4 Strong Scalability
5.6 Summary and Conclusion
6 Summary and Outlook
Bibliography
Curriculum Vitae
Own Publications
1.1 Hierarchical structure and interplay of the different parts of TCAD.
1.2 General overview of a TCAD simulation workflow
1.3 2D meshes of a surface of an etching simulation
1.4 Two exemplary 3D tetrahedral meshes
1.5 Examples of a structured and an unstructured mesh
1.6 Schematics of a distributed- and shared memory computer system
1.7 Example graph with corresponding coloring
1.8 Exemplary partitioning of a FinFET into independent sets
2.1 General graph
2.2 Simple graph
2.3 A graph and one possible distance-1 coloring
2.4 Balanced and unbalanced population of color classes
2.5 Examples of finite point sets and their convex hulls
2.6 A tetrahedron (or 3-simplex)
2.7 A 2D Delaunay triangulation of a given point set V
2.8 Conforming and non-conforming mesh
2.9 Template-based refinement scheme for a triangle
2.10 Edge flip operation on triangular mesh elements
2.11 Edge collapse operation
2.12 Laplacian smoothing of a 2D mesh
2.13 Main building blocks of the stored-program digital computer
2.14 A data-centric view of a cache-based computer design
2.15 Different examples of multi-core designs
2.16 Example of a hexa-core design
2.17 Example design of a UMA system
2.18 An example of four locality domains comprising a (cc)NUMA system
2.19 A distributed-memory system
3.1 Degree distributions of the test graphs
3.2 Color populations of the test graphs using different algorithms
3.3 Speedups for the test graphs
4.1 Fundamental workflow of the coarse-grained mesher
4.2 Two different geometries investigated in this study
4.3 Refinement and healing procedure using a so-called outbox
4.4 Example showing the healing issue
4.5 Population of the different Color IDs
4.6 Strong scaling results for the two cube geometries
4.7 Initial mesh quality distributions of the different test meshes
4.8 Resulting mesh quality distributions of the different test meshes
5.1 Processing steps for the self-aligned Dual-Damascene process
5.2 An exemplary multi-material stack
5.3 The multi-material schematic process
5.4 Top layer across a material interface
5.5 Simulation geometry for the etching simulation
5.6 Influence of different level-set resolutions in an etching simulation
5.7 Surface of simulation domain with the cells of the sparse set in red
5.8 Ratio x_\text {rel}, relative speedup S_{rel}, and maximum surface deviation (Dev)
5.9 Relative average speedups S^{avg}_\text {rel}and average ratios x_{\text {rel}}^{avg}
5.10 Average runtimes and speedups at various level-set resolutions
5.11 Contributions of the four major steps in the sparse flux calculation