List of Figures

• 2.1. SAXPY in a vector unit
• 2.2. Master-Slave
• 2.3. Pipe
• 2.4. The Ring.
• 2.5. Optimal tree in binary representation
• 2.6. Hypercube $d=0,\ldots ,3$
• 2.7. Embedding of a ring in a 3d hypercube
• 2.8. Characteristics of topologies
• 2.9. DeBrujin network $d=3$ : 8 nodes, 14 edges
• 3.1. Gauß-Seidel on a systolic array
• 3.2. Functional parallelism on 2 processors/units
• 3.3. Undefined status.
• 3.4. Results in an undefined status
• 3.5. Dinner for five
• 3.6. Release of a semaphore
• 3.7. Exclusive access with help of semaphores
• 3.8. Synchronization of characteristics using semaphores
• 3.9. Blocking communication
• 3.10. Non-blocking communication
• 3.11. Monitoring concept
• 3.12. EXCHANGE non-blocking
• 3.13. EXCHANGE blocking
• 3.14. Reduce operation in binary tree
• 3.15. All-Reduce in hypercube
• 3.16. Several Speedups
• 3.17. system times for Gauß, cg, pcg [Dr. Pester, Chemnitz]
• 4.1. Cyclic reduction $n=8$
• 4.2. Matrix distributed as block rows
• 4.3. Matrix distributed as block columns
• 4.4. Non-overlapping domain decomposition.
• 4.5. Non-overlapping elements.
• 4.6. Non-overlapping elements with a revised discretization.
• 4.7. Non-overlapping nodes.
• 4.8. Overlapping elements.
• 4.9. Overlapping nodes.
• 5.1. Data flow of Jacobi iteration
• 5.2. Data flow of Gauß-Seidel forward iteration
• 5.3. Data flow in Red-Black-Gauß-Seidel forward iteration
• 5.4. Domain decomposition of unit square
• 5.5. 2 super elements (=subdomains) with discretization
• 5.6. Non-overlapping element distribution on two nested grids
• 6.1. Static data dependencies in the Givens rotation
• 6.2. Flow chart on a shared memory computer : Givens rotation
• 6.3. Flow chart on a distributed memory computer: Givens rotation
• 6.4. Illustration to the rang-r-modification
• 6.5. Tridiagonal matrix and classical elimination tree
• 6.6. Matrix and elimination tree after rearranging by cyclic reduction.
• 6.7. Split of subscripts
• 6.8. Flow chart of FFT
• 7.1. Notations in the volume element $T_j$.
• 7.2. Flux between volume elements $T_j$ and $T_l$ (Steger and Warming).
• 7.3. Distributed boxes
• 7.4. Split boxes
• 7.5. Dual mesh
• 7.6. Dual mesh and domain decomposition

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