Parallel Numerics

Content

1. Parallel Numerics
2.     overview
3.     Partial Differential Equations
4.     Solution Methods for Partial Differential Equations
5.     different aspects of parallelism
6.     Parallelism in hardware view
7.     Parallelism in software view
8.     Parallelism in performance view
9.     Parallelism in algorithmic view
10.     parallel operations on independent sets of data 1
11.     Vectorization: multiple gather
12.     Vectorization: scattering data
13.     F90: array syntax
14.     F90: index vectors
15.     F95: forall ... end forall different from do ... enddo
16.     parallel operations on independent sets of data 2
17.     recursive task generation 1
18.     recursive task generation 2
19.     functional decomposition 1
20.     functional decomposition 2
21.     neighbourhoods
22.     Finite Differences (Approximation of Differential Operators by Differences)
23.     Finite Differences 2
24.     Matrix for regular grid with 5-points stencil
25.     Finite Volumes (Flux Balance over neighbouring sides)
26.     finite volume and finite differences
27.     Finite Volume
28.     Triangular Grid with Relation Matrix
29.     Finite Elements (local matrices form a global matrix)
30.     unstructured self adaptive grids: CEQ 1
31.     unstructured self adaptive grids: CEQ 2
32.     unstructured for self adaptive grids: CEQ 3
33.     unstructured self adaptive grids: CEQ 4
34.     domain decomposition: overlapping grids and communication
35.     domain decomposition: properties
36.     domain decomposition: communicated surface for cubus
37.     regular grid partitioning of regular grid
38.     domain decomposition: irregular grid partitioning of regular grid
39.     domain decomposition: recursive Spectral Bisection
40.     domain decomposition:
41.     Recursive Spectral Bisection
42.     Recursive Spectral Bisection
43.     Partitioning Software
44. Large Systems
45.     Large Systems
46.     two different approaches
47.     main directions of linear solvers
48.     direct solvers
49.     simple iterative procedures: Gauss-Seidel
50.     simple iterative procedures: Jakobi
51.     Krylov space algorithms
52.     Conjugate Gradient Squared (CGS)
53.     BiCGSTAB(2)
54.     operations of Krylov space algorithms
55.     operations of Krylov space algorithms
56.     preconditioning
57.     MILU for general matrix
58.     overlapping domain decomposition
59.     non overlapping domain decompostion
60.     nonoverlapping Domain Decomposition
61.     nonoverlapping DD: several 2D domains
62.     nonoverlapping DD:
63.     nonoverlapping DD: separation of inner and boundary nodes
64.     nonoverlapping Domain Decomposition
65.     nonoverlapping DD: Schur complement
66.     nonoverlapping DD:
67.     nonoverlapping DD: dividing boundary nodes
68.     nonoverlapping DD: Preconditioner 1
69.     nonoverlapping DD: Preconditioner 2
70.     nonoverlapping DD: reference
71.     coloring: defining independent sets
72.     coloring of a graph: any neighbour has different color
73.     coloring
74.     Multigrid 1
75.     Multigrid 2
76.     Hierarchy of triangles
77.     hardware and implementation
78.     High Performance for Fast Methods
79.     parameters of performance limits
80.     bandwidth
81.     latency
82.     overcoming latency
83.     Latency from processor to various locations
84.     dependency of bandwidth and latency
85.     dependency of bandwidth and latency 2
86.     Bandwidth-Performance relation for multi-block grid with cubes
87.     Example multiblock technique (optimal case)
88.     distributions in quadratic patches
89.     distribution in line patches
90.     High Performance Systems
91.     ASCI White IBM[2000]
92.     Earth-Simulator Project: end 2001
93.     programming techniques
94.     getting processor performance by loops with arrays
95.     flexible but expensive: linked list 1
96.     flexible but expensive: linked list 2
97.     nice but expensive: recursive calls
98.     recursive calls 2
99.     modifying a hierarchical grid
100.     inhibiting processor performance
101.     good for performance
102.     cache reuse for heat transfer: different implementations on SGI R10000
103.     object oriented programming
104.     Formulation of flexible neighbourhoods
105.     discrete operators and sparse matrices
106.     handling sparse matrices
107.     Sparse matrix example
108.     Sparse matrix: row ordered example
109.     Row ordered and jagged diagonal matrices:data structure
110.     Row ordered: matrix vector multiplication
111.     Sparse matrices: jagged diagonal example
112.     jagged diagonal matrix: matrix vector multiplication
113.     Row ordered and jagged diagonal matrix diagonal matrix formulation: performance
114.     Conclusion
115.     Books and URLs 1
116.     Books and URLs 2
117.     End