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Ortega J.M., Voigt R.G. — Solution of Partial Differential Equations on Vector and Parallel Computers
Ortega J.M., Voigt R.G. — Solution of Partial Differential Equations on Vector and Parallel Computers

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Название: Solution of Partial Differential Equations on Vector and Parallel Computers

Авторы: Ortega J.M., Voigt R.G.


This volume reviews, in the context of partial differential equations, algorithm development that has been specifically aimed at computers that exhibit some form of parallelism. Emphasis is on the solution of PDEs because these are typically the problems that generate high computational demands. The authors discuss architectural features of these computers insomuch as they influence algorithm performance, and provide insight into algorithm characteristics that allow effective use of hardware.
Both direct and indirect methods are given for elliptic equations as well as explicit and implicit methods for initial boundary-value problems. The intent is to point out attractive methods as well as areas where this class of computer architecture cannot be fully utilized because of either hardware restrictions or the lack of adequate algorithms.

Язык: en

Рубрика: Computer science/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1987

Количество страниц: 100

Добавлена в каталог: 01.11.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
Предметный указатель
Acoustic wave propagation, parallel computing and      62
Adaptive computation      56
Adaptive finite element system      57
Adaptive grids      56
ADI method      48
Aerodynamics computations      59
Algorithm speedup      6
Algorithm(s)      see also "Individual algorithm names"
Algorithm(s), consistent, definition of      34
Algorithm(s), development of, for sparse matrices      2
Algorithm(s), flux-corrected transport      58
Algorithm(s), multigrid      45
Algorithm(s), sequential      3
Alternating Direction Implicit method      48
Amdahl's Law      10
Annihilation patterns      24
Architecture, parallel      1
Architecture, pipeline      1
Asynchronization, Jacobi iteration and      44
Asynchronous, iteration      44
Banyan switch      17
Benard Rayleigh problem, parallel computing and      58
Binary k-cube structure      16
Block algorithm, for tridiagonal systems      36
Block elimination algorithm      22
Block factorization methods, for sparse matrices      30
Block Gaussian elimination      22
Block method, for sparse matrices      30
Block partitioning, algorithms of      22
Block SOR method      48
Block SOR method, transonic flow problems and      60
Block tridiagonal matrices, cyclic reduction for      35
Block tridiagonal systems      17
Block tridiagonal systems, algorithm for      36
Block tridiagonal systems, cyclic reduction for      34
Blocking, in sparse matrices      31
Boltzmann equation, Monte Carlo method for      58
Boolean Vector Machine processor      19
Brailovskaya's method, vector computing and      58
Burroughs Scientific Processor      2
Bus array      14 15 16
C.mmp      17
C.mmp, switch array as      15
Capacitance matrix methods      54
Cayley — Hamilton theorem, Gaussian elimination and      26
Cedar project      19
Cedar project, architecture      57
CG methods      49
Chaining, on Cray      11 12
Chaotic relaxation methods      44
Checkerboard method, timing and      60
CHiP computer      18
Choleski decomposition      20 25
Classical multigrid algorithm      47
CM* array      16
Coefficients, variable, methods using      53
Column sweep algorithm      21
Communication, among processors      13
Communication, cost of      4
Communication, multigrid algorithms and      46
Compilers, Fortran      4
Compress instruction      10
Compressible flow problems, parallel computing and      59
Computation rates, maximum, for Cyber 203      9
Computation, adaptive      56
Computational complexity analysis      3
Computers, parallel, types of      12
Computing, parallel, books on      2
Configurable highly parallel computer      18
Conjugate gradient methods      49
Consistent algorithm(s)      36
Consistent algorithm(s), definition of      34
Control vector, in Jacobi's method      41
Convection problems, parallel computing and      58
Convergence, in CG methods      49
Convex Inc.      2
Cosmic cube structure      16
Cramer's rule, tridiagonal systems and      36
Crank — Nicolson scheme      55
Cray computers      10
Cray computers, multigrid algorithm for      46
Cray computers, performance of      11
Cray computers, schematic of      11
Crosspoint switch, in parallel computing      17
Cube-connected-cycles      19
Cyber 200      8
Cyber 200, multigrid algorithm for      46
Cyber 200, schematic of      9
Cyclic Chebyshev-SI method      49
Cyclic elimination      35
Cyclic reduction, methods for      34
DAP computer      12
Dataflow computer      19
Decomposition, matrix      see also "Matrix decomposition"
Degree of parallelism      20
Delayed Wavefront algorithm for triangular systems      26
Digital optical computing      7
Direct methods for linear equations      19
Discrete elliptic equations, iterative methods for      40
Discretization stencil      44
Dissection, nested      27 see
Dissection, one-way      27
Distributed Array Processor      14
Divide and conquer principle      5
DO loops, rearrangement of      3
Domains, irregular      54
Driven cavity problem      58
Dufort — Frankel differencing, for convection problems      58
Earthquake analysis, parallel computing and      62
Efficiency measure, definition of      7
EGPA, matrix decomposition and      39
Elimination algorithms      20
Elimination methods for linear equations      20
Elimination methods for solving linear equations      19
Elimination methods, Gaussian      20
Elxsi      2
ENIAC      7
Erlangen General Purpose Array system, matrix decomposition and      39
Execution time, measurement of      6
Explicit methods, vs. implicit methods      54
FACR algorithm      39
Factorization methods for solving linear equations      19
Fan-out tree array      15
Fast Fourier Transform      3
Fast Fourier Transform, algorithms using      37
Fast Fourier Transform, perfect shuffle and      38
Fast Poisson solvers for linear equations      19
Fast Poisson solvers, cyclic reduction as      39
Fast Poisson solvers, Fast Fourier Transform in      38
Fast Poisson solvers, methods for      37
Fast Poisson solvers, multigrid algorithm and      40 46
FCT algorithm      58
FEARS project      57
FFT      see "Fast Fourier Transform"
Finite Element Machine      18
Finite Element Machine, linear equation algorithms for      22
Finite element method, adaptive      57
Finite element method, structural analysis and      62
Flexible Computer Inc.      2
Floating point number, communication of      5
Floating point pipeline      8
Fluid dynamics, parallel computing in      58
Flux-corrected transport algorithm      58
Fortran compilers      4
Four-color ordering for parallel computing      43
Four-color ordering, ICCG algorithm and      51
Frontal method for sparse matrices      30
Gather instruction      10
Gauss — Jordan algorithm      21
Gauss — Seidel iteration      41
Gaussian elimination      20
George algorithm, nested dissection and      28
Givens annihilation patterns      24
Givens reduction      23
Givens transformations      23
Givens transformations, pivoting for stability and      36
Global weather forecasting      61
Graves' method, vector computing and      58
Half-performance length      10
Hardware instructions      10
Hardware, review of      7—19
Hep      17
Heterogeneous Element Processor      17
Holland Machine      12
Householder transformations      23
Hydrodynamics, parallel computing and      58
Hyperbolic equations, methods for      54 56
ICCG methods      50
Illiac computer      2 12
Illiac computer, lattice interconnection in      13
Implicit methods, vs. explicit methods      54
Incomplete block cyclic reduction, ICCG algorithm and      51
Incomplete Choleski conjugate gradient methods      50
Incompressible inviscid homogeneous fluid problems      59
Inconsistency in algorithms for tridiagonal systems      34
Indirect addressing in sparse matrices      30
Interchange strategy, into Gaussian elimination      23
Interconnection schemes      13 14
Irregular domains      54
Irregular regions      54
Iterative methods      40—58
Iterative methods, tridiagonal systems and      36
Jacobi iteration method      40
Jacobi iteration method, implementation of      44
Jacobi iteration method, overrelaxed      45
Jacobi-Overrelaxed Quadrant Interlocking method      45
Jacobi-SI method      49
Japanese supercomputers      12
JOQI method      45
Laplace equation, iterative and time marching methods and      40
Lattice arrays      14
Lattice arrays, in Illiac computer      13
Lax — Wendroff scheme      56
Least squares problems, orthogonal reduction and      24
Linear equations, direct methods for      19—40
Linked triads      9
Loop unrolling      4
LU factorization, using systolic arrays      14
Machine cycles, elimination methods and      20
Manchester Data Flow Machine      19
Massively Parallel Processor      14
Matrices, sparse      see "Sparse matrices"
Matrix decomposition, Fast Fourier Transform and      38
Matrix multiplication, using systolic arrays      14
Maximum parallelism      26
Memory, tridiagonal systems and      37
Merge instruction      10
Method of lines      53
MIDAS processor      18
MIMD systems      12
Minsky conjecture      7
Molecular dynamics, parallel computing and      62
Monte Carlo method, for Boltzmann equation      58
MPP      14
Multi-dimensional lattices      16
Multicolor ordering in SOR iterations      42
Multicolor ordering, ICCG algorithm and      51
Multigrid algorithm as fast Poisson solver      40
Multigrid algorithm, adaptive computation and      57
Multigrid algorithms      45 46
Multiple CPUs, in Cray      11
Multiple Instruction Multiple Data systems      12
NASTRAN, for structural analysis      62
Navier — Stokes equations, parallel computing and      59
Nearest neighbor connections, nested dissection and      29
Nested dissection      27
Nested dissection as substructuring technique      32
Nested dissection for linear equations      19
Nested dissection, diagonal variant of      28
Nested dissection, ordering in      27
Nested DO loops, rearrangement of      4
Nested grids, multigrid algorithms and      46
NON-VON computer, tree structure for      16
Nontridiagonal matrices, methods for      37
Numerical stability in QIF elimination      25
Numerical weather prediction      61
O'Leary's $P_{3}$ ordering, for parallel computing      43
Odd-even elimination      35
Odd-even reduction in sparse matrices      31
Odd-even reduction, algorithm of      34
Odd-even reduction, algorithm of, performance of      17
Odd-even reduction, ICCG algorithm and      51
Off-diagonal elements, cyclic reduction and      35
Omega networks      19
One-dimensional heat equation      55
One-way dissection      27
Operation counts      3
Optimal paracomputer, multigrid algorithm in      47
Orthogonal reduction, for parallel architecture      23
Overrelaxed Jacobi methods      45
PACS machine      18
Parabolic equations, methods for      54
Paracomputer      5
Paracomputer, optimal, multigrid algorithm in      47
Parallel architecture      1
Parallel arrays, multigrid algorithms for      46
Parallel computers, applications of      58–64
Parallel computers, books on      2
Parallel computers, hardware for      12
Parallelism, blocking for      31
Parallelism, definition of      8
Parallelism, degree of      4 20
Parallelism, maximum      26
Partial differential equations, parallel computing and      62
Partial differential equations, spectral methods for      57
Partitioning in triangular systems      26
PCG algorithm      50
Perfect parallel algorithm, Jacobi method as      41
Perfect shuffle interconnection scheme      38
Perfectly shuffled nearest neighbor array      47
Performance measurement of parallel algorithm      5
Pipeline architecture      1
Pipelining      8
Pivoting strategy in elimination      23
Pivoting strategy in tridiagonal systems      35
Plasma physics, parallel computing and      62
Poisson's equation, cyclic reduction for      34
Polyalgorithm, using cyclic reduction      35
Preconditioned Conjugate Gradient Algorithm      50
Preconditioned conjugate gradient methods      49
Pringle system      16
QIF      25
Quadrant Interlocking Factorization elimination      25
Recurrence relations in tridiagonal systems      32
Recursive doubling in tridiagonal systems      33
Red-black ordering in Gauss — Seidel iterations      42
Red-black ordering in SLOR      48
Red-black ordering, ICCG algorithm and      51
Red-black ordering, transonic flow problems and      60
Reduction, cyclic, methods for      34
Relaxation methods      44 45
Relaxation methods in multigrid algorithms      46
Relaxation methods, simultaneous      47
Reordering principle      5
Reservoir simulation, parallel computing and      61
Row-oriented elimination      21
Sameh — Kuck algorithm, for reduction      23
Sameh — Kuck Givens annihilation pattern      24
Scalar algorithms and arithmetic complexity consistency      3
Scalar computation, as speedup measurement      6
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