INDEX

Abstract data structures, 70

Abstraction, 70, 89, 93, 107

Accuracy, 18, 555

ACE/gr, 51–56

Adams-Bashforth-Moulton, 204

Address, see Memory 555

Advection, 508–510

Airy functions, 421

Algorithm, 9, 11, 555

Alias, 241

Amdahl’s law, 365

Analog, 555

filters, 250

Animations, 5, 64, 312, 314, 428, 432, 494, 495, 515, 555, 568, 586–592, 627

Antiferromagnet, 392

Applets, 222, 228, 565, 627

Architecture, 158, 169, 352–363, 368, 374, 376, 378, 555, see also Memory

Arithmetic unit, 357–360, 555

Arrays, 165, 555,

dimension, 557, see also Matrices

Asymptotes, 293

Attractors, 292–294, 313

predictable, 309

strange, 309

Autocorrelation function, 246–250

awt, 565

Backtracking, 156, 163

Ballistic deposition, 332–333, 338–339

correlated, 338–339

Base, 20, 556

BASIC beginner’s code, 7n

Basic machine language, 7, 556

Batch, 556, 598

Beating, 210

Beowulf, 363–364, 593

Bessel functions, 36–39, 202, 546

Bias, 20

Bifurcation, 292–300, 313–315

diagram, 294

dimension of, 343

Binary numbers, 17, 556

Binary point, 19

Binning, 295

Bisection algorithm, 152–154

Bits, 17, 556

reversal, 258

Block walls, 392

Blocking, 619

Blue Gene, see IBM Blue, 373

Boltzmann distribution, 393

Boolean, 19, 556

Bootable cluster, 620

Bound states, 152–154, 211–221, 225, 408, 411–420, 435, 540–545

Boundary conditions, 198, 429, 437

Box counting, 335–337, 342

Box–Muller method, 141–145

Break command, 451

Broadcast, 373, 609

Buffers, 354, 603, 604

Burgers’ equation, 510–514

Bus, 362, 556

Butterfly operation, 258

Byte, 17, 556

code, 8, 376, 556

C language, 8, 58, 624–627

Cache, 385, 556

data, 385

misses, 385–387

programming for, 385–388

Canonical ensemble, 393, 425

Capacitors, 67, 448–452

Catenary, 488–491

CD contents, 626

Cellular automata, 343–345

Central difference, 148

Central processing unit, see CPU, 353

Central storage, 354

Chaos, 289–299, 302, 307–315

Fourier analysis of, 317

of pendulum, 302

in phase space, 307–312

Chi squared measure, 186

Child, 106, 556

CISC, 357

Classes, 71–102, 556, 565–567

daughter, 85, 99

member, 106

multiple, 90, 104

structure, 106

superclass, 99

variables, 71–93, 100

CLASSPATH, 562

Column-major order, 165, 353, 556

Command-line interpreter, 7

Communications, 368, 593–621

collective, 619

time, 365

Communicator, 605

Compilers, 8, 556, 566

just-in-time, 377, 558

Complex numbers, 67

Composition, 93, 95

Compression, 264, 635

lossless, 268

Computational

physics, 1

science, 1, 2

Concurrent processing, see Parallel computing, 557

Constructors, 73–100

default, 74

Convolution, 248, 250

Correlations, 246, 248, 338

auto, 246

coefficient, 187

growth, 338

Courant stability condition, 502, 504, 512, 513

Course grain parallel, 362

Covariance, 187

CPU, 352–355, 357–360, 366, 372, 376, 385–386, 556

RISC, 357

time, 358

Crank-Nicolson method, 472–475

Cubic splines, see Splines, 179

Cumulative distribution, 143

Curie temperature, 392

Curve fitting, see Data fitting, 176

Cycle time, 358, 557

Cygwin, 568

Data

cache, see Cache 385

compression, 264, 635

dependency, 362, 557

encapsulation, 89

fitting, 176

hiding, 101

parallel, 362

structures, 70

types, 18, 69, 71, 96, 557

Daughter class, 85

Deadlock, 372, 618

Decay

exponential, 119, 184

spontaneous, 184

Density of states, 400

Dependency, 362, 557

Deposition, 332

ballistic, 333

correlated ballistic, 337

Derivatives, 146–151, 197

central difference, 148, 151, 413n, 431

error in, 149

extrapolated difference, 149

forward difference, 147, 201

second, 151, 180, 200, 216, 431

Differential equations, 194–229

algorithms, 200

boundary conditions, 198

dynamical form, 198

Euler’s rule, 201

initial conditions, 198

order, 196

partial, see PDEs 437

Runge–Kutta algorithm, 202

types of, 196, 437

Differentiation, see Derivatives 147

Diffusion-limited aggregation, 339

Digital, 18, 557

Dimension, 557

array, 165

fractional, 326–329, 335–337, 342

Hausdorf-Besicovitch, 326

logical, 167

physical, 165, 167

schemes, 166

Directories, 90, 95, 557, 565

Discrete Fourier transform, 237–243, 249

Dispersion, 427, 509, 514–516

relation, 509, 515

Distributed memory, 363

Documentation, Java, 16

Dot operator, 73, 76, 77

Double

pendulum, 315–317

precision, 18, 25, 557

Doubles, 19, 96

Drag, see Friction 226

DRAM, 354

drand, 114

Driving force, 211

Duffing oscillator, 318

DX, see OpenDX 45

Eigenvalues, 164, 170, 174, 198, 212–221, 245, 491, 540

Electrostatic potential, 439

Elliptic integral, 304

Encapsulation, 89, 100, 106

Entropy, 299

Environmental variables, 562, 595

Equations

Korteweg–de Vries, 515

Burgers’, 510

differential, 194

discrete, 119, 290

integral, 540, 541, 547

of motion, 226

Schrödinger, 212, 318, 492

Van der Pool, 318

Ergodic, 395

Errors, 30–44

algorithm, 30, 40, 128

approximation, see Algorithm 30

in differentiation, 149

empirical, 39, 132

in integration, 128, 132

minimum, 42

multiplicative, 34

N-D integration, 139

random, 30

roundoff, 28, 31, 34–36, 39, 41, 42, 44, 110, 124, 129, 132, 138, 149, 200, 201, 518

total, 39, 40

types of, 30

Euler’s rule, 201–203, 413n, 416

Exceptions, 13

Exchange energy, 391

Exponential decay, 119, 184

Extinction, 293

Extract part, 91, 97

Extrapolated difference, 148

Fast Fourier transform, see FFT 256

Feigenbaum constants, 297

Ferromagnet, 392

Fetch, 360

Feynman

path integrals, 409–423

postulates, 411

propagator, 409

FFT, 241, 256–263

Filters

analog, 250

digital, 252, 283

sinc, 253

windowed, 253

Fine grain parallel, 362

Finite

difference equation, 120

difference time domain, 499–506

differences, 120, 443, 493, 527, 532

elements, 453–463

Fitting, 176–193

best, 176

global, 185

goodness, 186

least squares, 184–193

linear least square, 186–191

Newton–Raphson, 193

nonlinear, 191–193

Fixed points in maps, 291, 307

Fixed-point numbers, 18

Floating-point numbers, 18–24, 31, 558

FLOPS, 206, 372, 558

Fluid Dynamics, 508–539

Fortran, 8, 627

vs Java, 380

Forward difference, see Derivatives 147

Fourier

autocorrelation relation, 249

discrete transform, see Discrete Fourier transform 237

fast transform, see FFT 256

of half-wave, 235

integral, 236

PDE solution via, 440

of sawtooth, 234

series, 231, 235

short-time transform, 268

theorem, 232

transform, 231, 236, 580, see also FFT

Fractals, 326–350

coastline, 334

dimension, see Dimension 326

plants, 329, 331, 332

Pollock painting, 342

Friction, 209–210, 307, 309, 317, 521, 533

in oscillations, 209, 211

in waves, 483, 486, 487

in pendulum, 302–308

in projectile motion, 226–228

Functional, 408

integration, 411–423

Galerkin decomposition, 456–459

Game of Life, 343

Garbage, 30, 558

Gaussian

distribution, 144

elimination, 551

quadrature, 130–132

Gibbs overshoot, 235, 254

Global array languages, 361

Glossary, 555–561

Gnuplot, 45, 56–65, 447, 492, 520, 538, 568, 570

prompt, 57

Grace, 51–56

Granularity, 363

Green’s function, 250, 408

Grid engine, 594, 597

Grid points, 132, 503, 512, 513, 519, 546, 551

Growth models, 289–297, 319–345

Guests, 367, 598–610

Hénon–Heiles potential, 318

Half-wave function, 235

Hamilton’s principle, 408

Hardware, 352–388

Harmonics, 232

Heap, 383

Heat bath, 424

Heat equation, 463–476

Hexadecimal, 558

High performance computing, 352–388

Hilbert transform, 549

Host, 605–613

HPC, see High performance computing 375

HTML, 16, 564

Huygens’s principle, 408

Hyperbolic point, 307

I/O, see Input/output 13

IBM Blue Gene, 372–374

IEEE floating point, 18–19

Impedance, 70

import, 90

Importance sampling, 140

Inheritance, see Objects 89

Initial conditions, 198

Input/Output (I/O), 12–14

streams, 566

Instances, 71–74

Instructions

stack, 353, 558

streams, 362

Integral equations, 541–553

Integration, 123–145

error in, 128–132

from splines, 181

Gaussian quadrature, 130

mapping points, 131

Monte Carlo, 136–145

multi-dimensional, 138

rejection techniques for, 136

Simpson’s rule, 126–129

trapezoid rule, 125–129

variance reduction, 140

via mean value, 137

via von Neumann rejection, 140

Integro-differential equation, 540

Interface, 102, 105

Intermittency, 293

Interpolation

Lagrange, 177–179

splines, 179

Interpreter, 8, 558

Inverse, 164

Ising model, 390–407 2-D, 393, 400

Jacobi method, 445

Jacobian matrix, 162

JAMA, 168, 170–173, 187, 190, 193, 463, 545, 551, 552, 623

Java

vs Fortran, 380

developer’s kit, 564

I/O, 12

matrix storage, 353

programs on CD, 626

virtual machine, 376

javadoc, 16

JDK, 562, 564

Just-In-Time compiler, 377

Kernel, 7, 408, 558

Korteweg-de Vries equation, 515

Lag time, 246

Lagrange interpolation, 177–179

Languages

BASIC, 7

compiled, 8, 556, 557

computer, 6

high-level, 7, 558

interpreted, 8

low-level, 6–7, 559

LAPACK, 168, 623, 624

Laplace’s equation, 439–463, 531

Latency, 354, 366, 373

Lattice computations, 390, 413n, 414, 421

Lattice points, see Grid points 390

Lax–Wendroff algorithm, 511–514

Leap frog, see Time stepping, 464

Least-squares fitting, 184–193

Length of coastline, 334

Libraries, see Subroutines 169

Limit cycles, 308

Linear

algebra, 158, 170

congruent method, 110

least square fitting, 186

regression, 186

superposition, 197

Link, 8

Lippmann–Schwinger equation, 547

Load, 8

balancing, 367

module, 8

Logical size, 167

Logistic map, 289–297

Loop unrolling, 383, 385

Lorenz attractor, 318

Lotka-Volterra model, 320–324

Lyapunov coefficients, 298–300

Machine

numbers, 18

precision, 25, 26, 245–559

Magnetic materials, 390–407

Mantissa, 18, 559

Master and slave, 605, see also Tasks 650

Matrices, 158–176, 555

column-major order, 165

diagonalization, 164

equations, 547

inversion, 162, 163, 551–553

row-major order, 165, 560

subroutine libraries, 168–173

tri-diagonal, 474

Maxwell’s Equations, 499–506

Mean value theorem, 137

Memory, 352–357, 378

architecture, 158, 353

conflicts, 365, 375

distributed, 363

dynamic allocation, 167

heap, 383

pages, 165

virtual, 165, 356

Message passing, 362–363, 368–372, 593–620

Methods

dynamic, 91

override, 99

static/nonstatic, see Static/Nonstatic 76

Metropolis algorithm, 394–398, 400, 413

Microcanonical ensemble, 393, 424

Microcode, 357

Miller’s device, 37

MIMD, 363, 368, 559

Mode locking, 211, 308

Molecular dynamics, 423–436

Momentum space, 540–553

Monte Carlo

error in, 139

integration, 136–145

simulations, 35, 109, 116, 119, 136–145, 339, 390, 394, 417, 424, 429, 609, see also Metropolis

Mother class, 85

MPI, 593–622

commands, 621

Multiple-core processors, 358

Multiresolution analysis, 274

Multitasking, 356–357, 367–368

NAN, 24

Navier–Stokes equation, 509, 521–532

Netlib, 169

Newton–Raphson

algorithm, 153–157, 160–193, 221

backtracking, 156

N-dimensional, 160–163

Nodes, 179, 362

Noise

Perlin addition, 345

reduction, 246

Nonlinear

dynamics, 289–324

maps, 291, 298

ODE, 197

oscillations, see Oscillations 194

Nonlocal potentials, 540, 547

Nonstatic, see Static/Nonstatic 71

Normal

distribution, 144

mode expansions, 232, 440, 480

numbers, 19

Numbers binary, 17

complex, 67–70, 79, 102

fixed-point, 17, 18

floating-point, 18–24, 558

hexadecimal, 17, 558

IEEE, 19

machine, 18

normal/subnormal, 19

octal, 17

ranges of, 19–24

representations of, 18–24

uniform, 116

Numerov method, 216–219

Nyquist criterion, 242

Nyquist-Shannon interpolation, 254

Objects, 67–72, 559

code, 8

composition, 93, 95, 98

hierarchies, 98

inheritance, 98, 99, 107

oriented programs, 67, 80–108

properties, 71

Octal numbers, 17

ODEs, 196–207, 216–219

second order, 227

One cycle population, 291

OOP, see Objects oriented programs 80

OpenDX, 45, 65, 347, 452, 492, 538, 568–592

Operands, 353

Operating system, 7

Optimization, 39, 158, 169, 207, 375–388, 611, 614, 627

Oscillations

anharmonic/harmonic, 194, 206, 232

damped, 209, 210

driven, 210

Fourier analysis of, 232

from errors, 177, 179, 254

in phase space, 306

isochronous, 206

nonlinear, 194–229, 232

of pendulum, 302–318

populations, 291

other.object, 78

Over relaxation, see Relaxation 446

Overdetermined, 163

Overflows, 18, 24

Overhead, 365, 368, 378, 609, 614

Packages, 562–567

Padding of signals, 243

Page, 165, 354

fault, 355

Parallel computing, 352, 360–374, 593–622

Beowulf, 593

granularity, 362

master, slave, 369

message passing, 368

performance, 364

subroutines, 362, 367

tuning, 611

types of, 361

Parent class, 99, 106

Partial differential equations, see PDEs 437

Path integration, 390, 411–423

PDEs, 197, 437–539

elliptic, 439

explicit solution of, 493

hyperbolic, 478

implicit solution, 493

parabolic, 437, 464

types of, 437

weak form of, 455

Pendulum, 302–316

analytic solution, 304

bifurcation diagram, 313

chaotic, 302, 309, 313

Performance, see Tuning 378

Period doubling, see Bifurcation 292

Periodic boundary conditions, 429

Perlin noise, 345–350

Phantom bit, 20

Phase space, 302, 305–312, 315–317, 320, 321, 520

Phase transitions, 390

Pipelined CPU, 357

Planetary motion, 229

Plots, 45–65

animation, 64

complex, 60

contour, 56, 61

field, 62

parametric, 83

surface, 56, 60, 447, 584

vector, 62, 583

Pointers, 167, 605

Poisson’s equation, 439–440, 443–445, 454

Polymorphism, 89, 105

Population dynamics, 289–297, 301, 319–324

PostScript (.ps), 447, 560

Potentials

delta shell, 544

Lennard-Jones, 426

momentum space, 544

Pov-Ray, 348

Power spectrum, 249

Precision

machine, 25

tests of, 208

Predator–Prey models, 319–324

Predictor-corrector methods, 205

Primitive data types, 70

Principal values, 549

printf, 12

Private objects, 100

Problem solving paradigm, 2

Programming, 8, 9

design, 10

for parallel, 368

structured, 10

for virtual memory, 356

visual, 579

Programs, 626

Projectile motion, 86, 225–228

Propagator, 409

Pseudocode, 8, 9, 28, 560

Pseudorandom, see

Random numbers 110

PtPlot, 46–51, 562

Pyramid FFT, 279

Quadrature, 123

Quantum

bouncer, 421

mechanics, 152, 216

scattering, 546, see also Bound states, Scattering

Race condition, 372

Radioactive decay, 119

Radix, 18

RAM, 165, 354–386, 556, 560

Random numbers, 109–116, 297, 329

generators, 110, 297

linear congruent, 110

nonuniform, 141

tests of, 114–115

for random walk, 40, 116–118, 338–339, 401–402

Rank, 605

Ray tracing, 348

Recursion, 36–38, 202, 560

Reference calls, 72, 96, 624

Registers, 25, 353, 386, 560

Rejection techniques, 136, 396

Relaxation, 445–446, 451, 527–538

Rendering, 572

Resonances, 79, 210

Reynolds number, 533

RISC, 357–374, 560

rk4/rk45, 202–203, 205, 224

RLC circuits, 67

Romberg extrapolation, 136

Root mean square, 116–117

Row-major order, 165, 560

Runge-Kutta, 202–203, 205

Sampling, 136, 237, 395

importance, 140

Sawtooth function, 234

scanf, 12, 58

Scattering, 546, 553

Scheduler, 594

Schrödinger equation, 212–221, 492, 497, 540–553,

time dependent, 492, see also Quantum 650

Script, 64, 590, 591, 596, 598, 601–603

Searching, see Trial and error 215

Section size, 360

Secular equation, 164

Seeds, 110, 291

Self

affine connection, 329

affinity, 329, 332

limiting, 318

similar, 296, 328, 329

Separatrix, 208, 305, 520

Serial computing, 362, 365, 366, 368, 560, 600, 616

Series summation, 27

Shannon Entropy, 299

Shells, 7

Shock waves, 508–515

Sierpiski gasket, 327–329, 343

Sign bit, 22

Signal processing, 246

Significant figures/parts, 31

SIMD, 363

Simpson’s rule, 127, 128

Sinc filter, 253

Single precision, 18, 19, 25

Singular integrals, 548

SISD, 363

SLATEC, 168, 169

Slave, 369, 605

SMP, 360, 361

Solitons, 508–520

crossing, 520

KdeV, 517

water wave, 515

Speedup, 610

Splines, 179

natural, 180

Spontaneous decay, 119, 121, 182, 184, 187, 290

SRAM, 354

Stable states, 293

Static/Nonstatic methods, 71–79, 91, 101

Statistical Mechanics, 393, 424–429

Stochastic, see Monte Carlo 119

Strange attractors, 309

Stride, 386, 388, 561

see also Matrices 650

Subnormal numbers, 19

Subroutines, 8, 561

libraries, 158, 168–173, 623–625

Subscripts, see Dimension 166

Subtractive cancellation, 32–34, 37, 44, 147, 182, 187, 200, 206, 548

Successive

over-relaxation, see Relaxation 528

Supercomputers, 352–374, 561

Superscalar, 357, 561

Swap space, 354–357

Symmetric multi processor, see SMP 360

Tasks, 361–368

Template methods, 91

Text editor, 563

Thermodynamics, 390–407, 416, 424, 428–429

this.object, 78

Three body problem, 229

Threshold in compression, 635, 637–638

Time delay, 225

Time stepping, 464, 465–468, 478, 482–484, 493–496, 510, 512–514

Top-down programming, 9

Transients, 211, 293, 294, 296, 312, 314

Trapezoid rule, 125–126

Trial and error, 146, 151–157, 161–163, 184, 185, 191–193, 198, 214–216, 219–222, 395, 396, 398, 402, 417, 422, 451, 455

Trivial solutions, 164, 543

Tuning, see Optimization 375

Two cycle, 292

Two’s complement, 18, 25

Typename, see Data 71

Uncertainty principle, 266

Underflows, 18, 24

Uniform

distribution, 109–110, 115–116, 131, 144, 297

sequences, 110, 116

tests, 114–116

weights, 144

Unix, 569

Value pass, 72

Van der Pool equation, 318

Variables

class, 71–101

dynamic, 91

multitype, 105

static/nonstatic, 91

Variance, 140, 187

reduction, 140, 394

Vector processors, 359

Vectors, 360, 452, 561

fields, 499

Velocity Verlet algorithm, 431

Verlet algorithm, 431

Virtual machine, 376

Virtual memory, 165, 354–356, 375–378

Viscosity, 521, 533

Visual programming, 569

Visualization, 5, 45–65, 295, 568–592

of vectors, 452

Volume rendering, 46, 586

von Neumann rejection, 140, 396

stability assessment, 434, 450, 468–470, 473, 475, 482, 483, 485, 502, 503

Vorticity, 530–538

Wang–Landau Sampling (WLS), 400–409

Wave

electromagnetic, 478, 499–506

equation, 478–481, 491

functions, 412, 418, 546, 553

on catenary, 488–491

on string, 478–491

packets, 236, 478, 491–499,

shallow water, 515, see also Wavelets 650

Wavelets, 264–288

basis sets, 270

Daubechies, 283

discrete transform (DWT), 274, 287

for compression, 635

multiresolution analysis, 274

transform, 269, 273

Weak form of PDE, 455

Word length, 17

Worker, see Slave 605

Working set size, 376

Wrappers, 597