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Index (showing section)


absorption, 12.1
acceleration, 2.1
accuracy, 2.2
adaptive
     step-length, 3.3
advection, 4.1, 4.2, 8.3, 13.4
aliasing, 13.2
amplification factor, 2.2, 2.4, 5.2, 5.2, 7.3, 7.3
     Gauss-Seidel, 6.2
anisotropic, 7.1, 9.2
anisotropy, 13.4
Arnoldi method, 13.3
artifacts in fitting, 1.3
atomistic simulation, 2.4, 10.0
attenuation-length, 8.4, 12.1

backslash operator, 1.2
backward time, 5.2
basis function, 1.2, 1.3
     localized, 13.1
Bessel's correction, 11.1
best fit, 1.2
BGK collision term, 8.4
bi-conjugate gradient, 13.3
bilinear form, 13.3
binomial, 3.3
bisection, 3.2
block
     matrix, 5.4
     neigbor algorithm, 10.1
     spatial, 10.1
     tridiagonal, 5.4, 5.5
Boltzmann equation, 8.2, 8.2
boundary condition, 1.4, 2.2, 3.0, 3.3, 4.2
     block, 5.4
     Dirichlet, 3.3
     discrete, 3.3
     Neumann, 3.3
     parabolic, 5.1
     periodic, 3.3, 5.5
     Robin, 3.3
boundary value problem, 4.2
box functions, 13.1
BTCS scheme, 5.2
buckling, 9.3

cartesian, 4.3
Cauchy problem, 4.2
centered, 2.4, 3.3, 3.4, 4.3
centered in space, 5.2, 7.3
central limit theorem, 11.1
CFL, 7.4, 7.4
characteristic, 8.3
characteristic equation, 8.4
charge assignment, 10.2
charge density, 3.1, 4.1, 7.1
charge-exchange, 8.4
charged particle, 2.1
chi-squared, 1.2
chordal measurement, 1.3
classification of PDEs, 4.2, 4.3
closure, 7.1, 13.4
cloud in cell, 10.2
cluster potential, 10.1
collision, 8.0, 8.2, 8.4
     first, 12.1
     in PIC code, 10.2
     tally, 12.2
     type, 12.1
compressible fluid, 7.2
computational cost, 5.5
computer memory, 5.4
conditioning, 3.3
conductivity, 3.1
     thermal, 3.1
conjugacy, 13.3
conjugate, 13.3
conjugate gradient, 6.3, 13.3
conservation
     particles, 8.2
conservation equation, 7.2, 13.1
conservation properties, 2.4
conservative form, 3.4, 7.1
constant along orbit, 8.3, 8.4
constitutive relation, 7.1
continuity, 7.1
continuity equation, 4.1
continuum, 8.0
control rod, 9.3
convection, 7.1
convergence, 3.2, 6.2
     Gauss-Seidel, 6.2
Cormack, A. M., 1.3
correlation, 13.4
cost (computational), 3.2, 5.5
     logarithmic, 3.2
     matrix multiplication, 5.5
     pair force, 10.1
     PIC, 10.2
coupled equations, 2.1, 2.1, 7.3, 13.2
Courant-Friedrichs-Lewy, 7.3
Crank-Nicholson scheme, 5.2, 5.5
criticality, 9.3
cross-section, 9.1
crystal lattice, 10.1
CT scanning, 1.3
cumulative
     flux probability, 11.3
cumulative probability, 11.2
curl, 4.1
currency property, 13.3
current density, 4.1
curvilinear coordinates, 4.3
cyclotron frequency Ω, 2.1
cylindrical, 3.1
cylindrical coordinates, 4.3

Debye length, 10.2
degrees of freedom, 1.2
density, 1.3, 8.1, 9.2
     charge, 3.1, 7.1
     energy, 8.1
     heat flux, 3.1
     uncertainty, 12.3
dependent variable, 2.1, 3.0
derivative, 2.1
     2-dimensional, 4.3
     higher, 4.3
determinant, 1.1, A.2
diagonal
     representation, 7.3
diagonal matrix, 1.2
differential, 2.1
diffusion, 4.1, 5.1, 9.3
     coefficient, 4.1
     equation, 4.1, 5.1
     finite difference, 5.2
     numerical, 7.3
diffusion equation, 9.2
dimensionality, 11.3
direct numerical simulation, 13.4
direction vector Ω, 9.1
discrete, 3.3
     derivative, 2.2
     representation, 2.2, 4.3
discreteness of particles, 8.1
dispersion, 13.4
displacement vector, 13.1
distribution
     mean, 11.1
     variance, 11.1
distribution function, 8.1
distribution, 1-dimensional, 8.1
divergence, 3.1
divergenceless, 8.3
DNS, 13.4
drift step, 2.4
DSMC codes, 10.2
dyadic, 7.1

eddy, 13.4
eddy viscosity, 13.4
efficiency, 3.2
     inversion, 1.4
     rejection method, 11.2
eigenanalysis, 1.2, A.4
eigenvalue, 2.3, 2.4, 7.3, A.4
     generalized, 9.3
     of Jacobian, 7.2
     reactor, 9.3
     real, 7.2, 8.3
eigenvector, 2.3, 2.4, 7.3, A.4
elastic scattering, 8.4
electric
     field, 3.1, 4.1
     force, 7.1
     screening, 6.4
electron, 10.2
electrostatic, 3.1, 4.1
elimination, 2.1
     tridiagonal, 5.3, 5.4
elliptic, 4.2, 4.3, 6.1
emission
     spontaneous, 12.1
     stimulated, 12.1
energy density, 8.1
energy flux, 7.1
energy resolved diffusion, 9.2
equation of state, 13.4
error
     order, 2.2
     Runge-Kutta, 2.2
Euler method, 2.2, 2.4
explicit, 2.2, 2.4, 5.2, 13.4
     method, 2.2

fast Fourier transform, 13.2
Fick's law, 9.2
finite difference, 2.2, 4.3
finite elements, 13.1
finite volumes, 3.4
first derivative, 3.3
     discrete, 3.3
first-order, 2.2
     accuracy, 3.3, 5.2, 5.2, 13.4
fission reaction, 9.1
fit
     best, 1.2
     function, 1.1, 1.1
     Gaussian, 1.4
     linear, 1.1
     nonlinear, 1.4
     polynomial, 1.1
     with boundaries, 1.4
FLOP, 5.5
flow, 2.1
     velocity, 8.1
fluid, 2.1, 7.1
     compressible, 7.2
     continuity, 7.1
     flow, 4.1
     incompressible, 7.1
     momentum conservation, 7.1
flux, 11.3
     density, 4.1, 11.3
     of momentum, 7.1
     uncertainty, 12.3
     vector, 7.2
flux conservation, 3.1
force
     evaluation, 10.1
force density, 7.1
force interatomic, 10.1
force vector, 13.1
Fortran order, 5.4
forward in time, 5.2, 7.3
Fourier
     discrete analysis, 13.2
     methods, 13.2
     representation, 4.3, 5.2, 6.2
Fourier transform, 13.2
     discrete, 13.2
     fast, 13.2
fourth-order, 2.2
FTCS, 5.2, 6.1, 7.3

Galerkin method, 13.1
Gauss theorem, 4.1, 7.1, 13.1
Gauss-Seidel method, 6.1
Gaussian, 1.4, 11.1
generalized eigenvalue, 9.3
GMRES, 6.3, 13.3
gradient, 4.1
gravity, 7.1
grid, 3.3
grounded, 3.1
groups, 9.3
guess
     initial, 3.2

half-step position tn+1/2 , 2.4
heat conduction, 3.1, 5.1
heat flux, 3.1, 3.4
hexahedron, 4.3
high-dimensionality, 11.3
higher-dimension, 2.1
homogeneous equation, 6.4
hybrid PIC, 10.2
hyperbolic, 4.2, 7.2, 8.3, 8.3
     finite difference, 7.3, 7.4
     FTCS, 7.3
     Jacobian eigenvalue, 7.2
     stability, 7.3
hypersphere, 11.3

ignorable coordinate, 13.2
image reconstruction, 1.3
implicit, 2.2, 2.4, 5.2, 13.4, 13.4
     parabolic, 5.3
     schemes, 2.2
importance weighting, 12.2
incompressible, 7.1, 13.4
independent variable, 2.1, 3.0
index, 2.2
indexing
     multiple dimensions, 5.4
initial guess, 3.2
initial value problem, 2.2
initial values
     leap-frog, 2.4
injection
     particle, 11.3
integral
     along orbit, 8.3
     form, 3.4, 13.1
integrating, 2.2
integration
     along orbit, 8.3
integro-differential, 8.4, 9.2
interatomic force, 10.1
interatomic potential, 10.1
inverse, A.3
inverse problem, 1.3
inverse-square interaction, 10.2
ion, 10.2
isotropic, 7.1
iteration, 3.2, 3.2, 6.1, 6.4, 13.3
iterative
     eigensolution, 9.3

Jacobi method, 6.1, 6.4
     convergence, 6.2
Jacobi-preconditioning, 13.3
Jacobian matrix, 7.2, 13.3
Jacobian-free method, 13.3

k-spectrum, 13.4
kick step, 2.4
kinetic energy, 8.1
kinetic theory, 8.1
Knudsen number, 10.2
Krylov, 6.3
Krylov techniques, 13.3

Laplacian, 1.3, 4.1
     eigenmode, 9.3
     finite difference, 4.3
large eddy simulation, 13.4
lattice, 11.3
     crystal, 10.1
lattice crystal, 10.1
lattice integration, 11.3
Lax-Friedrichs method, 7.3, 7.4
Lax-Wendroff method, 7.3, 7.3
leakage operator, 9.3
Leap-Frog scheme, 2.4
least squares, 1.2
Lennard-Jones potential, 10.1
LES, 13.4
limiter methods, 13.4
linear collision term, 8.4
linear least squares, 1.2
linearization, 2.3, 6.4, 6.4, 6.4
liquid, 7.1
liquids, 13.4
logarithmic time, 3.2

macroscopic cross-section, 8.4, 9.1, 12.1
magnetic
     field, 2.1, 4.1, 7.1
     force, 2.1
mass conservation, 4.1, 4.1
Matlab, 1.4
matrix
     block, 9.3
     conditioning, 3.3, 3.4
     determinant, A.2
     diagonal, 1.2, 9.3
     equation, 1.1, 3.3
     inverse, 1.1, A.3
     inversion, 2.3, 5.3
     inversion cost, 6.1
     iterative solution, 6.1, 13.3
     Jacobian, 7.2, 7.3
     multiplication, A.1
     multiplication cost, 5.5
     non-square, 1.2
     notation, 1.1
     orthogonal, 1.2
     solution, 1.1
     sparse, 1.4, 13.3
     transpose, A.1
matrix trace, 7.1
Maxwell's equations, 3.1, 4.1
mean, 11.1
mean velocity, 9.2
mean-free-path, 8.0, 10.2
mesh, 3.3
method of characteristics, 8.3
minimum residual, 13.3
molecular dynamics, 10.1
molecular speed, 10.1
molecular vibration, 10.1
moments
     velocity distribution, 9.2
Monte Carlo, 11.0
     integration, 11.2, 11.3
Morse potential, 10.1
multiple dimensions, 5.4, 7.4

nanoscale, 10.1
Navier Stokes, 7.1, 13.4
nearest grid point, 10.2
neighbor, 10.1
neighbor list, 10.1
neutron, 9.1
neutron flux-density, 9.2
neutron transport, 5.1
neutron transport equation, 9.1
Newton method, 3.2, 6.4, 13.3
Newton-Krylov, 6.3
Newton-Krylov method, 13.3
noise, 1.3
noisy data, 1.2
non-equilibrium, 9.0
non-linearity, 13.2
nonlinear, 1.4
     equations, 6.4
     iteration, 6.4, 6.4
     stability, 2.3
nonsingularity, 3.1
normal distribution, 11.1
nuclear reactor, 9.3
     homogeneous, 9.3
numerical dissipation, 13.4
numerical viscosity, 13.4
Nyquist limit, 13.2

Octave, 1.2, 1.4, 5.3
ODE, 2.2, 3.0
orbit, 2.1, 8.3
     integration, 2.4
order
     of differential, 2.1
     of system, 2.1
     reduction, 2.1, 2.4
order of elements, 5.4
ordinary differential equation, 2.0
orthogonality
     mutual, 13.3
orthonormal, 1.2
oscillations, 13.4
over-relaxation, 6.3
over-specified, 1.2, 1.2

parabolic, 4.2
partial differential equations, 4.1
particle
     creation, 8.2
particle diffusion, 5.1
particle injection, 11.3
particle-in-cell, 2.4, 10.2
PDE, 4.1
     classification, 4.2
periodic
     boundary condition, 3.3, 5.5, 10.2
permeability, 4.1
permittivity, 3.1, 4.1
phase-shift, 13.4
phase-space, 8.1
     divergence, 8.3
photon, 1.4
PIC, 2.4, 10.2
     resolution, 10.2
piecewise linear, 13.1
pixel, 1.3
plasma, 6.4
Poisson distribution, 11.3
Poisson equation, 3.1, 4.1, 4.3, 6.1, 10.2, 13.4
polyhedra, 13.1
polynomial, 1.1
polynomial fit, 1.1
potential, 3.1
power method eigensolution, 9.3
preconditioning, 13.3
     Jacobi, 13.3
pressure, 7.1
pressure correction, 13.4
pressure tensor, 7.1
probability, 11.1
     cumulative, 11.1
     distribution, 11.1
pseudo-inverse, 1.2, 1.2, 1.2
pseudo-particle, 10.0, 10.2, 10.2
pseudo-random, 11.2

quadratic form, 4.2, 4.3
quadrilateral, 4.3
quantum mechanics, 10.1
quasi-random numbers, 11.2

radial differences, 3.4
radiation transport, 12.1
random number
     generator, 11.2
random walk, 12.1
range of force, 10.1
RANS equation, 13.4
rate of strain, 7.1
reactions, 4.1, 9.0
reactivity factor, 9.3
red-black order, 6.2
reduction of order, 2.1
regularization, 1.2
rejection method, 11.2
reordering of mesh elements, 5.4
residual, 1.2, 1.2, 6.4, 13.1, 13.3
resolution
     PIC mesh, 10.2
Reynolds averaged Navier Stokes, 13.4
Reynolds number, 13.4
Reynolds stress, 13.4
Robin boundary condition, 3.3
robustness, 3.2
root finding
     bisection, 11.2
root-finding, 3.2
roughness, 1.2
Runge's phenomenon, 1.1
Runge-Kutta schemes, 2.2

sample, 11.1
     mean, 11.1
     standard deviation, 11.1
     variance, 11.1
scattering, 8.4
     angle, 12.1
second derivative, 3.3
     discrete, 3.3
second-order, 2.2, 3.1
     accuracy, 3.4, 4.3, 5.2, 7.3
     differences, 3.3
seed, random, 11.2
self-scattering, 8.4
separable coordinates, 8.1, 13.2
separable solution, 9.3
separation constant, 9.3
shear stress, 7.1
shocks, 13.4
shooting method, 3.2
simple harmonic oscillator, 2.1
simultaneous equations, 1.1
Singular Value Decomposition, 1.2
sink of particles, 8.4
slab, 3.1
smoothing, 1.2
smoothing spline, 1.2
solid angle Ω, 8.4
SOR, 6.3
     convergence, 6.3, 6.4
     optimal, 6.3, 6.4
     stability, 6.3
sound speed, 13.4
source, 3.1, 8.3
     density, 4.1
     of particles, 8.4
sparse, 1.4, 5.3, 6.4, 13.3
spatial resolution, 10.2
spectral methods, 13.2
spectral representation, 13.2
spectrum, 1.4
speed
     groups, 9.3
     of light, 4.1
     of sound, 7.2
speed-distribution, 9.2
spontaneous emission, 12.1
stability, 2.2, 2.2
     diffusion equation, 5.2
     hyperbolic, 7.3
     of ODE solution, 2.2
stability condition
     Crank-Nicholson, 5.2
     diffusion, 5.2, 6.1
staggered values, 2.4
standar error, 11.1
standard deviation, 11.1
state vector, 7.2
stationary targets, 8.4
statistical uncertainty, 12.2
steady state, 6.1, 8.4
stencil, 4.3, 4.3, 5.4
step
     length, 12.1
step size, 2.2
step-length
     adaptive, 3.3
stiff equations, 2.3
stiffness, 2.3, 13.4
stiffness matrix, 13.1
streamline, 2.1, 4.2
stress, 7.1
stress tensor, 7.1
structured mesh, 4.3
subcritical eigenvalue, 9.3
subspace
     Krylov, 13.3, 13.3
successive over-relaxation, 6.3
supercritical eigenvalue, 9.3
SVD, 1.2
symmetric, 9.2
     stress, 7.1

tally, 12.2
Taylor expansion, 2.2, 6.4
temperature, 3.1, 9.2
tensor, 7.1
tent functions, 13.1
tetrahedral
     interpolation, 13.1
     mesh, 13.1
thermodynamic equilibrium, 8.1
theta-implicit, 5.2
tolerance, 3.2, 3.2
tomography, 1.3
total variation, 13.4
trace, of matrix, 7.1
trajectory, 8.3
transport, 12.1
trapped orbit, 8.4
triangle functions, 13.1
tridiagonal, 3.3, 5.3, 13.1
tridiagonal elimination, 5.4, 10.2
turbulence, 13.4
two-point boundary conditions, 3.0

uncertainty
     statistical, 12.2
uncoupled representation, 7.3
under-determined problem, 1.3
uniform deviate, 11.2
uniform mesh, 4.3
unstructured mesh, 4.3, 13.1
upwind differencing, 13.4

variance, 11.1
vector calculus, 4.1
vector equations, 2.1
velocity moments, 9.2
velocity-space, 8.1
Verlet scheme, 10.1
viscosity, 7.1, 13.4, 13.4
     shear, 7.1
Vlasov equation, 8.4, 8.4, 10.2
Von Neumann stability, 6.4, 7.3

wave equation, 4.1
wave propagation, 7.2
weak form of equation, 13.1
weighting
     importance, 12.2

x-ray, 1.3

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