- 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
|