Index

Symbols | A | B | C | D | E | F | G | H | I | J | L | M | N | O | P | R | S | T | U | V | W

Symbols

3D visualization

A

alternating mesh
amplification factor
animation
argparse (Python module)
ArgumentParser (Python class)
arithmetic mean
array computing
array slices
averaging
arithmetic
geometric, [1]
harmonic

B

boundary condition
open (radiation)
boundary conditions
Dirichlet
Neumann
periodic

C

C extension module
C/Python array storage
callback function
centered difference
central difference approximation
Cholesky factorization
closure
column-major ordering
conjugate gradient method
continuation method, [1]
correction terms
Courant number
Cython
cython -a (Python-C translation in HTML)

D

decay ODE
declaration of variables in Cython
diffusion coefficient
non-constant
piecewise constant
diffusion equation
1D
1D, Crank-Nicolson scheme
1D, Forward Euler scheme
1D, Fourier number
1D, Implementation
1D, boundary condition
1D, discrete equations
1D, explicit scheme
1D, implementation (FE)
1D, implicit schemes
1D, initial boundary value problem
1D, initial condition
1D, mesh Fourier number
1D, numerical experiments
1D, theta rule
1D, tridiagonal matrix
1D, verification (BE)
1D, verification (CN)
1D, verification (FE)
2D
2D, banded matrix
2D, implementation
2D, implementation (sparse)
2D, numbering of mesh points
2D, sparse matrix
2D, verification (conv. rates)
2D, verification (exact num. sol.)
axi-symmetric diffusion
diffusion coefficient
implementation
source term
spherically-symmetric diffusion
stationary solution, [1]
diffusion limit of random walk
dimensionless number
Dirichlet conditions
discrete Fourier transform
distutils
DOF (degree of freedom)
domain

E

energy estimates (diffusion)
energy principle
error
global
Euler-Cromer scheme
explicit discretization methods

F

finite differences
backward
centered, [1]
forward
fixed-point iteration
Flash (video format)
Fokker-Planck equation
forced vibrations
Fortran array storage
Fortran subroutine
forward difference approximation
forward-backward Euler-Cromer scheme
Fourier series
Fourier transform
fractional step methods
frequency (of oscillations)

G

Gauss-Seidel method
geometric mean, [1]
Gnuplot

H

harmonic average
heat equation
homogeneous Dirichlet conditions
homogeneous Neumann conditions
HTML5 video tag
Hz (unit)

I

index set notation, [1]
interrupt a program by Ctrl+c

J

Jacobi method

L

lambda function (Python)
Laplace equation
linearization
Picard iteration
explicit time integration
fixed-point iteration
successive substitutions
LU factorization

M

making movies
Mayavi
mechanical energy
mechanical vibrations
mesh
finite differences, [1]
mesh function, [1], [2]
mesh points
MP4 (video format)

N

Neumann conditions
nonlinear restoring force
nonlinear spring
nose, [1]

O

Ogg (video format)
open boundary condition
operator splitting
oscillations

P

parallelism
period (of oscillations)
periodic boundary conditions
phase plane plot
Picard iteration
plotslopes.py
Plotter class (SciTools)
preconditioning, [1]
pytest, [1]

R

radiation condition
random walk
red-black numbering
relaxation
(nonlinear equations)
resonance
Richardson iteration
row-major ordering

S

scalar code
scitools movie command
scitools.avplotter
seed (random numbers)
setup.py
single Picard iteration technique
slice
slope marker (in convergence plots)
SOR method
splitting ODEs
stability criterion, [1]
staggered Euler-Cromer scheme
staggered mesh
stationary solution
stencil
1D wave equation
Neumann boundary
stochastic difference equation
stochastic ODE
Stoermer-Verlet algorithm
stopping criteria (nonlinear problems), [1]
Strang splitting
successive substitutions
symplectic scheme

T

test function, [1]
truncation error
Backward Euler scheme
Crank-Nicolson scheme
Forward Euler scheme
correction terms
general
table of formulas

U

unit testing, [1]
upwind difference

V

vectorization, [1], [2], [3]
verification, [1]
convergence rates
hand calculations
polynomial solution
polynomial solutions
vibration ODE
video formats
visualization of 2D scalar fields

W

wave equation
1D
1D, analytical properties
1D, exact numerical solution
1D, finite difference method
1D, implementation
1D, stability
2D, implementation
waves
on a string
WebM (video format)
Wiener process
wrapper code