Index

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