xviii
6.9 The results for SOPSWR method for the system of PDEs. . . 145
6.10 Numerical resolution of the wave equation for Dirichlet bound-
ary (Δx =Δy =1/32, τ
n
=1/64, D
1
=1,D
2
=1)....... 150
6.11 Numerical resolution of the wave equation for Neumann bound-
ary (Δx =Δy =1/32, τ
n
=1/64, D
1
=1,D
2
=0.5). . . . . . 152
6.12 Dirichlet boundary condition: numerical solution (right figure)
and error function (left figure) for the spatial dependent test
example............................... 154
6.13 Neumann boundary condition: numerical solution (left figure)
and error function (right figure) for the spatial dependent test
example............................... 156
6.14 Flow field for a two-dimensional calculation. . . . . . . . . . . 162
6.15 Concentration of U-236 at the time point t = 100[a]andt =
10000[a]............................... 163
6.16 Flow field for a three-dimensional calculation. . . . . . . . . . 164
6.17 Concentration of U-236 at the time points t = 100[a]andt =
10000[a]............................... 165
6.18 The numerical results of the second example after 10 iterations
(left) and 20 iterations (right). . . . . . . . . . . . . . . . . . 171
6.19 The underlying apparatus given as an axis-symmetric domain
withthedifferentmaterialregions................ 174
6.20 Left: Location of the heat sources; Right: Computed tem-
perature field for the isotropic case α
1
r
= α
1
z
=1,wherethe
isothermsarespacedat80K................... 175
6.21 Computed temperature fields for the moderately anisotropic
cases................................ 176
6.22 The 2-logarithm of the error along a line, the error decays with
O(h
4
) ............................... 181
6.23 The 2-logarithm of the error along a line, the error decays with
O(h
2
) ............................... 182
6.24 The x-component of the solution for a singular point force at
time t = 1 and spatial grid step h =0.0125. . . . . . . . . . . 184
6.25 Contour plot of the y-component on a plane for the 3D case
withasingularforce........................ 187
6.26 Left: Magnetization on the point (0, 0), right: magnetization
on the point (1, 0) with the coordinates: red = x, green = y,
blue = z. ............................. 191
6.27 Figures top-down and left-right present time-sequence of a mag-
netic layer in a pure isotropic case. . . . . . . . . . . . . . . . 192
6.28 Figures top-down and left-right present time-sequence of a mag-
netic layer influenced by an external magnetic field H
e
xt =
(1, 0, 40)............................... 194
A.1 Vector-matrix graph for efficient saving. . . . . . . . . . . . . 205
A.2 Application of r
3
t. ........................ 209
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