1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
|
<?xml version="1.0" encoding="UTF-8"?>
<simulation xmds-version="2">
<testing>
<xsil_file name="bessel_transform_rectangular.xsil" expected="bessel_transform_rectangular_expected.xsil" absolute_tolerance="1e-6" relative_tolerance="1e-5" />
</testing>
<name>bessel_transform_rectangular</name>
<author>Graham Dennis</author>
<description>
Solve the wave equation on a disk of radius 1 utilising cylindrical symmetry
by using the Bessel function transform. The Bessel function transform implicitly
assumes Dirichlet boundary conditions at the edge of the disk.
</description>
<features>
<benchmark />
<bing />
<globals>
<![CDATA[
const real T = 10.0;
const real mass = 1e-3;
const real length = 1.0;
const real mu = mass/length;
]]>
</globals>
</features>
<geometry>
<propagation_dimension> t </propagation_dimension>
<transverse_dimensions>
<dimension name="x" lattice="100" spectral_lattice="50" domain="(0, 1)" transform="bessel" />
</transverse_dimensions>
</geometry>
<vector name="main" initial_basis="x" type="complex">
<components>
u uDot
</components>
<initialisation>
<![CDATA[
u = exp(-100.0*(x-0.25)*(x-0.25));
uDot = 0.0;
]]>
</initialisation>
</vector>
<sequence>
<integrate algorithm="ARK45" tolerance="1e-6" interval="8e-3">
<samples>100 73</samples>
<operators>
<operator kind="ex" constant="yes" fourier_space="kx">
<operator_names>L</operator_names>
<![CDATA[
L = -T*kx*kx/mu;
]]>
</operator>
<integration_vectors>main</integration_vectors>
<![CDATA[
du_dt = uDot;
duDot_dt = L[u];
]]>
</operators>
</integrate>
</sequence>
<output format="binary">
<sampling_group initial_sample="yes">
<dimension name="x" fourier_space="no" />
<moments>amp</moments>
<dependencies>main</dependencies>
<![CDATA[
amp = u.Re();
]]>
</sampling_group>
<sampling_group initial_sample="no">
<dimension name="x" fourier_space="yes" />
<moments>amp</moments>
<dependencies>main</dependencies>
<![CDATA[
amp = u.Re();
]]>
</sampling_group>
</output>
<info>
Script compiled with xpdeint version VERSION_PLACEHOLDER (SUBVERSION_REVISION_PLACEHOLDER)
See http://www.xmds.org for more information.
</info>
<XSIL Name="moment_group_1">
<Param Name="n_independent">2</Param>
<Array Name="variables" Type="Text">
<Dim>3</Dim>
<Stream><Metalink Format="Text" Delimiter=" \n"/>
t x amp
</Stream>
</Array>
<Array Name="data" Type="double">
<Dim>101</Dim>
<Dim>100</Dim>
<Dim>3</Dim>
<Stream><Metalink Format="Binary" UnsignedLong="uint64" precision="double" Type="Remote" Encoding="LittleEndian"/>
bessel_transform_rectangular_expected_mg0.dat
</Stream>
</Array>
</XSIL>
<XSIL Name="moment_group_2">
<Param Name="n_independent">2</Param>
<Array Name="variables" Type="Text">
<Dim>3</Dim>
<Stream><Metalink Format="Text" Delimiter=" \n"/>
t kx amp
</Stream>
</Array>
<Array Name="data" Type="double">
<Dim>73</Dim>
<Dim>50</Dim>
<Dim>3</Dim>
<Stream><Metalink Format="Binary" UnsignedLong="uint64" precision="double" Type="Remote" Encoding="LittleEndian"/>
bessel_transform_rectangular_expected_mg1.dat
</Stream>
</Array>
</XSIL>
</simulation>
|
