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5 | ·c1905ac570198068f9069c41addd3310·201520·libdevel·optional·libdolfinx-dev_0.9.0-5_i386.deb | 5 | ·c1905ac570198068f9069c41addd3310·201520·libdevel·optional·libdolfinx-dev_0.9.0-5_i386.deb |
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7 | ·d87b17df26785fb68171ff7d022b6040·10994160·debug·optional·libdolfinx-real0.9-dbgsym_0.9.0-5_i386.deb | 7 | ·d87b17df26785fb68171ff7d022b6040·10994160·debug·optional·libdolfinx-real0.9-dbgsym_0.9.0-5_i386.deb |
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920 | -rw-r--r--···0·root·········(0)·root·········(0)····11424·2024-12-02·15:55:08.000000·./usr/share/doc/dolfinx-doc/python/_downloads/e8b180b39a27d7b04c2f666d14475ee3/demo_cahn-hilliard.py | 920 | -rw-r--r--···0·root·········(0)·root·········(0)····11424·2024-12-02·15:55:08.000000·./usr/share/doc/dolfinx-doc/python/_downloads/e8b180b39a27d7b04c2f666d14475ee3/demo_cahn-hilliard.py |
921 | drwxr-xr-x···0·root·········(0)·root·········(0)········0·2024-12-02·15:55:08.000000·./usr/share/doc/dolfinx-doc/python/_downloads/f6f3cc4d9540871af057920d1ddb5561/ | 921 | drwxr-xr-x···0·root·········(0)·root·········(0)········0·2024-12-02·15:55:08.000000·./usr/share/doc/dolfinx-doc/python/_downloads/f6f3cc4d9540871af057920d1ddb5561/ |
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1 | { | 1 | { |
2 | ····"cells":·[ | 2 | ····"cells":·[ |
3 | ········{ | 3 | ········{ |
4 | ············"cell_type":·"markdown", | 4 | ············"cell_type":·"markdown", |
5 | ············"id":·" | 5 | ············"id":·"b75f4c45", |
6 | ············"metadata":·{}, | 6 | ············"metadata":·{}, |
7 | ············"source":·[ | 7 | ············"source":·[ |
8 | ················"#·Matrix-free·conjugate·gradient·solver·for·the·Poisson·equation\n", | 8 | ················"#·Matrix-free·conjugate·gradient·solver·for·the·Poisson·equation\n", |
9 | ················"\n", | 9 | ················"\n", |
10 | ················"This·demo·illustrates·how·to·solve·the·Poisson·equation·using·a\n", | 10 | ················"This·demo·illustrates·how·to·solve·the·Poisson·equation·using·a\n", |
11 | ················"matrix-free·conjugate·gradient·(CG)·solver.·In·particular,·it\n", | 11 | ················"matrix-free·conjugate·gradient·(CG)·solver.·In·particular,·it\n", |
12 | ················"illustrates·how·to\n", | 12 | ················"illustrates·how·to\n", |
Offset 68, 84 lines modified | Offset 68, 84 lines modified | ||
68 | ················"\n", | 68 | ················"\n", |
69 | ················"The·modules·that·will·be·used·are·imported:" | 69 | ················"The·modules·that·will·be·used·are·imported:" |
70 | ············] | 70 | ············] |
71 | ········}, | 71 | ········}, |
72 | ········{ | 72 | ········{ |
73 | ············"cell_type":·"code", | 73 | ············"cell_type":·"code", |
74 | ············"execution_count":·null, | 74 | ············"execution_count":·null, |
75 | ············"id":·" | 75 | ············"id":·"69a5d155", |
76 | ············"metadata":·{}, | 76 | ············"metadata":·{}, |
77 | ············"outputs":·[], | 77 | ············"outputs":·[], |
78 | ············"source":·[ | 78 | ············"source":·[ |
79 | ················"from·mpi4py·import·MPI" | 79 | ················"from·mpi4py·import·MPI" |
80 | ············] | 80 | ············] |
81 | ········}, | 81 | ········}, |
82 | ········{ | 82 | ········{ |
83 | ············"cell_type":·"code", | 83 | ············"cell_type":·"code", |
84 | ············"execution_count":·null, | 84 | ············"execution_count":·null, |
85 | ············"id":·" | 85 | ············"id":·"0639e63c", |
86 | ············"metadata":·{}, | 86 | ············"metadata":·{}, |
87 | ············"outputs":·[], | 87 | ············"outputs":·[], |
88 | ············"source":·[ | 88 | ············"source":·[ |
89 | ················"import·numpy·as·np" | 89 | ················"import·numpy·as·np" |
90 | ············] | 90 | ············] |
91 | ········}, | 91 | ········}, |
92 | ········{ | 92 | ········{ |
93 | ············"cell_type":·"code", | 93 | ············"cell_type":·"code", |
94 | ············"execution_count":·null, | 94 | ············"execution_count":·null, |
95 | ············"id":·" | 95 | ············"id":·"c218cd23", |
96 | ············"metadata":·{}, | 96 | ············"metadata":·{}, |
97 | ············"outputs":·[], | 97 | ············"outputs":·[], |
98 | ············"source":·[ | 98 | ············"source":·[ |
99 | ················"import·dolfinx\n", | 99 | ················"import·dolfinx\n", |
100 | ················"import·ufl\n", | 100 | ················"import·ufl\n", |
101 | ················"from·dolfinx·import·fem,·la\n", | 101 | ················"from·dolfinx·import·fem,·la\n", |
102 | ················"from·ufl·import·action,·dx,·grad,·inner" | 102 | ················"from·ufl·import·action,·dx,·grad,·inner" |
103 | ············] | 103 | ············] |
104 | ········}, | 104 | ········}, |
105 | ········{ | 105 | ········{ |
106 | ············"cell_type":·"markdown", | 106 | ············"cell_type":·"markdown", |
107 | ············"id":·" | 107 | ············"id":·"4383f228", |
108 | ············"metadata":·{}, | 108 | ············"metadata":·{}, |
109 | ············"source":·[ | 109 | ············"source":·[ |
110 | ················"We·begin·by·using·{py:func}`create_rectangle\n", | 110 | ················"We·begin·by·using·{py:func}`create_rectangle\n", |
111 | ················"<dolfinx.mesh.create_rectangle>`·to·create·a·rectangular\n", | 111 | ················"<dolfinx.mesh.create_rectangle>`·to·create·a·rectangular\n", |
112 | ················"{py:class}`Mesh·<dolfinx.mesh.Mesh>`·of·the·domain,·and·creating·a\n", | 112 | ················"{py:class}`Mesh·<dolfinx.mesh.Mesh>`·of·the·domain,·and·creating·a\n", |
113 | ················"finite·element·{py:class}`FunctionSpace·<dolfinx.fem.FunctionSpace>`\n", | 113 | ················"finite·element·{py:class}`FunctionSpace·<dolfinx.fem.FunctionSpace>`\n", |
114 | ················"on·the·mesh." | 114 | ················"on·the·mesh." |
115 | ············] | 115 | ············] |
116 | ········}, | 116 | ········}, |
117 | ········{ | 117 | ········{ |
118 | ············"cell_type":·"code", | 118 | ············"cell_type":·"code", |
119 | ············"execution_count":·null, | 119 | ············"execution_count":·null, |
120 | ············"id":·" | 120 | ············"id":·"c6b77459", |
121 | ············"metadata":·{}, | 121 | ············"metadata":·{}, |
122 | ············"outputs":·[], | 122 | ············"outputs":·[], |
123 | ············"source":·[ | 123 | ············"source":·[ |
124 | ················"dtype·=·dolfinx.default_scalar_type\n", | 124 | ················"dtype·=·dolfinx.default_scalar_type\n", |
125 | ················"real_type·=·np.real(dtype(0.0)).dtype\n", | 125 | ················"real_type·=·np.real(dtype(0.0)).dtype\n", |
126 | ················"comm·=·MPI.COMM_WORLD\n", | 126 | ················"comm·=·MPI.COMM_WORLD\n", |
127 | ················"mesh·=·dolfinx.mesh.create_rectangle(comm,·[[0.0,·0.0],·[1.0,·1.0]],·[10,·10],·dtype=real_type)" | 127 | ················"mesh·=·dolfinx.mesh.create_rectangle(comm,·[[0.0,·0.0],·[1.0,·1.0]],·[10,·10],·dtype=real_type)" |
128 | ············] | 128 | ············] |
129 | ········}, | 129 | ········}, |
130 | ········{ | 130 | ········{ |
131 | ············"cell_type":·"code", | 131 | ············"cell_type":·"code", |
132 | ············"execution_count":·null, | 132 | ············"execution_count":·null, |
133 | ············"id":·" | 133 | ············"id":·"b70e4c73", |
134 | ············"metadata":·{}, | 134 | ············"metadata":·{}, |
135 | ············"outputs":·[], | 135 | ············"outputs":·[], |
136 | ············"source":·[ | 136 | ············"source":·[ |
137 | ················"#·Create·function·space\n", | 137 | ················"#·Create·function·space\n", |
138 | ················"degree·=·2\n", | 138 | ················"degree·=·2\n", |
139 | ················"V·=·fem.functionspace(mesh,·(\"Lagrange\",·degree))" | 139 | ················"V·=·fem.functionspace(mesh,·(\"Lagrange\",·degree))" |
140 | ············] | 140 | ············] |
141 | ········}, | 141 | ········}, |
142 | ········{ | 142 | ········{ |
143 | ············"cell_type":·"markdown", | 143 | ············"cell_type":·"markdown", |
144 | ············"id":·" | 144 | ············"id":·"28d0718d", |
145 | ············"metadata":·{}, | 145 | ············"metadata":·{}, |
146 | ············"source":·[ | 146 | ············"source":·[ |
147 | ················"The·second·argument·to·{py:class}`functionspace\n", | 147 | ················"The·second·argument·to·{py:class}`functionspace\n", |
148 | ················"<dolfinx.fem.functionspace>`·is·a·tuple·consisting·of·`(family,\n", | 148 | ················"<dolfinx.fem.functionspace>`·is·a·tuple·consisting·of·`(family,\n", |
149 | ················"degree)`,·where·`family`·is·the·finite·element·family,·and·`degree`\n", | 149 | ················"degree)`,·where·`family`·is·the·finite·element·family,·and·`degree`\n", |
150 | ················"specifies·the·polynomial·degree.·In·this·case·`V`·consists·of\n", | 150 | ················"specifies·the·polynomial·degree.·In·this·case·`V`·consists·of\n", |
151 | ················"third-order,·continuous·Lagrange·finite·element·functions.\n", | 151 | ················"third-order,·continuous·Lagrange·finite·element·functions.\n", |
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156 | ················"and·then·retrieving·all·facets·on·the·boundary·using\n", | 156 | ················"and·then·retrieving·all·facets·on·the·boundary·using\n", |
157 | ················"{py:func}`exterior_facet_indices·<dolfinx.mesh.exterior_facet_indices>`." | 157 | ················"{py:func}`exterior_facet_indices·<dolfinx.mesh.exterior_facet_indices>`." |
158 | ············] | 158 | ············] |
159 | ········}, | 159 | ········}, |
160 | ········{ | 160 | ········{ |
161 | ············"cell_type":·"code", | 161 | ············"cell_type":·"code", |
162 | ············"execution_count":·null, | 162 | ············"execution_count":·null, |
163 | ············"id":·" | 163 | ············"id":·"77f987e9", |
164 | ············"metadata":·{}, | 164 | ············"metadata":·{}, |
165 | ············"outputs":·[], | 165 | ············"outputs":·[], |
166 | ············"source":·[ | 166 | ············"source":·[ |
167 | ················"tdim·=·mesh.topology.dim\n", | 167 | ················"tdim·=·mesh.topology.dim\n", |
168 | ················"mesh.topology.create_connectivity(tdim·-·1,·tdim)\n", | 168 | ················"mesh.topology.create_connectivity(tdim·-·1,·tdim)\n", |
169 | ················"facets·=·dolfinx.mesh.exterior_facet_indices(mesh.topology)" | 169 | ················"facets·=·dolfinx.mesh.exterior_facet_indices(mesh.topology)" |
170 | ············] | 170 | ············] |
171 | ········}, | 171 | ········}, |
172 | ········{ | 172 | ········{ |
173 | ············"cell_type":·"markdown", | 173 | ············"cell_type":·"markdown", |
174 | ············"id":·" | 174 | ············"id":·"4d953804", |
175 | ············"metadata":·{}, | 175 | ············"metadata":·{}, |
176 | ············"source":·[ | 176 | ············"source":·[ |
177 | ················"We·now·find·the·degrees·of·freedom·that·are·associated·with·the·boundary\n", | 177 | ················"We·now·find·the·degrees·of·freedom·that·are·associated·with·the·boundary\n", |
178 | ················"facets·using\n", | 178 | ················"facets·using\n", |
179 | ················"{py:func}`locate_dofs_topological·<dolfinx.fem.locate_dofs_topological>`" | 179 | ················"{py:func}`locate_dofs_topological·<dolfinx.fem.locate_dofs_topological>`" |
180 | ············] | 180 | ············] |
181 | ········}, | 181 | ········}, |
182 | ········{ | 182 | ········{ |
183 | ············"cell_type":·"code", | 183 | ············"cell_type":·"code", |
184 | ············"execution_count":·null, | 184 | ············"execution_count":·null, |
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1 | { | 1 | { |
2 | ····"cells":·[ | 2 | ····"cells":·[ |
3 | ········{ | 3 | ········{ |
4 | ············"cell_type":·"markdown", | 4 | ············"cell_type":·"markdown", |
5 | ············"id":·" | 5 | ············"id":·"e50b217a", |
6 | ············"metadata":·{}, | 6 | ············"metadata":·{}, |
7 | ············"source":·[ | 7 | ············"source":·[ |
8 | ················"#·Mixed·formulation·for·the·Poisson·equation" | 8 | ················"#·Mixed·formulation·for·the·Poisson·equation" |
9 | ············] | 9 | ············] |
10 | ········}, | 10 | ········}, |
11 | ········{ | 11 | ········{ |
12 | ············"cell_type":·"markdown", | 12 | ············"cell_type":·"markdown", |
13 | ············"id":·" | 13 | ············"id":·"abc4a017", |
14 | ············"metadata":·{}, | 14 | ············"metadata":·{}, |
15 | ············"source":·[ | 15 | ············"source":·[ |
16 | ················"This·demo·illustrates·how·to·solve·Poisson·equation·using·a·mixed\n", | 16 | ················"This·demo·illustrates·how·to·solve·Poisson·equation·using·a·mixed\n", |
17 | ················"(two-field)·formulation.·In·particular,·it·illustrates·how·to\n", | 17 | ················"(two-field)·formulation.·In·particular,·it·illustrates·how·to\n", |
18 | ················"\n", | 18 | ················"\n", |
19 | ················"*·Use·mixed·and·non-continuous·finite·element·spaces.\n", | 19 | ················"*·Use·mixed·and·non-continuous·finite·element·spaces.\n", |
20 | ················"*·Set·essential·boundary·conditions·for·subspaces·and·$H(\\mathrm{div})$·spaces.\n" | 20 | ················"*·Set·essential·boundary·conditions·for·subspaces·and·$H(\\mathrm{div})$·spaces.\n" |
21 | ············] | 21 | ············] |
22 | ········}, | 22 | ········}, |
23 | ········{ | 23 | ········{ |
24 | ············"cell_type":·"markdown", | 24 | ············"cell_type":·"markdown", |
25 | ············"id":·" | 25 | ············"id":·"4a505c8b", |
26 | ············"metadata":·{}, | 26 | ············"metadata":·{}, |
27 | ············"source":·[ | 27 | ············"source":·[ |
28 | ················"```{admonition}·Download·sources\n", | 28 | ················"```{admonition}·Download·sources\n", |
29 | ················":class:·download\n", | 29 | ················":class:·download\n", |
30 | ················"\n", | 30 | ················"\n", |
31 | ················"*·{download}`Python·script·<./demo_mixed-poisson.py>`\n", | 31 | ················"*·{download}`Python·script·<./demo_mixed-poisson.py>`\n", |
32 | ················"*·{download}`Jupyter·notebook·<./demo_mixed-poisson.ipynb>`\n", | 32 | ················"*·{download}`Jupyter·notebook·<./demo_mixed-poisson.ipynb>`\n", |
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99 | ················"\n", | 99 | ················"\n", |
100 | ················"##·Implementation" | 100 | ················"##·Implementation" |
101 | ············] | 101 | ············] |
102 | ········}, | 102 | ········}, |
103 | ········{ | 103 | ········{ |
104 | ············"cell_type":·"code", | 104 | ············"cell_type":·"code", |
105 | ············"execution_count":·null, | 105 | ············"execution_count":·null, |
106 | ············"id":·" | 106 | ············"id":·"45e7a3b5", |
107 | ············"metadata":·{}, | 107 | ············"metadata":·{}, |
108 | ············"outputs":·[], | 108 | ············"outputs":·[], |
109 | ············"source":·[ | 109 | ············"source":·[ |
110 | ················"\n", | 110 | ················"\n", |
111 | ················"try:\n", | 111 | ················"try:\n", |
112 | ················"····from·petsc4py·import·PETSc\n", | 112 | ················"····from·petsc4py·import·PETSc\n", |
113 | ················"\n", | 113 | ················"\n", |