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Poisson1#

Poisson equation with unit load.

Reference: https://scikit-fem.readthedocs.io/en/latest/listofexamples.html#example-1-poisson-equation-with-unit-load

$u$
15 import matplotlib.pyplot as plt
16
17 from EasyFEA import Display, ElemType, Models, Simulations
18 from EasyFEA.FEM import Field, BiLinearForm, LinearForm
19 from EasyFEA.Geoms import Domain
20
21 if __name__ == "__main__":
22     Display.Clear()
23
24     # ----------------------------------------------
25     # Mesh
26     # ----------------------------------------------
27
28     contour = Domain((0, 0), (1, 1), 1 / 2**6)
29
30     mesh = contour.Mesh_2D([], ElemType.TRI3, isOrganised=True)
31
32     nodes = mesh.Nodes_Tags(["L0", "L1", "L2", "L3"])
33
34     # ----------------------------------------------
35     # Formulations
36     # ----------------------------------------------
37
38     field = Field(mesh.groupElem, 1)
39
40     @BiLinearForm
41     def bilinear_form(u: Field, v: Field):
42         return u.grad.dot(v.grad)
43
44     @LinearForm
45     def linear_form(v: Field):
46         return 1.0 * v
47
48     weakForms = Models.WeakForms(field, computeK=bilinear_form, computeF=linear_form)
49
50     # ----------------------------------------------
51     # Simulation
52     # ----------------------------------------------
53
54     simu = Simulations.WeakForms(mesh, weakForms)
55
56     simu.add_dirichlet(nodes, [0], ["u"])
57
58     simu.Solve()
59
60     # ----------------------------------------------
61     # Results
62     # ----------------------------------------------
63
64     Display.Plot_Result(simu, "u")
65
66     plt.show()

Total running time of the script: (0 minutes 0.223 seconds)

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