In [1]:

    

from getfem import Mesh, MeshFem, Fem, MeshIm, Integ, Model
from numpy import arange


    

In [2]:

    

m = Mesh('cartesian', arange(0,1.1,0.1), arange(0,1.1,0.1))


    

In [3]:

    

mf = MeshFem(m, 1)


    

In [4]:

    

mf.set_fem(Fem('FEM_QK(2,2)'))


    

In [5]:

    

print Fem('FEM_QK(2,2)').poly_str()


    

    




('1 - 3*x - 3*y + 2*x^2 + 9*x*y + 2*y^2 - 6*x^2*y - 6*x*y^2 + 4*x^2*y^2', '4*x - 4*x^2 - 12*x*y + 12*x^2*y + 8*x*y^2 - 8*x^2*y^2', '-x + 2*x^2 + 3*x*y - 6*x^2*y - 2*x*y^2 + 4*x^2*y^2', '4*y - 12*x*y - 4*y^2 + 8*x^2*y + 12*x*y^2 - 8*x^2*y^2', '16*x*y - 16*x^2*y - 16*x*y^2 + 16*x^2*y^2', '-4*x*y + 8*x^2*y + 4*x*y^2 - 8*x^2*y^2', '-y + 3*x*y + 2*y^2 - 2*x^2*y - 6*x*y^2 + 4*x^2*y^2', '-4*x*y + 4*x^2*y + 8*x*y^2 - 8*x^2*y^2', 'x*y - 2*x^2*y - 2*x*y^2 + 4*x^2*y^2')

In [6]:

    

mim = MeshIm(m, Integ('IM_EXACT_PARALLELEPIPED(2)'))


    

In [7]:

    

border = m.outer_faces()


    

In [8]:

    

m.set_region(42, border)


    

In [9]:

    

md = Model('real')


    

In [10]:

    

md.add_fem_variable('u', mf)


    

In [11]:

    

md.add_Laplacian_brick(mim, 'u');


    

In [12]:

    

g = mf.eval('x*(x-1) - y*(y-1)')
md.add_initialized_fem_data('DirichletData', mf, g)
md.add_Dirichlet_condition_with_multipliers(mim, 'u', mf, 42, 'DirichletData')


    

    
Out[12]:





1

In [13]:

    

md.solve()


    

    
Out[13]:





(0, 1)

In [14]:

    

u = md.variable('u')


    

In [15]:

    

mf.export_to_pos('u.pos',u,'Computed solution')


    

In [16]:

    

%%writefile gscript
Print "A_step-by-step_basic_example_python_image1.png";
Exit;


    

    




Writing gscript

In [17]:

    

!cat gscript


    

    




Print "A_step-by-step_basic_example_python_image1.png";
Exit;

In [18]:

    

!gmsh u.pos gscript


    

In [19]:

    

from IPython.core.display import Image


    

In [20]:

    

Image('A_step-by-step_basic_example_python_image1.png')


    

    
Out[20]:

In [21]:

    

f = mf.eval('5')
md.add_initialized_fem_data('VolumicData', mf, f)
md.add_source_term_brick(mim, 'u', 'VolumicData')


    

    
Out[21]:





2

In [22]:

    

md.solve()
u = md.variable('u')
mf.export_to_pos('u.pos',u,'Computed solution')


    

In [23]:

    

%%writefile gscript
Print "A_step-by-step_basic_example_python_image2.png";
Exit;


    

    




Overwriting gscript

In [24]:

    

!gmsh u.pos gscript


    

In [25]:

    

Image('A_step-by-step_basic_example_python_image2.png')


    

    
Out[25]:

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