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Fem-fenics: Difference between revisions
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The equation being solved is | The equation being solved is | ||
<div style="width: 100%;"> | |||
<div style="float:left; width: 48%"> | |||
{{Code|Define Poisson problem|<syntaxhighlight lang="octave" style="font-size:13px"> | |||
pkg load fem-fenics msh | |||
import_ufl_Problem ('Poisson') | |||
# Create mesh and define function space | |||
x = y = linspace (0, 1, 33); | |||
mesh = Mesh(msh2m_structured_mesh (x, y, 1, 1:4)); | |||
# File Poisson.ufl | |||
# element = FiniteElement("Lagrange", triangle, 1) | |||
V = FunctionSpace('Poisson', mesh); | |||
# Define boundary condition | |||
bc = DirichletBC(V, @(x, y) 0.0, [2;4]); | |||
# Define variational problem | |||
# File Poisson.ufl | |||
# u = TrialFunction(element) | |||
# v = TestFunction(element) | |||
# f = Coefficient(element) | |||
# g = Coefficient(element) | |||
f = Expression ('f', | |||
@(x,y) 10*exp(-((x - 0.5)^2 + (y - 0.5)^2) / 0.02)); | |||
g = Expression ('g', @(x,y) sin (5.0 * x)); | |||
# File Poisson.ufl | |||
# a = inner(grad(u), grad(v))*dx | |||
# L = f*v*dx + g*v*ds | |||
a = BilinearForm ('Poisson', V); | |||
L = Poisson_LinearForm ('Poisson', V, f, g); | |||
# Compute solution | |||
[A, b] = assemble_system (a, L, bc); | |||
sol = A \ b; | |||
u = Function ('u', V, sol); | |||
{{Code|Define Poisson problem|<syntaxhighlight lang=" | # Save solution in VTK format | ||
save (u) | |||
# Plot solution | |||
plot (u); | |||
</syntaxhighlight>}} | |||
</div> | |||
<div style="float:right; width: 48%"> | |||
{{Code|Define Poisson problem|<syntaxhighlight lang="python" style="font-size:13px"> | |||
from dolfin import * | |||
# Create mesh and define function space | |||
mesh = UnitSquareMesh(32, 32) | |||
V = FunctionSpace(mesh, "Lagrange", 1) | |||
# Define Dirichlet boundary (x = 0 or x = 1) | |||
def boundary(x): | |||
return x[0] < DOLFIN_EPS or x[0] > 1.0 - DOLFIN_EPS | |||
# Define boundary condition | |||
u0 = Constant(0.0) | |||
bc = DirichletBC(V, u0, boundary) | |||
# Define variational problem | |||
u = TrialFunction(V) | |||
v = TestFunction(V) | |||
f = Expression("10*exp(-(pow(x[0] - 0.5, 2) + pow(x[1] - 0.5, 2)) / 0.02)") | |||
g = Expression("sin(5*x[0])") | |||
a = inner(grad(u), grad(v))*dx | |||
L = f*v*dx + g*v*ds | |||
# Compute solution | |||
u = Function(V) | |||
(A, b) = assemble_system (a, L, bc); | |||
solve(A, u.vector(), b, "gmres", "default") | |||
# Save solution in VTK format | |||
file = File("poisson.pvd") | |||
file << u | |||
# Plot solution | |||
plot(u, interactive=True) | |||
</syntaxhighlight>}} | </syntaxhighlight>}} | ||
</div> | |||
</div> | |||
<div style="clear:both"></div> | |||
[[Category:OctaveForge]] | [[Category:OctaveForge]] | ||
[[Category:Packages]] | [[Category:Packages]] | ||