FEniCS-examples
Example Python codes for FEniCS
bvp1.py is the simplest example and solves the linear
2-point boundary value problem
-u"(x)=-1
with the boundary conditions
u(0) = 0, u'(1) = 1
bvp2.py solves a system of two coupled boundary value problems
-u1" + u2 = f1
u1 - u2" = f2
with the boundary conditions
u1(0)=0, u1(1)=1
u2(0)=1, u2(1)=0
nl_system3.py solves a system of 3 nonlinear boundary value problems
-u1" + u2' + u3 + u1*u3 = f1
-u1' - u2" + u3 + - 16*u2*u3 = f2
u1 + u2 - u3" + u1*u3 - 16*u2*u3 + u3^2 = 0
with the boundary conditions
u1(0) = 0, u1(1) = 1
u2(0) = 1, u2(1) = 0
u3(0) = 0, u3(1) = 0
adv_diff.py solves the advection diffusion equation
u_t + a*u_x = d*u_xx
with a given initial condition and homogeneous Neumann conditons
u_x(-1) = u_x(+1) = 0
`newton.py' solves the nonlinear boundary value problem
(exp(a*u)*u')' = 0
u(0) = 0, u(1) = 1
Using a manual Newton's method with continuation/homotopy
`newton_sys2.py' solves the two coupled nonlinear boundary value problems
-u1" + a*exp(u2)*u1 = 0
-u2" + a*exp(u1)*u2 = 0
u1(0) = 0, u1(1) = 1
u2(1) = 1, u2(0) = 0
finite_well.py computes eigenvalues and eigenfunctions for
a finite potential quantum well.
'nonuniform.py' constructs a nonuniform 1D grid with clustering at desired locations and then solves a boundary value problem which has a rapidly varying solution at those locations.
-[p(x)u']' = 1
u(0) = u(1) = 0
p(x) = 1.001 + cos(4*pi*x)
'quantum_dot.py' computes the ground state in a hemispherical quantum dot using the inverse iteration with repeated Cholesky solves via PETScLUSolver