# Hermes2D: Example 07 (general)
# This example solves a general second-order linear equation with non-constant
# coefficients, and shows how integration orders in linear and bilinear forms
# can be defined manually.
#
# PDE: -d/dx(a_11(x,y)du/dx) - d/dx(a_12(x,y)du/dy) - d/dy(a_21(x,y)du/dx) - d/dy(a_22(x,y)du/dy)
# + a_1(x,y)du/dx + a_21(x,y)du/dy + a_0(x,y)u = rhs(x,y)
#
# Domain: arbitrary
#
# BC: Dirichlet for boundary marker 1: u = g_D(x,y)
# Natural for any other boundary marker: (a_11(x,y)*nu_1 + a_21(x,y)*nu_2) * dudx
# + (a_12(x,y)*nu_1 + s_22(x,y)*nu_2) * dudy = g_N(x,y)
# The following parameters can be changed
P_INIT = 2 # Initial polynomial degree of all mesh elements.
INIT_REF_NUM = 4 # Number of initial uniform refinements
# Import modules
from hermes2d import Mesh, MeshView, OrderView, H1Shapeset, PrecalcShapeset, H1Space, \
LinSystem, WeakForm, DummySolver, Solution, ScalarView, VonMisesFilter, \
OrderView
from hermes2d.examples.c07 import set_bc, set_forms
from hermes2d.examples import get_07_mesh
# Initialize and load the mesh
mesh = Mesh()
mesh.load(get_07_mesh())
# Initial mesh refinements
for i in range(INIT_REF_NUM):
mesh.refine_all_elements()
# Initialize the shapeset and the cache
shapeset = H1Shapeset()
pss = PrecalcShapeset(shapeset)
# Create finite element space
space = H1Space(mesh, shapeset)
space.set_uniform_order(P_INIT)
set_bc(space)
# Enumerate degrees of freedom
space.assign_dofs()
# Initialize the weak formulation
wf = WeakForm(1)
set_forms(wf)
# Initialize the linear system and solver
solver = DummySolver()
ls = LinSystem(wf, solver)
ls.set_spaces(space)
ls.set_pss(pss)
# Assemble the stiffness matrix and solve the system
sln = Solution()
ls.assemble()
ls.solve_system(sln)
# View the solution
sln.plot(filename="a.png")
# View the mesh
mesh.plot(space=space, filename="b.png")
# Positioning the images
print """<html><table border=1><tr><td><span><img src="cell://a.png"></span></td><td><img src="cell://b.png" width="540" height="405"></td></tr></table></html>"""
