```python
import numpy as np
import time
from fealpy.mesh import MeshFactory as MF
from fealpy.functionspace import LagrangeFiniteElementSpace
from fealpy.boundarycondition import DirichletBC
from fealpy.timeintegratoralg import UniformTimeLine
from scipy.sparse.linalg import spsolve
from scipy.sparse import csr_matrix
import matplotlib.pyplot as plt

class BoxDomain:
    def __init__(self, lx, ly):
        self.lx = lx
        self.ly = ly

    def init_mesh(self, nx, ny):
        self.mesh = MF.boxmesh2d([0, self.lx, 0, self.ly], nx=nx, ny=ny, meshtype='tri')

    def displacement(self, u):
        pass  # Define displacement

    def strain(self, epsilon):
        pass  # Define strain

    def stress(self, sigma):
        pass  # Define stress

    def source(self, f):
        pass  # Define source

    def dirichlet_boundary(self, p):
        # Example condition, modify as needed
        return (p[0] == 0) | (p[1] == 0)

    def neumann_boundary(self, p):
        # Example condition, modify as needed
        return (p[0] == self.lx) | (p[1] == self.ly)

    def fracture_boundary(self, p):
        # Example condition, modify as needed
        return False

class IterationCounter:
    def __init__(self):
        self.count = 0

    def __call__(self, rk=None):
        self.count += 1
        print(f"Iteration: {self.count}")

class FastSolver:
    def __init__(self):
        pass

    def precondition(self):
        pass  # Define preconditioning steps

    def solve(self, A, b):
        # Example solver, replace with a more efficient implementation if necessary
        self.precondition()
        return spsolve(A, b)

# Main part
box_domain = BoxDomain(lx=1.0, ly=1.0)
box_domain.init_mesh(nx=10, ny=10)

space = LagrangeFiniteElementSpace(box_domain.mesh, p=1)

# Define boundary conditions
def dirichlet(p):
    return box_domain.dirichlet_boundary(p)

def neumann(p):
    return box_domain.neumann_boundary(p)

dbc = DirichletBC(space, dirichlet)

# Define source function
f = lambda p: np.array([0, -9.8])

# Stiffness matrix and linear elasticity matrix
A = space.stiff_matrix()
b = space.source_vector(f)

# Apply boundary conditions
isDirichlet = space.boundary_dof()
A[isDirichlet] = 0
A[isDirichlet, isDirichlet] = 1
b[isDirichlet] = 0

print(f"Matrix shape: {A.shape}")

# Solve system
solver = FastSolver()
start_time = time.time()
u = solver.solve(A, b)
print(f"Time to solve: {time.time() - start_time} seconds")

# Plot original mesh
fig, ax = plt.subplots()
box_domain.mesh.add_plot(ax)
plt.show()
```