neuron_morphology.transforms.streamline

Module Contents

Functions

solve_laplace_2d(V: fem.FunctionSpace, domain, bcs: List[fem.bcs.DirichletBCMetaClass])	Solves the laplace equation with boundary conditions bcs on V
compute_gradient(uh, W, bcs=[])
generate_laplace_field(top_line: List[Tuple], bottom_line: List[Tuple], mesh_res: float = 20, top_value: float = 1.0, bottom_value: float = 0.0, eps_bounds: float = 1e-08)	Solve Laplace equation inside a polygon bounded

neuron_morphology.transforms.streamline.solve_laplace_2d(V: fem.FunctionSpace, domain, bcs: List[fem.bcs.DirichletBCMetaClass])

Solves the laplace equation with boundary conditions bcs on V

Parameters:

V: Fenics FunctionSpace object created from a mesh

bcs: List of Fenics DirichletBC Boundary Conditions

neuron_morphology.transforms.streamline.compute_gradient(uh, W, bcs=[])

neuron_morphology.transforms.streamline.generate_laplace_field(top_line: List[Tuple], bottom_line: List[Tuple], mesh_res: float = 20, top_value: float = 1.0, bottom_value: float = 0.0, eps_bounds: float = 1e-08)

Solve Laplace equation inside a polygon bounded by two lines (top_line and bottom_line) and the artificial straight side lines connecting the ends of the two lines. Apply Dirichlet BC on top_line and bottom_line and zero Neuman BC on the side lines.

Demo of fenics: https://github.com/hplgit/fenics-tutorial/

blob/master/pub/python/vol1/ft01_poisson.py

If top_value and bottom_value defaults are used, value_field will be the normalized distance to the top_line

Parameters:

top_line: line that will have top_value boundary condition

bottom_line: line that will have bottom_value boundary condition

mesh_res: resolution of the mesh

top_value: value for top Dirichlet Boundary

bottom_value: value for bottom Dirichlet Boundary

Returns:

u: returns value at input point e.g. 0.5 = u((0.5, 0.5))

grad_u: returns gradient at input point e.g. [0, 1] = u((0.5, 0.5))

mesh_coords: coordinates of each vertex in the mesh

mesh_values: values at each vertex in the mesh

gradient_mesh: gradient at each vertex in the mesh