BoundaryConditions

BoundaryConditions stores node-indexed boundary rows for a rectangular SourceGrid.

from gbmsc_pde import BoundaryConditions

boundary_conditions = BoundaryConditions(grid)

Dirichlet Conditions

Dirichlet rows impose:

u_i = value_i

Example:

nodes = grid.boundary_indices()["all"]
boundary_conditions.add_dirichlet(nodes, 0.0)

Values may be scalar or an array with one entry per node.

Neumann Conditions

Neumann rows impose:

du/dn = flux

Example:

left = grid.boundary_indices()["left"]
boundary_conditions.add_neumann(
    left,
    outwardnormal=(-1.0, 0.0),
    fluxes=0.0,
)

The normal may contain scalar components or arrays matching the node count.

Robin Conditions

Robin rows impose:

alpha * u + beta * du/dn = value

Example:

right = grid.boundary_indices()["right"]
boundary_conditions.add_robin(
    right,
    outwardnormal=(1.0, 0.0),
    alphas=1.0,
    betas=0.5,
    values=0.0,
)

alphas, betas, and values may be scalars or arrays with one entry per node.

Applying Conditions Manually

Most users apply boundary conditions through LinearSolver. To apply them manually:

A, b, Mx, My, Mxx, Myy = pde.assemble()
A_bc, b_bc = boundary_conditions.apply(A, b, Mx, My)

Dirichlet rows replace the matrix row by an identity row. Neumann and Robin rows use the derivative matrices:

n_x Mx[i, :] + n_y My[i, :]

Second Neumann Rows

The compatibility method add_neumann_as_second_condition can impose Neumann equations on user-selected matrix rows:

boundary_conditions.add_neumann_as_second_condition(
    nodes,
    outwardnormal=(nx, ny),
    fluxes=flux,
    rows=rows,
)

This is intended for augmented systems where a Neumann equation should be added as a separate row rather than replacing the row associated with the source node.