Create a 1D Mesh for Temporal SPDE Models — tulpa_mesh

Generates a 1D mesh (interval partition) for temporal components of spatio-temporal SPDE models. Returns 1D FEM matrices (tridiagonal mass and stiffness) that can be combined with 2D spatial FEM matrices via Kronecker products in tulpa's space-time Q-builder.

Usage

tulpa_mesh_1d(knots, boundary = NULL, n_extend = 3L)

# S3 method for class 'tulpa_mesh_1d'
print(x, ...)

Arguments

knots: Numeric vector of mesh knot locations (e.g., time points). Will be sorted and deduplicated.
boundary: Two-element numeric vector c(lower, upper) defining the mesh domain. Defaults to range(knots).
n_extend: Number of extra knots to add beyond each boundary, spaced at the median knot interval. Default 3.
x: A tulpa_mesh_1d object.
...: Additional arguments (ignored).

Value

A tulpa_mesh_1d object with components:

knots: sorted numeric vector of mesh knot locations
n: number of knots
C: consistent mass matrix (tridiagonal, n x n sparse)
G: stiffness matrix (tridiagonal, n x n sparse)
C0: lumped (diagonal) mass matrix

The tulpa_mesh_1d object x, returned invisibly.