Meshes

generate_mesh(mp::GeometryBasics.MultiPoint, buffer_width::Real,
              interior_mesh_size::Real;
              exterior_mesh_size::Real = 2 * interior_mesh_size,
              element_order::Int = 1, save_path=nothing)

Generate a mesh for a spatial point cloud, with a buffer to counteract boundary effects from the SPDE discretization.

Input

• mp – MultiPoint object
• buffer_width – Width of the buffer around the convex hull
• interior_mesh_size – Mesh size inside the convex hull
• exterior_mesh_size – Mesh size outside the convex hull
• element_order – Order of the element basis functions
• save_path – Optional path to save the mesh

Output

A Ferrite.Grid object

Algorithm

1. Create the convex hull of the point cloud via LibGEOS
2. Create the buffer around the convex hull
3. Create a mesh for the buffered polygon using Gmsh
4. Transfer the Gmsh information to Ferrite

generate_mesh(points, buffer_width::Real, interior_mesh_size::Real;
              exterior_mesh_size::Real=2 * interior_mesh_size,
              element_order::Int=1, save_path=nothing)

Generate a mesh from a list of points using Gmsh.

Input

• points – List of points
• buffer_width – Width of the buffer around the convex hull
• interior_mesh_size – Mesh size inside the convex hull
• exterior_mesh_size – Mesh size outside the convex hull
• element_order – Order of the elements
• save_path – Path to save the mesh

Output

A Ferrite.Grid object

create_inflated_rectangle(x0, y0, dx, dy, boundary_width, interior_mesh_size,
exterior_mesh_size = 2 * interior_mesh_size; element_order = 1)

Create a triangular FEM discretization of a rectangle with an inflated boundary. Useful for FEM discretizations of SPDEs, where the domain is often artificially inflated to avoid undesirable boundary effects. Mesh has physical groups "Domain", "Interior", "Interior boundary" and possibly "Exterior boundary".

Arguments

• x0::Real: x-coordinate of the bottom-left corner of the rectangle
• y0::Real: y-coordinate of the bottom-left corner of the rectangle
• dx::Real: Width of the rectangle
• dy::Real: Height of the rectangle
• boundary_width::Real: Width of the inflated boundary. If 0.0, mesh will not be inflated at all.
• interior_mesh_size::Real: Mesh size in the interior of the rectangle
• exterior_mesh_size::Real: Mesh size in the exterior of the rectangle
• element_order::Int: Order of the FEM elements

Returns

• grid::Ferrite.Grid: the FEM discretization of the rectangle
• boundary_tags::Vector{Int}: the indices of the boundary nodes