From 76eba51836cd8e40faed7cab6454ab5e6f318775 Mon Sep 17 00:00:00 2001
From: Andreas Dutzler <a.dutzler@gmail.com>
Date: Sat, 15 Feb 2025 23:44:46 +0100
Subject: [PATCH] Add `MeshContainer.as_vertex_mesh()`

---
 src/felupe/__init__.py          |  2 ++
 src/felupe/element/__init__.py  |  2 ++
 src/felupe/element/_vertex.py   | 47 +++++++++++++++++++++++++++++++++
 src/felupe/mesh/_container.py   |  5 ++++
 src/felupe/region/__init__.py   |  2 ++
 src/felupe/region/_templates.py | 11 ++++++++
 6 files changed, 69 insertions(+)
 create mode 100644 src/felupe/element/_vertex.py

diff --git a/src/felupe/__init__.py b/src/felupe/__init__.py
index a5e16468..f5c10429 100644
--- a/src/felupe/__init__.py
+++ b/src/felupe/__init__.py
@@ -113,6 +113,7 @@
     RegionTriangleMINI,
     RegionTriQuadraticHexahedron,
     RegionTriQuadraticHexahedronBoundary,
+    RegionVertex,
 )
 from .tools import hello_world, newtonrhapson, project, runs_on, save, topoints
 from .view import ViewField, ViewMesh
@@ -235,6 +236,7 @@
     "RegionTriangleMINI",
     "RegionTriQuadraticHexahedron",
     "RegionTriQuadraticHexahedronBoundary",
+    "RegionVertex",
     "newtonrhapson",
     "project",
     "save",
diff --git a/src/felupe/element/__init__.py b/src/felupe/element/__init__.py
index 9ecbc8f7..461d54ff 100644
--- a/src/felupe/element/__init__.py
+++ b/src/felupe/element/__init__.py
@@ -15,6 +15,7 @@
 from ._quad import BiQuadraticQuad, ConstantQuad, Quad, QuadraticQuad
 from ._tetra import QuadraticTetra, Tetra, TetraMINI
 from ._triangle import QuadraticTriangle, Triangle, TriangleMINI
+from ._vertex import Vertex
 
 __all__ = [
     "Element",
@@ -37,4 +38,5 @@
     "lagrange_line",
     "lagrange_quad",
     "lagrange_hexahedron",
+    "Vertex",
 ]
diff --git a/src/felupe/element/_vertex.py b/src/felupe/element/_vertex.py
new file mode 100644
index 00000000..b180c353
--- /dev/null
+++ b/src/felupe/element/_vertex.py
@@ -0,0 +1,47 @@
+# -*- coding: utf-8 -*-
+"""
+This file is part of FElupe.
+
+FElupe is free software: you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation, either version 3 of the License, or
+(at your option) any later version.
+
+FElupe is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License
+along with FElupe.  If not, see <http://www.gnu.org/licenses/>.
+"""
+
+import numpy as np
+
+from ._base import Element
+
+
+class Vertex(Element):
+    r"""A vertex element formulation with constant shape functions.
+
+    Notes
+    -----
+    The vertex element is defined by one point.
+    """
+
+    def __init__(self):
+        self.points = np.array([[0.0]])
+        self.cells = np.arange(len(self.points)).reshape(1, -1)
+        self.cell_type = "vertex"
+
+    def function(self, r):
+        "Return the shape functions at given coordinate (r)."
+        return np.ones(1)
+
+    def gradient(self, r):
+        "Return the gradient of shape functions at given coordinate (r)."
+        return np.zeros((1, 1))
+
+    def hessian(self, rs):
+        "Return the hessian of shape functions at given coordinate (r)."
+        return np.zeros((1, 1, 1))
diff --git a/src/felupe/mesh/_container.py b/src/felupe/mesh/_container.py
index 17baa2ad..da17d445 100644
--- a/src/felupe/mesh/_container.py
+++ b/src/felupe/mesh/_container.py
@@ -279,6 +279,11 @@ def as_meshio(self, combined=True, **kwargs):
 
         return meshio.Mesh(self.points, cells, **kwargs)
 
+    def as_vertex_mesh(self):
+        "Return a merged vertex-mesh."
+        cells = np.unique([mesh.cells.ravel() for mesh in self.meshes]).reshape(-1, 1)
+        return Mesh(self.points, cells, cell_type=None)
+
     def copy(self):
         "Return a deepcopy of the mesh container."
         return deepcopy(self)
diff --git a/src/felupe/region/__init__.py b/src/felupe/region/__init__.py
index 8569957b..4086467b 100644
--- a/src/felupe/region/__init__.py
+++ b/src/felupe/region/__init__.py
@@ -22,6 +22,7 @@
     RegionTriangleMINI,
     RegionTriQuadraticHexahedron,
     RegionTriQuadraticHexahedronBoundary,
+    RegionVertex,
 )
 
 __all__ = [
@@ -48,4 +49,5 @@
     "RegionTriangleMINI",
     "RegionTriQuadraticHexahedron",
     "RegionTriQuadraticHexahedronBoundary",
+    "RegionVertex",
 ]
diff --git a/src/felupe/region/_templates.py b/src/felupe/region/_templates.py
index 3cdac385..ec25f8cb 100644
--- a/src/felupe/region/_templates.py
+++ b/src/felupe/region/_templates.py
@@ -32,6 +32,7 @@
     Triangle,
     TriangleMINI,
     TriQuadraticHexahedron,
+    Vertex,
 )
 from ..mesh import Mesh
 from ..quadrature import GaussLegendre, GaussLegendreBoundary
@@ -852,3 +853,13 @@ class RegionQuadraticTetra(Region):
     def __init__(self, mesh, quadrature=TetraQuadrature(order=2), grad=True, **kwargs):
         element = QuadraticTetra()
         super().__init__(mesh, element, quadrature, grad=grad, **kwargs)
+
+
+class RegionVertex(Region):
+    "A region with a vertex element."
+
+    def __init__(
+        self, mesh, quadrature=GaussLegendre(order=0, dim=1), grad=False, **kwargs
+    ):
+        element = Vertex()
+        super().__init__(mesh, element, quadrature, grad=grad, **kwargs)