Simplify Element

and add `element.Element` to the top-level namespace

CHANGELOG.md

@@ -11,6 +11,7 @@ All notable changes to this project will be documented in this file. The format
 - Add `BoundaryDict` as a subclassed dict with methods to `plot()`, `screenshot()` and `imshow()`.
 - Add a new argument to apply a callable on the assembled vector/matrix of a solid body, `SolidBody(..., apply=None)`. This may be used to sum the list of sub-blocks instead of stacking them together, `SolidBody(..., block=False, apply=None)`. This is useful for mixed formulations where both the deformation gradient and the displacement values are required.
 - Add support for non-symmetric bilinear mixed forms in `IntegralForm`.
+- Add `element.Element` to the top-level package namespace.
 
 ### Changed
 - The first Piola-Kirchhoff stress tensor is evaluated if `ViewSolid(stress_type=None)`.
@@ -25,6 +26,9 @@ All notable changes to this project will be documented in this file. The format
 ### Fixed
 - Fix `Boundary(..., mode="and")` by ignoring any undefined axis.
 
+### Removed
+- Remove the unused `shape`-argument in `element.Element(shape)`. Adopt the arbitrary-lagrange element to use its own `dim`-argument. This simplifies the creation of custom finite element formulations.
+
 ## [9.1.0] - 2024-11-23
 
 ### Added

src/felupe/__init__.py

@@ -46,6 +46,7 @@
     BiQuadraticQuad,
     ConstantHexahedron,
     ConstantQuad,
+    Element,
     Hexahedron,
     Line,
     Quad,
@@ -173,6 +174,7 @@
     "BiQuadraticQuad",
     "ConstantHexahedron",
     "ConstantQuad",
+    "Element",
     "Hexahedron",
     "Line",
     "Quad",

src/felupe/element/_base.py

@@ -20,9 +20,6 @@
 
 
 class Element:
-    def __init__(self, shape):
-        self.shape = shape
-        self.dim = self.shape[1]
 
     def view(self, point_data=None, cell_data=None, cell_type=None):
         """View the element with optional given dicts of point- and cell-data items.
@@ -91,7 +88,7 @@ def plot(
         )
         if add_point_labels:
             plotter.add_point_labels(
-                points=np.pad(self.points, ((0, 0), (0, 3 - self.shape[1]))),
+                points=np.pad(self.points, ((0, 0), (0, 3 - self.points.shape[1]))),
                 labels=[f"{a}" for a in np.arange(len(self.points))],
                 font_size=font_size,
                 show_points=show_points,
@@ -108,19 +105,19 @@ def plot(
             actor.SetNormalizedShaftLength((0.9, 0.9, 0.9))
             actor.SetNormalizedTipLength((0.1, 0.1, 0.1))
 
-            if self.shape[1] == 3:
+            if self.points.shape[1] == 3:
                 actor.SetTotalLength([1.3, 1.3, 1.3])
-            elif self.shape[1] == 2:
+            elif self.points.shape[1] == 2:
                 actor.SetZAxisLabelText("")
                 actor.SetTotalLength([1.3, 1.3, 0])
-            elif self.shape[1] == 1:
+            elif self.points.shape[1] == 1:
                 actor.SetYAxisLabelText("")
                 actor.SetZAxisLabelText("")
                 actor.SetTotalLength([1.3, 0, 0])
 
             plotter.camera.zoom(0.7)
 
-        if self.shape[1] == 3:
+        if self.points.shape[1] == 3:
             plotter.camera.azimuth = -17
 
         return plotter

src/felupe/element/_hexahedron.py

@@ -69,7 +69,6 @@ def __init__(self):
         )
         self.cells = np.arange(len(self.points)).reshape(1, -1)
         self.cell_type = "hexahedron"
-        super().__init__(shape=(1, 3))
 
     def function(self, rst):
         "Return the shape functions at given coordinates (r, s, t)."
@@ -140,7 +139,6 @@ def __init__(self):
         )
         self.cells = np.arange(len(self.points)).reshape(1, -1)
         self.cell_type = "hexahedron"
-        super().__init__(shape=(8, 3))
 
     def function(self, rst):
         "Return the shape functions at given coordinates (r, s, t)."
@@ -263,7 +261,6 @@ def __init__(self):
         )
         self.cells = np.arange(len(self.points)).reshape(1, -1)
         self.cell_type = "hexahedron20"
-        super().__init__(shape=(20, 3))
 
     def function(self, rst):
         "Return the shape functions at given coordinates (r, s, t)."
@@ -471,8 +468,6 @@ class TriQuadraticHexahedron(Element):
     """
 
     def __init__(self):
-        super().__init__(shape=(27, 3))
-
         self.points = np.array(
             [
                 [-1, -1, -1],

src/felupe/element/_lagrange.py

@@ -260,15 +260,14 @@ def __init__(self, order, dim, interval=(-1, 1), permute=True):
         self._npoints = self._nshape**dim
         self._nbasis = self._npoints
         self._interval = interval
+        self._dim = dim
 
         self.permute = None
         if permute:
             self.permute = [None, lagrange_line, lagrange_quad, lagrange_hexahedron][
                 dim
             ](order)
 
-        super().__init__(shape=(self._npoints, dim))
-
         # init curve-parameter matrix
         n = self._nshape
         self._AT = np.linalg.inv(
@@ -278,7 +277,7 @@ def __init__(self, order, dim, interval=(-1, 1), permute=True):
         # indices for outer product in einstein notation
         # idx = ["a", "b", "c", ...][:dim]
         # subscripts = "a,b,c -> abc"
-        self._idx = [letter for letter in alphabet][: self.dim]
+        self._idx = [letter for letter in alphabet][:dim]
         self._subscripts = ",".join(self._idx) + "->" + "".join(self._idx)
 
         # init points
@@ -322,10 +321,10 @@ def gradient(self, r):
         k = [self._AT @ np.append(0, self._polynomial(ra, n)[:-1]) for ra in r]
 
         # init output
-        dhdr = np.zeros((n**self.dim, self.dim))
+        dhdr = np.zeros((n**self._dim, self._dim))
 
         # loop over columns
-        for i in range(self.dim):
+        for i in range(self._dim):
             g = copy(h)
             g[i] = k[i]
             dhdr[:, i] = np.einsum(self._subscripts, *g).ravel("F")

src/felupe/element/_line.py

@@ -45,7 +45,6 @@ class Line(Element):
     """
 
     def __init__(self):
-        super().__init__(shape=(2, 1))
         self.points = np.array([-1, 1], dtype=float).reshape(-1, 1)
         self.cells = np.arange(len(self.points)).reshape(1, -1)
         self.cell_type = "line"

src/felupe/element/_quad.py

@@ -52,7 +52,6 @@ class ConstantQuad(Element):
     """
 
     def __init__(self):
-        super().__init__(shape=(1, 2))
         self.points = np.array([[-1, -1], [1, -1], [1, 1], [-1, 1]], dtype=float)
         self.cells = np.arange(len(self.points)).reshape(1, -1)
         self.cell_type = "quad"
@@ -106,7 +105,6 @@ class Quad(Element):
     """
 
     def __init__(self):
-        super().__init__(shape=(4, 2))
         self.points = np.array([[-1, -1], [1, -1], [1, 1], [-1, 1]], dtype=float)
         self.cells = np.arange(len(self.points)).reshape(1, -1)
         self.cell_type = "quad"
@@ -188,7 +186,6 @@ class QuadraticQuad(Element):
     """
 
     def __init__(self):
-        super().__init__(shape=(8, 2))
         self.points = np.array(
             [
                 [-1, -1],
@@ -289,8 +286,6 @@ class BiQuadraticQuad(Element):
     """
 
     def __init__(self):
-        super().__init__(shape=(9, 2))
-
         self._lagrange = ArbitraryOrderLagrange(order=2, dim=2, permute=False)
 
         self._vertices = np.array([0, 2, 8, 6])

src/felupe/element/_tetra.py

@@ -57,7 +57,6 @@ class Tetra(Element):
     """
 
     def __init__(self):
-        super().__init__(shape=(4, 3))
         self.points = np.array(
             [[0, 0, 0], [1, 0, 0], [0, 1, 0], [0, 0, 1]], dtype=float
         )
@@ -117,7 +116,6 @@ class TetraMINI(Element):
     """
 
     def __init__(self, bubble_multiplier=1.0):
-        super().__init__(shape=(5, 3))
         self.points = np.array(
             [[0, 0, 0], [1, 0, 0], [0, 1, 0], [0, 0, 1], [1 / 3, 1 / 3, 1 / 3]],
             dtype=float,
@@ -237,7 +235,6 @@ class QuadraticTetra(Element):
     """
 
     def __init__(self):
-        super().__init__(shape=(10, 3))
         self.points = np.zeros(self.shape)
         self.points[:4] = np.array(
             [[0, 0, 0], [1, 0, 0], [0, 1, 0], [0, 0, 1]], dtype=float

src/felupe/element/_triangle.py

@@ -58,7 +58,6 @@ class Triangle(Element):
     """
 
     def __init__(self):
-        super().__init__(shape=(3, 2))
         self.points = np.array([[0, 0], [1, 0], [0, 1]], dtype=float)
         self.cells = np.arange(len(self.points)).reshape(1, -1)
         self.cell_type = "triangle"
@@ -115,7 +114,6 @@ class TriangleMINI(Element):
     """
 
     def __init__(self, bubble_multiplier=1.0):
-        super().__init__(shape=(4, 2))
         self.points = np.array([[0, 0], [1, 0], [0, 1], [1 / 3, 1 / 3]], dtype=float)
         self.cells = np.arange(len(self.points) - 1).reshape(1, -1)
         self.cell_type = "triangle"
@@ -198,7 +196,6 @@ class QuadraticTriangle(Element):
     """
 
     def __init__(self):
-        super().__init__(shape=(6, 2))
         self.points = np.zeros(self.shape)
         self.points[:3] = np.array([[0, 0], [1, 0], [0, 1]], dtype=float)
         self.points[3] = np.mean(self.points[[0, 1]], axis=0)