Base Mesh Implementation with GMSH Support, Comprehensive Documentation, Type Hints, Code Refactoring, and Bug Fixes

pyproject.toml

@@ -6,9 +6,7 @@ build-backend = "setuptools.build_meta"
 name = "pyquasar"
 version = "0.1.0"
 dependencies = ["numpy", "scipy", "gmsh"]
-authors = [
-  { name="Ilya Stupakov", email="istupakov@gmail.com" },
-]
+authors = [{ name = "Ilya Stupakov", email = "istupakov@gmail.com" }]
 description = "Finite and boundary element methods on Python"
 readme = "README.md"
 requires-python = ">=3.9"
@@ -17,3 +15,29 @@ classifiers = [
     "License :: OSI Approved :: MIT License",
     "Operating System :: OS Independent",
 ]
+
+[tool.ruff]
+line-length = 140
+indent-width = 2
+
+[tool.ruff.lint]
+select = ["E4", "E7", "E9", "F"]
+ignore = []
+
+fixable = ["ALL"]
+unfixable = []
+
+dummy-variable-rgx = "^(_+|(_+[a-zA-Z0-9_]*[a-zA-Z0-9]+?))$"
+
+[tool.ruff.format]
+quote-style = "double"
+indent-style = "space"
+skip-magic-trailing-comma = false
+line-ending = "auto"
+docstring-code-format = false
+docstring-code-line-length = "dynamic"
+
+[tool.pyright]
+venv = '.venv'
+venvPath = "."
+typeCheckingMode = "off"

src/pyquasar/__init__.py

@@ -1,5 +1,7 @@
-from .load_mesh import load_mesh
 from .fem_domain import FemDomain
 from .bem_domain import BemDomain
 from .feti_problem import FetiProblem, FetiProblemNotRed
 from .coils import Coil2D
+from .mesh import Mesh
+
+__all__ = ["FemDomain", "BemDomain", "FetiProblem", "FetiProblemNotRed", "Coil2D", "Mesh"]

src/pyquasar/bem.py

@@ -1,113 +1,242 @@
+from typing import Callable, Optional
 import numpy as np
 from scipy import sparse
 from scipy.integrate import quad_vec, fixed_quad
+import numpy.typing as npt
 
 from .fem import FemLine2
 
-class BemLine2(FemLine2):
-  def __init__(self, elem_vert, elements, quad, weight):
-    super().__init__(elem_vert, elements, quad, weight);
-    self.basis_func = [lambda t: np.array([np.ones_like(t)]), lambda t: np.array([1-t, t]), lambda t: np.array([1-t**2, t**2])]
-    self.basis_indices = [np.arange(len(elements))[:, None], elements, elements]
 
-  def potentials(self, points):
+class BemLine2(FemLine2):
+  """Represents a boundary element line element."""
+
+  def __init__(
+    self,
+    element_verts: npt.NDArray[np.floating],
+    elements: npt.NDArray[np.signedinteger],
+    quad_points: npt.NDArray[np.floating],
+    weights: npt.NDArray[np.floating],
+  ):
+    super().__init__(element_verts, elements, quad_points, weights)
+    self._basis_func = [
+      lambda t: np.array([np.ones_like(t)]),
+      lambda t: np.array([1 - t, t]),
+      lambda t: np.array([1 - t**2, t**2]),
+    ]
+    self._basis_indices = [np.arange(len(elements), dtype=np.uint)[:, None], elements, elements]
+
+  @property
+  def basis_func(self) -> list[Callable]:
+    """Basis functions of the boundary element line."""
+    return self._basis_func
+
+  @property
+  def basis_indices(self) -> list[npt.NDArray[np.uint]]:
+    """Indices of the boundary element line basis functions."""
+    return self._basis_indices
+
+  def potentials(
+    self, points: npt.NDArray[np.floating]
+  ) -> tuple[
+    npt.NDArray[np.floating],
+    npt.NDArray[np.floating],
+    npt.NDArray[np.floating],
+    npt.NDArray[np.floating],
+    npt.NDArray[np.floating],
+  ]:
+    """Compute the potentials at the given points.
+
+    Parameters
+    ----------
+    points : NDArray[float]
+      The points where the potentials are evaluated.
+
+    Returns
+    -------
+    tuple[NDArray[float], NDArray[float], NDArray[float], NDArray[float], NDArray[float]]
+      The single layer, double layer and Newton potentials.
+    """
     dr = points[..., None, :] - self.center
-    l = self.J.flatten()
-    a = np.sum(self.dir * dr, axis=-1)/l
+    lenghts = self.J.flatten()
+    a = np.sum(self.dir * dr, axis=-1) / lenghts
     h = -np.sum(self.normal * dr, axis=-1)
 
     eps = 1e-30
     r0 = a**2 + h**2
-    r1 = (l-a)**2 + h**2
+    r1 = (lenghts - a) ** 2 + h**2
     log0 = np.log(r0 + eps)
     log1 = np.log(r1 + eps)
-    atan0 = np.arctan(-a/(h + eps))
-    atan1 = np.arctan((l - a)/(h + eps))
+    atan0 = np.arctan(-a / (h + eps))
+    atan1 = np.arctan((lenghts - a) / (h + eps))
 
-    slpot = -((l - a)*log1 + a*log0 + 2*h*(atan1 - atan0) - 2*l)/(4*np.pi)
-    slpot_t = slpot*a/l - (r1*log1 - r0*log0 + a**2 - (l-a)**2)/(8*np.pi)/l
-    dlpot = -(atan1 - atan0)/(2*np.pi)
+    slpot = -((lenghts - a) * log1 + a * log0 + 2 * h * (atan1 - atan0) - 2 * lenghts) / (4 * np.pi)
+    slpot_t = slpot * a / lenghts - (r1 * log1 - r0 * log0 + a**2 - (lenghts - a) ** 2) / (8 * np.pi) / lenghts
+    dlpot = -(atan1 - atan0) / (2 * np.pi)
     dlpot[np.isclose(h, 0, atol=1e-10)] = 0
-    dlpot_t = dlpot*a/l - h*(log1 - log0)/(4*np.pi)/l
-    nwpot = h*(l/(8*np.pi) + slpot/2)
+    dlpot_t = dlpot * a / lenghts - h * (log1 - log0) / (4 * np.pi) / lenghts
+    nwpot = h * (lenghts / (8 * np.pi) + slpot / 2)
 
     return slpot, slpot_t, dlpot, dlpot_t, nwpot
 
-  def mass_matrix(self, shape, row_basis_order = 1, col_basis_order = 1):
-    row_basis = self.basis_func[row_basis_order](self.quad[:, 0])
-    col_basis = self.basis_func[col_basis_order](self.quad[:, 0])
-    data = self.J[:, None] * ((row_basis[None, :] * col_basis[:, None]) @ self.weight)
+  def mass_matrix(self, shape: tuple[int, ...], row_basis_order: int = 1, col_basis_order: int = 1) -> sparse.coo_array:
+    """Compute the mass matrix of the boundary element line.
+
+    Parameters
+    ----------
+    shape : tuple[int, ...]
+      The shape of the mass matrix.
+    row_basis_order : int
+      The order of the basis functions for the rows.
+    col_basis_order : int
+      The order of the basis functions for the columns.
+
+    Returns
+    -------
+    sparse.coo_array
+    """
+    row_basis = self.basis_func[row_basis_order](self.quad_points[:, 0])
+    col_basis = self.basis_func[col_basis_order](self.quad_points[:, 0])
+    data = self.J[:, None] * ((row_basis[None, :] * col_basis[:, None]) @ self.weights)
     i = np.broadcast_to(self.basis_indices[row_basis_order][:, None, :], data.shape)
     j = np.broadcast_to(self.basis_indices[col_basis_order][:, :, None], data.shape)
     return sparse.coo_array((data.flat, (i.flat, j.flat)), shape)
 
-  def load_vector(self, func, shape, basis_order = 1):
-    basis = self.basis_func[basis_order](self.quad[:, 0])
+  def load_vector(
+    self,
+    func: Callable[[npt.NDArray[np.floating], npt.NDArray[np.floating]], npt.NDArray[np.floating]] | npt.ArrayLike,
+    shape: tuple[int, ...],
+    basis_order: int = 1,
+  ) -> npt.NDArray[np.floating]:
+    """Compute the load vector of the boundary element line.
+
+    Parameters
+    ----------
+    func : Callable or ArrayLike
+      The function or array to be integrated.
+    shape : tuple[int, ...]
+      The shape of the load vector.
+    basis_order : int
+      The order of the basis functions, by default 1.
+
+    Returns
+    -------
+    NDArray[float]
+    """
+    basis = self.basis_func[basis_order](self.quad_points[:, 0])
     if callable(func):
-      f = func(self.center[:, None] + self.quad[None, :, 0, None] * self.dir[:, None], self.normal[:, None])
-      # def f(t):
-      #   basis = self.basis_func[basis_order](t)
-      #   f = func(self.center[:, None] + t[None, :, None] * self.dir[:, None], self.normal[:, None])
-      #   return basis * f[:, None]
-      # data = self.J * fixed_quad(f, 0, 1, n = 10)[0]
+      f = func(self.center[:, None] + self.quad_points[None, :, 0, None] * self.dir[:, None], self.normal[:, None])
     else:
-      f = func
-    data = self.J * ((basis * np.atleast_1d(f)[:, None]) @ self.weight)
+      f = np.asarray(func, dtype=np.float_)
+    data = self.J * ((basis * np.atleast_1d(f)[:, None]) @ self.weights)
     res = np.zeros(shape)
     np.add.at(res, self.basis_indices[basis_order], data)
     return res
 
-  def bem_matrices(self, quadrature_order = None):
+  def bem_matrices(
+    self, quad_order: Optional[int] = None
+  ) -> tuple[npt.NDArray[np.floating], npt.NDArray[np.floating], npt.NDArray[np.floating]]:
+    """Compute the BEM matrices of the boundary element line.
+
+    Parameters
+    ----------
+    quad_order : int, optional
+      The order of the quadrature, by default None. If None, the quadrature is performed with `scipy.integrate.quad_vec`.
+
+    Returns
+    -------
+    tuple[NDArray[float], NDArray[float], NDArray[float]]
+      The single layer V, double layer K and hypersingular D operators.
+    """
     inv = np.empty_like(self.basis_indices[1].T)
     inv[0, self.basis_indices[1][:, 0]] = np.arange(len(self.basis_indices[1]))
     inv[1, self.basis_indices[1][:, 1]] = np.arange(len(self.basis_indices[1]))
 
-    def f(t):
+    def f(t: npt.NDArray[np.floating]) -> npt.NDArray[np.floating]:
       t = np.atleast_1d(t)[:, None, None]
-      r = self.center + t*self.dir
-      slpot, slpot_t, dlpot, dlpot_t, nwpot = self.potentials(r)
+      r = self.center + t * self.dir
+      slpot, _, dlpot, dlpot_t, _ = self.potentials(r)
       dlpot_psi = np.take(dlpot - dlpot_t, inv[0], axis=-1) + np.take(dlpot_t, inv[1], axis=-1)
-      return np.moveaxis((slpot, dlpot_psi), 1, -1)
+      return np.moveaxis(np.asarray((slpot, dlpot_psi)), 1, -1)
 
-    V, K = self.J*(quad_vec(f, 0, 1)[0][..., 0] if quadrature_order is None else fixed_quad(f, 0, 1, n = quadrature_order)[0])
+    V, K = self.J * (quad_vec(f, 0, 1)[0][..., 0] if quad_order is None else fixed_quad(f, 0, 1, n=quad_order)[0])
 
-    D = V/np.outer(self.J, self.J)
+    D = V / np.outer(self.J, self.J)
     D = np.take(-D, inv[0], axis=0) + np.take(D, inv[1], axis=0)
     D = np.take(-D, inv[0], axis=1) + np.take(D, inv[1], axis=1)
 
     return V, K, D
 
-  def bem_matrices_p(self, order = None):
+  def bem_matrices_p(self, order: Optional[int] = None) -> tuple[npt.NDArray[np.floating], npt.NDArray[np.floating]]:
+    """Compute the BEM matrices of the boundary element line for the Neumann problem.
+
+    Parameters
+    ----------
+    order : int, optional
+      The order of the quadrature, by default None.
+      If None, the quadrature is performed with `scipy.integrate.quad_vec`.
+
+    Returns
+    -------
+    tuple[NDArray[float], NDArray[float]]
+      The single layer V and hypersingular D operators.
+    """
     inv = np.empty_like(self.basis_indices[1].T)
     inv[0, self.basis_indices[1][:, 0]] = np.arange(len(self.basis_indices[1]))
     inv[1, self.basis_indices[1][:, 1]] = np.arange(len(self.basis_indices[1]))
 
-    def f(t):
+    def f(t: npt.NDArray[np.floating]) -> npt.NDArray[np.floating]:
       t = np.atleast_1d(t)[:, None, None]
-      r = self.center + t*self.dir
-      slpot, slpot_t, dlpot, dlpot_t, nwpot = self.potentials(r)
+      r = self.center + t * self.dir
+      slpot, slpot_t, _, _, _ = self.potentials(r)
       slpot_psi = np.take(slpot - slpot_t, inv[0], axis=-1) + np.take(slpot_t, inv[1], axis=-1)
-      return np.moveaxis([(1-t)*slpot_psi, t*slpot_psi, t * slpot_t], 1, -1)
+      return np.moveaxis(np.asarray([(1 - t) * slpot_psi, t * slpot_psi, t * slpot_t]), 1, -1)
 
-    pot = self.J*(quad_vec(f, 0, 1)[0][..., 0] if order is None else fixed_quad(f, 0, 1, n = order)[0])
+    pot = self.J * (quad_vec(f, 0, 1)[0][..., 0] if order is None else fixed_quad(f, 0, 1, n=order)[0])
 
     Vp = np.take(pot[0], inv[0], axis=0) + np.take(pot[1], inv[1], axis=0)
 
-    Dp = pot[2]/np.outer(self.J, self.J)
+    Dp = pot[2] / np.outer(self.J, self.J)
     Dp = np.take(-Dp, inv[0], axis=0) + np.take(Dp, inv[1], axis=0)
     Dp = np.take(-Dp, inv[0], axis=1) + np.take(Dp, inv[1], axis=1)
 
     return Vp, Dp
 
-  def result_weights(self, points):
+  def result_weights(
+    self, points: npt.NDArray[np.floating]
+  ) -> tuple[npt.NDArray[np.floating], npt.NDArray[np.floating], npt.NDArray[np.floating]]:
+    """Compute the result weights at the given points.
+
+    Parameters
+    ----------
+    points : NDArray[float]
+      The points where the result weights are evaluated.
+
+    Returns
+    -------
+    tuple[NDArray[float], NDArray[float], NDArray[float]]
+      The single layer, double layer, and Newton potentials.
+    """
     inv = np.empty_like(self.basis_indices[1].T)
     inv[0, self.basis_indices[1][:, 0]] = np.arange(len(self.basis_indices[1]))
     inv[1, self.basis_indices[1][:, 1]] = np.arange(len(self.basis_indices[1]))
 
-    slpot, slpot_t, dlpot, dlpot_t, nwpot = self.potentials(points)
+    slpot, _, dlpot, dlpot_t, nwpot = self.potentials(points)
     dlpot_psi = np.take(dlpot - dlpot_t, inv[0], axis=-1) + np.take(dlpot_t, inv[1], axis=-1)
     return slpot, dlpot_psi, np.sum(nwpot, axis=-1)
 
-  def newton(self, points, trace = 0):
-    slpot, slpot_t, dlpot, dlpot_t, nwpot = self.potentials(points)
+  def newton(self, points: npt.NDArray[np.floating], trace: int = 0) -> npt.NDArray[np.floating]:
+    """Compute the Newton potential at the given points.
+
+    Parameters
+    ----------
+    points : NDArray[float]
+      The points where the Newton potential is evaluated.
+    trace : int, optional
+      The trace of the Newton potential, by default 0.
+
+    Returns
+    -------
+    NDArray[float]
+    """
+    slpot, _, _, _, nwpot = self.potentials(points)
     return np.sum(nwpot, axis=-1) if trace == 0 else -np.sum(slpot[..., None] * self.normal, axis=-2)