FiPy：如何在两个网格之间的界面处找到节点（顶点）

Question

我已经通过 Gmsh 在 FiPy 中定义了两个网格，并且想在两个网格之间的界面上找到节点。有没有办法在 FiPy 中做到这一点？

siliconGeometry = '''
SetFactory("OpenCASCADE");
//set node spacing
ns = 1e-1;
ns2 = 1e-2;
x1 = 0;
y1 = 0;
x2 = 1;
y2 = 0.5;
Point(1) = {x1, y1, 0, ns};
Point(2) = {x2, y1, 0, ns};
Point(3) = {x2, y2, 0, ns2};
Point(4) = {x1, y2, 0, ns2};
Line(1) = {1, 2};
Line(2) = {2, 3};
Line(3) = {3, 4};
Line(4) = {4, 1};
Curve Loop(1) = {1, 2, 3, 4};
Plane Surface(1) = {1};
Physical Surface("Silicon") = {1};
'''

oxideGeometry = '''
SetFactory("OpenCASCADE");
//set node spacing
ns = 1e-1;
ns2 = 1e-2;
x1 = 0;
y1 = 0.5;
x2 = 1;
y2 = 1;
Point(5) = {x1, y1, 0, ns2};
Point(6) = {x2, y1, 0, ns2};
Point(7) = {x2, y2, 0, ns};
Point(8) = {x1, y2, 0, ns};
Line(5) = {5, 6};
Line(6) = {6, 7};
Line(7) = {7, 8};
Line(8) = {8, 5};
Curve Loop(2) = {5, 6, 7, 8};
Plane Surface(2) = {2};
Physical Surface("Oxide") = {2};

m0 = Gmsh2D(siliconGeometry)
m1 = Gmsh2D(oxideGeometry)

我想获取网格 m0 和 m1 之间界面处的所有节点（或线）。

Answer 1

FiPy 有一个函数叫做 nearest 它获取两个向量的最接近值。因此，要从 m0 和 m1 中获取重叠的 ID，请使用

from fipy import Gmsh2D
from fipy.tools.numerix import nearest
import numpy as np

siliconGeometry = '''
...
'''

oxideGeometry = '''
...
'''
 
m0 = Gmsh2D(siliconGeometry)
m1 = Gmsh2D(oxideGeometry)

near_ids = nearest(m0.vertexCoords, m1.vertexCoords)
mask = np.all(np.isclose(m0.vertexCoords[:, near_ids], m1.vertexCoords), axis=0)
m1_close_ids = np.arange(len(m1.vertexCoords[0]))[mask]
m0_close_ids = near_ids[mask]

for i in range(len(m0_close_ids)):
    m0_id = m0_close_ids[i]
    m1_id = m1_close_ids[i]
    print()
    print(f'm0: {m0_id}, {m0.vertexCoords[:, m0_id]}')
    print(f'm1: {m1_id}, {m1.vertexCoords[:, m1_id]}')

我们使用 nearest 为 m0 获取 near_ids，然后使用 np.isclose 检查节点是否关闭。然后使用 mask 我们可以在两个网格之间构造相应的关闭 ID。

请注意，使用 Scipy 的 KDTree 查找最接近的值可能要快得多。然而，对于这个小问题，这并不重要，但对于一个非常大的网格，我认为这很重要。事实上，FiPy 真的应该在内部使用它（目前不是）。

此外，这里的另一个调整是你知道上下脸重叠，所以你可以简单地要求 m0.facesTop 和 m1.facesBottom 面具将问题减少到重叠的面，但这依赖于网格的先验知识。

Answer 2

感谢@wd15。这是我所做的：

m0 = Gmsh2D(siliconGeometry) 
m1 = Gmsh2D(oxideGeometry) 

m0_faces = m0.exteriorFaces 
m0_vertices = numerix.unique(m0.faceVertexIDs[..., m0_faces].flatten()) m0_vertexCoords = m0.vertexCoords[..., m0_vertices ] 

m1_faces = m1.exteriorFaces 
m1_vertices = numerix.unique(m1.faceVertexIDs[..., m1_faces].flatten()) m1_vertexCoords = m1.vertexCoords[..., m0_vertices ] 

surfVertexID = numerix.nearest(m0_vertexCoords , m1_vertexCoords)

FiPy：如何在两个网格之间的界面处找到节点（顶点）

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