def coarsen_poly(self, plot=True): node = np.array([[0, 0], [1, 0], [1, 1], [0, 1], [2, 0], [2, 1]], dtype=np.float) cell = np.array([[0, 1, 2], [0, 2, 3], [1, 4, 5], [2, 1, 5]], dtype=np.int) mesh = TriangleMesh(node, cell) mesh = HalfEdgeMesh2d.from_mesh(mesh) mesh.init_level_info() isMarkedCell = np.array([0, 0, 0, 1, 0], dtype=np.bool_) mesh.refine_poly(isMarkedCell) NC = mesh.number_of_all_cells() isMarkedCell = np.zeros(NC, dtype=np.bool_) isMarkedCell[[1, 2, 3, 4, 5, 6]] = True mesh.coarsen_poly(isMarkedCell) fig = plt.figure() axes = fig.gca() mesh.add_plot(axes) mesh.find_node(axes, showindex=True) mesh.find_cell(axes, showindex=True) mesh.add_halfedge_plot(axes, showindex=True) plt.show()
def coarsen_tri(self, maxit=2, method='rg', plot=True, rb=True): cell = np.array([[0, 1, 2], [0, 2, 3], [1, 4, 5], [2, 1, 5]], dtype=np.int) node = np.array([[0, 0], [1, 0], [1, 1], [0, 1], [2, 0], [2, 1]], dtype=np.float) if True: mesh = TriangleMesh(node, cell) mesh = HalfEdgeMesh2d.from_mesh(mesh) mesh.init_level_info() isMarkedCell = np.array([0, 1, 0, 0, 1], dtype=np.bool_) NE = mesh.ds.NE color = np.zeros(NE * 2, dtype=np.int_) mesh.hedgecolor = color mesh.refine_triangle_rg(isMarkedCell) NE = mesh.ds.NE color = np.zeros(NE * 2, dtype=np.int_) if 0: fig = plt.figure() axes = fig.gca() mesh.add_plot(axes) mesh.add_halfedge_plot(axes, showindex=True) mesh.find_node(axes, showindex=True) mesh.find_cell(axes, showindex=True) plt.show() if method == 'rg': if 1: NC = mesh.number_of_all_cells() isMarkedCell = np.zeros(NC, dtype=np.bool_) isMarkedCell[[1, 2, 5, 6, 7, 9]] = True print('*************lll*********') mesh.coarsen_triangle_rg(isMarkedCell) if 1: NC = mesh.number_of_all_cells() isMarkedCell = np.zeros(NC, dtype=np.bool_) isMarkedCell[[0, 1, 2, 3, 4, 5, 6, 7]] = True print('*************lll*********') mesh.coarsen_triangle_rg(isMarkedCell) NC = mesh.number_of_all_cells() isMarkedCell = np.ones(NC, dtype=np.bool_) print('*************lll*********') mesh.refine_triangle_rg(isMarkedCell) else: color[[2, 3, 10, 11]] = 1 mesh.hedgecolor = color isMarkedCell = np.array([0, 1, 1, 0, 0], dtype=np.bool_) #isMarkedCell = np.array([0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ,0], # dtype=np.bool_) mesh.refine_triangle_nvb(isMarkedCell) mesh.print() if plot: fig = plt.figure() axes = fig.gca() mesh.add_plot(axes) mesh.add_halfedge_plot(axes, showindex=True) mesh.find_node(axes, showindex=True) mesh.find_cell(axes, showindex=True) plt.show()
def data_structure(self, plot=True): node = np.array([[0,0],[1,0],[1,1],[0,1],[2,0],[2,1]], dtype = np.float) cell = np.array([[0,1,2],[0,2,3],[1,4,5],[2,1,5]],dtype = np.int) mesh = TriangleMesh(node, cell) mesh = HalfEdgeMesh2d.from_mesh(mesh) mesh.print() if plot: fig = plt.figure() axes = fig.gca() mesh.add_halfedge_plot(axes, showindex=True) mesh.find_node(axes, showindex=True) mesh.find_cell(axes, showindex=True) plt.show()
def refine_halfedge(self, plot=True): node = np.array([[0,0],[1,0],[1,1],[0,1],[2,0],[2,1]], dtype = np.float) cell = np.array([[0,1,2],[0,2,3],[1,4,5],[2,1,5]],dtype = np.int) mesh = TriangleMesh(node, cell) mesh = HalfEdgeMesh2d.from_mesh(mesh) isMarkedCell = np.array([0, 1, 0, 0, 0], dtype=np.bool_) isMarkedHEdge = mesh.mark_halfedge(isMarkedCell) mesh.refine_halfedge(isMarkedHEdge) mesh.print() if plot: fig = plt.figure() axes = fig.gca() mesh.add_halfedge_plot(axes, showindex=True) mesh.find_node(axes, showindex=True) #mesh.find_cell(axes, showindex=True) plt.show()
def coarsen_poly(self, plot=True): node = np.array([[0,0],[1,0],[1,1],[0,1],[2,0],[2,1]], dtype = np.float) cell = np.array([[0,1,2],[0,2,3],[1,4,5],[2,1,5]],dtype = np.int) mesh = TriangleMesh(node, cell) mesh = HalfEdgeMesh2d.from_mesh(mesh) isMarkedCell = np.array([0,0,0,1,0], dtype=np.bool_) mesh.refine_poly(isMarkedCell) isMarkedCell = np.array([0,0,0,0,1,1,1], dtype=np.bool_) mesh.coarsen_poly(isMarkedCell) fig = plt.figure() axes = fig.gca() mesh.add_plot(axes) mesh.find_node(axes, showindex=True) mesh.find_cell(axes, showindex=True) plt.show()
edge = totalEdge[i0] # 最终的边数组 print('edge:\n', edge) E = 3 # 每个三角形有 3 条边 NE = edge.shape[0] # 获得网格中边的个数, 即 `edge` 的行数 i1 = np.zeros(NE, dtype=np.int32) # 分配空间 i1[j] = range(3 * NC) # totalEdge0 的行数是 3*NC, j 的长度也是 3*NC print('i0:\n', i0) print('i1:\n', i1) edge2cell = np.zeros((NE, 4), dtype=np.int32) edge2cell[:, 0] = i0 // E # 得到每条边的左边单元 edge2cell[:, 1] = i1 // E # 得到每条边的右边单元 edge2cell[:, 2] = i0 % E # 得到每条边的在左边单元中的局部编号 edge2cell[:, 3] = i1 % E # 得到每条边在其右边单元中的局部编号 print('edge2cell:\n', edge2cell) mesh = TriangleMesh(node, cell) mesh.print() fig = plt.figure() axes = fig.gca() mesh.add_plot(axes) mesh.find_node(axes, showindex=True) mesh.find_cell(axes, showindex=True) mesh.find_edge(axes, showindex=True) plt.savefig('numpy-mesh-edge.png') plt.show()
node = mesh.entity('node') cell = mesh.entity('cell') tmesh = Tritree(node, cell) femspace = LagrangeFiniteElementSpace(mesh, p=1) uI = femspace.interpolation(peak) estimator = Estimator(uI[:], mesh, 0.2, 0.5) isExtremeNode = estimator.is_extreme_node() print(isExtremeNode.sum()) tmesh.adaptive_refine(estimator) mesh = estimator.mesh isExtremeNode = estimator.is_extreme_node() fig = plt.figure() axes = fig.gca() mesh.add_plot(axes) mesh.find_node(axes, index=isExtremeNode) fig2 = plt.figure() fig2.set_facecolor('white') axes = fig2.gca(projection='3d') x = mesh.node[:, 0] y = mesh.node[:, 1] cell = mesh.ds.cell femspace = LagrangeFiniteElementSpace(mesh, p=1) uI = femspace.interpolation(peak) axes.plot_trisurf(x, y, cell, estimator.rho, cmap=plt.cm.jet, lw=0.0) plt.show()
def refine_triangle_rbTest(self, l, plot=True, rb=True): cell = np.array([[0, 1, 2], [0, 2, 3], [1, 4, 5], [2, 1, 5]], dtype=np.int) node = np.array([[0, 0], [1, 0], [1, 1], [0, 1], [2, 0], [2, 1]], dtype=np.float) mesh = TriangleMesh(node, cell) #mesh.uniform_refine() mesh = HalfEdgeMesh.from_mesh(mesh) mesh.ds.cell2hedge = np.array([0, 3, 2, 11, 10]) c = np.array([0.2, 0.2]) r = 1.2 h = 1e-2 k = 0 NB = 0 start = time.time() while k < l: halfedge = mesh.ds.halfedge halfedge1 = halfedge[:, 3] node = mesh.node flag = node - c flag = flag[:, 0]**2 + flag[:, 1]**2 flag = flag <= r**2 flag1 = flag[halfedge[:, 0]].astype(int) flag2 = flag[halfedge[halfedge1, 0]].astype(int) markedge = flag1 + flag2 == 1 markedcell = halfedge[markedge, 1] markedcell = np.unique(markedcell) cell = np.unique(halfedge[:, 1]) nc = cell.shape[0] markedcell1 = np.zeros(nc) markedcell1[markedcell] = 1 if rb: mesh.refine_triangle_rb(markedcell1) else: mesh.refine_triangle_rbg(markedcell1) k += 1 print('循环', k, '次***************************') #print('node', node) #print('cell',cell) end = time.time() print(end - start) if plot: fig = plt.figure() axes = fig.gca() nindex = mesh.nodedata['level'] mesh.add_plot(axes) #mesh.add_halfedge_plot(axes, showindex=True) #mesh.find_node(axes, showindex=True, multiindex=nindex) plt.show() if 0: fig = plt.figure() axes = fig.gca() mesh.add_plot(axes) mesh.find_node(axes, showindex=True) mesh.find_cell(axes, showindex=True) cindex = np.arange(mesh.number_of_cells() - 1) + 1 fig = plt.figure() axes = fig.gca() mesh.add_plot(axes) mesh.find_node(axes, showindex=True) mesh.find_cell(axes, showindex=True, multiindex=cindex) NN = mesh.number_of_nodes() nindex = np.zeros(NN, dtype=np.int) halfedge = mesh.ds.halfedge nindex = mesh.nodedata['level'] cindex = mesh.get_data('cell', 'level') fig = plt.figure() axes = fig.gca() mesh.add_plot(axes) mesh.find_node(axes, showindex=True, multiindex=nindex) mesh.find_cell(axes, showindex=True, multiindex=cindex) plt.show()
def refine_tri(self, maxit=2, method='rg', plot=True, rb=True): cell = np.array([[0, 1, 2], [0, 2, 3], [1, 4, 5], [2, 1, 5]], dtype=np.int) node = np.array([[0, 0], [1, 0], [1, 1], [0, 1], [2, 0], [2, 1]], dtype=np.float) if False: mesh = TriangleMesh(node, cell) mesh = HalfEdgeMesh.from_mesh(mesh) mesh.ds.cell2hedge = np.array([0, 3, 2, 11, 10]) isMarkedCell = np.array([0, 1, 0, 0, 1], dtype=np.bool_) #mesh.refine_triangle_rbg(isMarkedCell) mesh.ds.NV = 3 cell = mesh.ds.cell_to_node() node = mesh.entity('node') mesh = TriangleMesh(node, cell) mesh = HalfEdgeMesh2d.from_mesh(mesh) mesh.init_level_info() if False: fig = plt.figure() axes = fig.gca() mesh.add_plot(axes) mesh.add_halfedge_plot(axes, showindex=True) mesh.find_node(axes, showindex=True) mesh.find_cell(axes, showindex=True) plt.show() NE = mesh.ds.NE color = np.zeros(NE * 2, dtype=np.int_) if method == 'rg': color[[4, 13, 17, 28]] = 1 color[[23, 27]] = 2 color[[22, 26]] = 3 mesh.hedgecolor = color isMarkedCell = np.array( [0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], dtype=np.bool_) mesh.refine_triangle_rg(isMarkedCell) else: color[[2, 3, 10, 11]] = 1 mesh.hedgecolor = color isMarkedCell = np.array([0, 1, 1, 0, 0], dtype=np.bool_) #isMarkedCell = np.array([0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ,0], # dtype=np.bool_) mesh.refine_triangle_nvb(isMarkedCell) mesh.print() if plot: fig = plt.figure() axes = fig.gca() mesh.add_plot(axes) mesh.add_halfedge_plot(axes, showindex=True) mesh.find_node(axes, showindex=True) mesh.find_cell(axes, showindex=True) plt.show() if True: mesh = TriangleMesh(node, cell) mesh = HalfEdgeMesh2d.from_mesh(mesh) mesh.init_level_info() NE = mesh.ds.NE color = np.zeros(NE * 2, dtype=np.int_) if method == 'nvb': color[[2, 3, 10, 11]] = 1 mesh.hedgecolor = color c = np.array([0.8, 0.8]) r = 0.9 h = 1e-2 k = 0 NB = 0 start = time.time() while k < maxit: halfedge = mesh.ds.halfedge halfedge1 = halfedge[:, 3] node = mesh.node flag = node - c flag = flag[:, 0]**2 + flag[:, 1]**2 flag = flag <= r**2 flag1 = flag[halfedge[:, 0]].astype(int) flag2 = flag[halfedge[halfedge1, 0]].astype(int) markedge = flag1 + flag2 == 1 markedcell = halfedge[markedge, 1] markedcell = np.unique(markedcell) cell = np.unique(halfedge[:, 1]) nc = cell.shape[0] markedcell1 = np.zeros(nc) markedcell1[markedcell] = 1 if method == 'rg': mesh.refine_triangle_rg(markedcell1.astype(np.bool_)) else: mesh.refine_triangle_nvb(markedcell1.astype(np.bool_)) k += 1 print('循环', k, '次***************************') end = time.time() print('用时', end - start) if plot: fig = plt.figure() axes = fig.gca() nindex = mesh.nodedata['level'] mesh.add_plot(axes) #mesh.add_halfedge_plot(axes, showindex=True) #mesh.find_node(axes, showindex=True, multiindex=nindex) #mesh.find_cell(axes, showindex=True) #print(np.c_[np.arange(len(mesh.hedgecolor)), mesh.hedgecolor]) plt.show()
def test_interpolation_plane(self): def u(p): x = p[..., 0] y = p[..., 1] return x * y node = np.array([(0, 0), (1, 0), (1, 1), (0, 1)], dtype=np.float) cell = np.array([(1, 2, 0), (3, 0, 2)], dtype=np.int) mesh = TriangleMesh(node, cell) node = mesh.entity('node') cell = mesh.entity('cell') tritree = Tritree(node, cell) mesh = tritree.to_conformmesh() space = LagrangeFiniteElementSpace(mesh, p=2) uI = space.interpolation(u) error0 = space.integralalg.L2_error(u, uI) fig = plt.figure() axes = fig.gca() mesh.add_plot(axes) mesh.find_node(axes, node=space.interpolation_points(), showindex=True) data = tritree.interpolation(uI) options = tritree.adaptive_options(method='numrefine', data={"q": data}, maxrefine=1, p=2) if 1: #eta = space.integralalg.integral(lambda x : uI.grad_value(x)**2, celltype=True, barycenter=True) #eta = eta.sum(axis=-1) eta = np.array([1, 0], dtype=np.int) tritree.adaptive(eta, options) else: tritree.uniform_refine(options=options) fig = plt.figure() axes = fig.gca() tritree.add_plot(axes) tritree.find_node(axes, showindex=True) mesh = tritree.to_conformmesh(options) space = LagrangeFiniteElementSpace(mesh, p=2) data = options['data']['q'] uh = space.to_function(data) error1 = space.integralalg.L2_error(u, uh) data = tritree.interpolation(uh) isLeafCell = tritree.is_leaf_cell() fig = plt.figure() axes = fig.gca() tritree.add_plot(axes) tritree.find_node(axes, node=space.interpolation_points(), showindex=True) tritree.find_cell(axes, index=isLeafCell, showindex=True) options = tritree.adaptive_options(method='numrefine', data={"q": data}, maxrefine=1, maxcoarsen=1, p=2) if 1: #eta = space.integralalg.integral(lambda x : uI.grad_value(x)**2, celltype=True, barycenter=True) #eta = eta.sum(axis=-1) eta = np.array([-1, -1, -1, -1, 0, 1], dtype=np.int) tritree.adaptive(eta, options) else: tritree.uniform_refine(options=options) mesh = tritree.to_conformmesh(options) space = LagrangeFiniteElementSpace(mesh, p=2) data = options['data']['q'] uh = space.to_function(data) fig = plt.figure() axes = fig.gca() mesh.add_plot(axes) mesh.find_node(axes, node=space.interpolation_points(), showindex=True) mesh.find_cell(axes, showindex=True) error2 = space.integralalg.L2_error(u, uh) print(error0) print(error1) print(error2) plt.show()
import numpy as np from fealpy.mesh import TriangleMesh import matplotlib.pyplot as plt node = np.array([[0.0, 0.0], [1.0, 0.0], [0.5, np.sqrt(3) / 2.0]], dtype=np.float) cell = np.array([[0, 1, 2]], dtype=np.int32) localEdge = np.array([[1, 2], [2, 0], [0, 1]], dtype=np.int32) bc = (node[localEdge[:, 0]] + node[localEdge[:, 1]]) / 2.0 mesh = TriangleMesh(node, cell) fig = plt.figure() axes = fig.gca() mesh.add_plot(axes) mesh.find_node(axes, showindex=True) #mesh.find_cell(axes, showindex=True) mesh.find_node(axes, node=bc, index=np.array([0, 1, 2], dtype=np.int32), showindex=True, markersize=150, color='g') plt.savefig('localedge.png') plt.show()
cell = np.array(mesh.elements, dtype = np.int) tmesh = TriangleMesh(node, cell) fig = plt.figure() axes = fig.gca() tmesh.add_plot(axes) cell = tmesh.entity('cell') node = tmesh.entity('node') NN = tmesh.number_of_nodes() isBdNode = tmesh.ds.boundary_node_flag() newNode = np.zeros((NN, 2), dtype=np.float) degree = np.zeros(NN, dtype=np.int) np.add.at(degree, cell, 1) for i in range(10): #bc = tmesh.entity_barycenter('cell') bc, R = tmesh.circumcenter() np.add.at(newNode, (cell, np.s_[:]), bc[:, np.newaxis, :]) newNode /= degree[:, np.newaxis] node[~isBdNode] = newNode[~isBdNode] newNode[:] = 0 fig = plt.figure() axes = fig.gca() tmesh.add_plot(axes) tmesh.find_node(axes, node=newNode, color='r') tmesh.find_node(axes, node=bc, color='b') plt.show()
# sedge[j] == stotalEdge arrayprint("stotalEdge:", stotalEdge) arrayprint("sedge[j]", sedge[j]) arrayprint("j", j) arrayprint("cell2edge", cell2edge) arrayprint("sedge:", sedge) # sedge == stotalEdge[i0] arrayprint("stotalEdge[i0]", stotalEdge[i0]) arrayprint("i0", i0) arrayprint("i1", i1) arrayprint("node", node) # (NN, 2) arrayprint("cell", cell) # (NC, 3) arrayprint("edge", edge) # (NC, 3) arrayprint("edge2cell", edge2cell) # (NE, 4) #edge = mesh.entity('edge') #arrayprint("edge", edge) # (NE, 2) #cell2edge = mesh.ds.cell_to_edge() #arrayprint("cell2edge", cell2edge) # (NC, 3) #edge2cell = mesh.ds.edge_to_cell() #arrayprint("edge2cell", edge2cell) # (NE, 4) fig = plt.figure() axes = fig.gca() mesh.add_plot(axes) mesh.find_node(axes, showindex=True, fontsize=28) mesh.find_edge(axes, showindex=True, fontsize=30) mesh.find_cell(axes, showindex=True, fontsize=32) plt.show()