Merge pull request #2141 from Hukai0/draft/kyle

修改注释

Author: AlbertZyy

fealpy/solver/__init__.py

@@ -20,3 +20,4 @@
 
 from .tpdv import DarcyForchheimerTPDv
 from .fast_solver import LinearElasticityHZFEMFastSolver
+

fealpy/solver/additive_schwarz.py

@@ -184,30 +184,3 @@ def projection(self, space0):
                        shape=(gdof, gdof0), dtype=phi.dtype)
 
         return M
-
-from fealpy.functionspace import TensorFunctionSpace, LagrangeFESpace,RaviartThomasFESpace
-from fealpy.fem import BilinearForm, LinearForm, BlockForm, LinearBlockForm
-from fealpy.fem import ScalarSourceIntegrator, ScalarNeumannBCIntegrator, ScalarMassIntegrator, GradPressureIntegrator,DivIntegrator,DivIntegrator2,DirichletBC    
-from fealpy.solver import spsolve,GAMGSolver
-from fealpy.model import PDEModelManager
-
-pde = PDEModelManager('darcyforchheimer').get_example(9)
-mesh = pde.init_mesh['uniform_tri'](nx=8, ny=8)
-p = 6
-q = p+3
-unit = mesh.edge_unit_normal()
-uspace = RaviartThomasFESpace(mesh, p=p)
-u_bform = BilinearForm(uspace)
-Mu = ScalarMassIntegrator(coef=1,q=q)
-u_bform.add_integrator(Mu)
-u_bform.add_integrator(DivIntegrator2(coef=1,q=q))
-
-M = u_bform.assembly()
-
-ulform = LinearForm(uspace)
-ulform.add_integrator(ScalarSourceIntegrator(pde.f, q=q))
-b = bm.random.rand(M.shape[0]) 
-F = M@b
-
-Solver = AdditiveSchwarz(uspace, M, spacetype='Hdiv',type='face' )
-b = Solver.solve(F)

fealpy/solver/ams.py

@@ -5,41 +5,32 @@
 class AMSSolver:
 
     def __init__(self):
-        """AMS预条件器求解类初始化。"""
-        # 初始化内部数据结构
-        self.A = None               # 边空间刚度矩阵 (稀疏矩阵)
-        self.G = None               # 离散梯度矩阵 G
+
+        self.A = None              
+        self.G = None               
         self.Pi_x = None
         self.Pi_y = None
         self.Pi_z = None
-        self.dim = None             # 空间维度 (2 或 3)
+        self.dim = None             
         self.n_nodes = 0
         self.n_edges = 0
-        self.vertices = None        # 顶点坐标数组
-        self.edges = None           # 每条边的顶点索引对 (取向已定)
-        # 平滑器与循环参数
+        self.vertices = None        
+        self.edges = None           
+        
         self.smoother = 'GaussSeidel'
         self.smooth_iters = 1
-        self.jacobi_weight = 1.0    # Jacobi 平滑的松弛因子
-        self.cycle_type = 'V'       # 多重网格循环类型 ('V' 或 'W')
-        # 子空间矩阵
-        self.A_G = None             # 梯度子空间矩阵 A_G = G^T * A * G
-        self.A_Pi = None            # 插值子空间矩阵 A_Pi = Pi^T * A * Pi
+        self.jacobi_weight = 1.0    
+        self.cycle_type = 'V'       
+    
+        self.A_G = None             
+        self.A_Pi = None          
 
     def AMSFEISetup(self, A, vertices, edges, dim=None):
-        """
-        初始化有限元结构，包括网格拓扑和自由度编号。
-        参数:
-        - A: H(curl)空间的刚度矩阵 (scipy.sparse 矩阵).
-        - vertices: 顶点坐标数组，形状 (num_vertices, dim).
-        - edges: 边的顶点索引对列表 (长度 num_edges，每个元素为 (v1, v2)).
-        - dim: 空间维度 (2 或 3)，可选参数，不提供则根据 vertices 列数推断。
-        """
-        # 设置维度
+
         if dim is None:
             dim = vertices.shape[1]
         self.dim = dim
-        # 存储矩阵和几何信息
+    
         self.A = A
         self.vertices = vertices
         self.n_nodes = self.vertices.shape[0]
@@ -55,8 +46,8 @@ def AMSComputeGPi(self):
         num_nodes = self.n_nodes
 
         edges = self.edges
-        ei = edges[:, 0].astype(int)            # 所有边的起点索引
-        ej = edges[:, 1].astype(int)            # 所有边的终点索引
+        ei = edges[:, 0].astype(int)            
+        ej = edges[:, 1].astype(int)            
         row = bm.repeat(bm.arange(num_edges, dtype=int), 2)  
         col = bm.empty(2 * num_edges, dtype=int)
         col[0::2] = ei
@@ -69,9 +60,7 @@ def AMSComputeGPi(self):
         self.A_G = (self.G.T)@(self.A@(self.G))
 
     def AMSSetAGradient(self, A_grad):
-        """
-        直接设置梯度子空间矩阵 A_G。
-        """
+
         self.A_G = A_grad
 
     def AMSComputePi(self):
@@ -117,7 +106,7 @@ def AMSSetCycle(self, cycle_type='V'):
 
     def AMSSolve(self, b, tol=1e-6, maxiter=100, x0=None):
 
-        # 初始解
+    
         if x0 is None:
             x = bm.zeros(self.n_edges,dtype=self.A.dtype)
         else:
@@ -126,20 +115,19 @@ def AMSSolve(self, b, tol=1e-6, maxiter=100, x0=None):
         b = bm.array(b)
 
         for it in range(maxiter):
-            # 计算残差 r = b - A x
+           
             r = b - self.A@x
             res_norm = bm.linalg.norm(r)
             if res_norm < tol:
-                return x, it  # 提前收敛
+                return x, it  
             el = spsolve(self.A.tril(), r,'scipy')
 
             for _ in range(self.smooth_iters):
                 el += spsolve(self.A.tril(), r - self.A @ el,'scipy')       
             x = x + el
-            r = b - self.A@x  # 更新残差
-            # 2. 梯度子空间校正：求解 A_G e_g = G^T r，然后 x <- x + G e_g
+            r = b - self.A@x  
 
-            r_g = self.G.T@r  # 将残差限制到节点梯度空间
+            r_g = self.G.T@r  
 
             e_g = spsolve(self.A_G, r_g,'scipy')
 
@@ -149,7 +137,7 @@ def AMSSolve(self, b, tol=1e-6, maxiter=100, x0=None):
             for _ in range(self.smooth_iters):
                 el += spsolve(self.A.tril(), r - self.A @ el,'scipy')
             x = x + el
-            r = b - self.A@x  # 更新残差
+            r = b - self.A@x  
             r_pi_combined = self.Pi.T@r
             e_pi_combined = bm.zeros(self.Pi.shape[0])
             ml = GAMGSolver(isolver='MG', ptype='V', sstep=3, theta=0.25)
@@ -162,11 +150,11 @@ def AMSSolve(self, b, tol=1e-6, maxiter=100, x0=None):
             for _ in range(self.smooth_iters):
                 el += spsolve(self.A.triu(), r - self.A @ el,'scipy')
             x = x + el
-            # 检查收敛
+            
             r = b - self.A@x
             res_norm = bm.linalg.norm(r)
             print("iter:", it, "res_norm:", res_norm)
             if res_norm < tol:
                 return x, it+1
-        # 未在 maxiter 内收敛，返回当前解
+        
         return x, maxiter