def __init__(self, model, p, NS=0, NT=100):
self.model = model # 物理模型
self.mesh0 = model.space_mesh(NS=NS, p=p) # 初始网格
self.mesh1 = model.space_mesh(NS=NS, p=p) # 计算网格
self.timeline = model.time_mesh(NT=NT) # 时间离散网格
# 运动学空间
self.cspace = ParametricLagrangeFiniteElementSpace(self.mesh1,
p=p,
spacetype='C')
# 热力学空间
self.dspace = ParametricLagrangeFiniteElementSpace(self.mesh1,
p=p - 1,
spacetype='D')
self.integrator = self.cspace.integralalg.integrator
bc = self.mesh0.entity_barycenter('cell')
# 物质密度
self.rho = model.init_rho(bc) # (NC, )
# 绝热指数
self.gamma = model.adiabatic_index(bc) #(NC, )
self.MV = self.cspace.mass_matrix(c=self.rho) # 运动空间的质量矩阵
self.ME = self.dspace.mass_matrix(c=self.rho) # 热力学空间的质量矩阵
GD = self.mesh1.geo_dimension()
self.x = self.cspace.function(dim=GD) # 位置
self.v = self.cspace.function(dim=GD) # 速度
self.e = self.dspace.function() # 能量
self.x[:] = self.mesh1.entity('node') # 初始化自由度位置
model.init_velocity(self.v) # 初始化速度
model.init_energe(self.e) # 初始化能量
self.cx = self.cspace.function(dim=GD) # 保存临时的解
self.cv = self.cspace.function(dim=GD)
self.ce = self.dspace.function()
self.cx[:] = self.mesh1.entity('node')
model.init_velocity(self.cv)
model.init_energe(self.ce)
self.mesh1.celldata['rho'] = self.rho
self.mesh1.celldata['gamma'] = self.gamma
self.mesh1.nodedata['velocity'] = self.cv
def plane_quad_interpolation(self, p=2, fname='plane.vtu'):
from fealpy.pde.poisson_2d import CosCosData
from fealpy.mesh import LagrangeQuadrangleMesh
pde = CosCosData()
node = np.array([(0, 0), (0, 1), (1, 0), (1, 1)], dtype=np.float64)
cell = np.array([(0, 1, 2, 3)], dtype=np.int_)
mesh = LagrangeQuadrangleMesh(node, cell, p=p)
for i in range(4):
space = ParametricLagrangeFiniteElementSpace(mesh, p=p)
uI = space.interpolation(pde.solution)
mesh.nodedata['uI'] = uI[:]
error0 = space.integralalg.error(pde.solution, uI.value)
error1 = space.integralalg.error(pde.gradient, uI.grad_value)
print(error0, error1)
if i < 3:
mesh.uniform_refine()
mesh.to_vtk(fname=fname)
def interpolation(self, p=2, n=1, fname='surface.vtu'):
from fealpy.geometry import SphereSurface
from fealpy.pde.surface_poisson_model_3d import SphereSinSinSinData
pde = SphereSinSinSinData()
surface = pde.domain()
mesh = pde.init_mesh(n=n)
node = mesh.entity('node')
cell = mesh.entity('cell')
mesh = LagrangeTriangleMesh(node, cell, p=p, surface=surface)
space = ParametricLagrangeFiniteElementSpace(mesh, p=p)
uI = space.interpolation(pde.solution)
mesh.nodedata['uI'] = uI[:]
error0 = space.integralalg.error(pde.solution, uI.value)
error1 = space.integralalg.error(pde.gradient, uI.grad_value)
print(error0, error1)
mesh.to_vtk(fname=fname)
mesh.uniform_refine(n=nrefine)
errorType = [
'$|| u - u_h||_{\Omega,0}$', '$||\\nabla u - \\nabla u_h||_{\Omega, 0}$',
'$|| u - u_I||_{\Omega,0}$', '$||\\nabla u - \\nabla u_I||_{\Omega, 0}$',
'$|| u_I - u_h ||_{\Omega, \infty}$'
]
errorMatrix = np.zeros((len(errorType), maxit), dtype=np.float64)
NDof = np.zeros(maxit, dtype=np.int_)
m = 4
for i in range(maxit):
print("The {}-th computation:".format(i))
space = ParametricLagrangeFiniteElementSpace(mesh, p=sdegree)
NDof[i] = space.number_of_global_dofs()
uI = space.interpolation(pde.solution)
A = space.stiff_matrix()
C = space.integral_basis()
F = space.source_vector(pde.source)
NN = mesh.number_of_corner_nodes()
NC = mesh.number_of_cells()
delta = (A @ uI - F)
A = bmat([[A, C.reshape(-1, 1)], [C, None]], format='csr')
F = np.r_[F, 0]
def __init__(self, mesh):
self.space = ParametricLagrangeFiniteElementSpace(mesh, p=1)
self.mesh = self.space.mesh
self.M = self.space.mass_matrix()
self.A = self.space.stiff_matrix()
parser.print_help() args = parser.parse_args() print(args) # 开始主程序 pde = PDE() mf = MeshFactory() # 创建一个双 p 次的四边形网格 mesh = mf.boxmesh2d(args.b, nx=args.n, ny=args.n, meshtype='quad', p=args.p) # 在 mesh 上创建一个双 p 次的有限元函数空间 space = ParametricLagrangeFiniteElementSpace(mesh, p=args.p, spacetype='C') # 数值解函数 uh = space.function() # 组装刚度矩阵 A = space.stiff_matrix() # 右端载荷 F = space.source_vector(pde.source) # 定义边界条件 bc = DirichletBC(space, pde.dirichlet) # 处理边界条件 A, F = bc.apply(A, F, uh)