The application of subdomain solution to the global domain when multiple fields are coupled

General
1

A multi-field coupling problem is being calculated, as shown in the figure, with the upper part calculated for the phase field and the overall grid calculated for the magnetic field.

  • My mesh function is as follows：
def mesh(Lx=1, Ly=5, grid_spacing=0.1/64, **namespace):
    mesh_init = df.RectangleMesh(df.Point(0.,-Ly/2), df.Point(Lx, Ly),
                            int(Lx/grid_spacing), int(1.5*Ly/grid_spacing))
    cell_makers = df.MeshFunction('bool',mesh_init,mesh_init.topology().dim())
    cell_makers.set_all(False)
    for cell in df.cells(mesh_init):
        if cell.midpoint().y() > 0:
            cell_makers[cell] =True
    return df.refine(mesh_init,cell_makers)

mesh = mesh(Lx=1, Ly=5, grid_spacing=0.1/64)

My submesh function is as follow:

def mesh_top(mesh_full, Ly, **namespace):
    domains = df.MeshFunction('size_t', mesh_full,mesh_full.topology().dim())
    domains.set_all(0)
    top_domain =TopDomain(Ly)
    top_domain.mark(domains,1)
    return df.MeshView.create(domains,1)

submesh = submesh(mesh,Ly)
  • The solution I get from the phase field which is from sub mesh iterates to the magnetic field, and the formula is as follows:
def ramp_veps(domain, phi, A ):
    x = ufl.SpatialCoordinate(domain)
    return ufl.conditional(ufl.lt(x[1],0.0),1.23*4.0e-7*math.pi, A[0]*0.5*(1.+phi) + A[1]*0.5*(1.-phi))

 veps_= ramp_veps(mesh,phi_flt_, permittivity)

The program reports an error:Unable to evaluate function at point.