nfem.set_default_mesh(the_mesh) the_mesh.save("themesh.nmesh") # conductivity (scalar) element_sigma = nfem.make_element("sigma", []) element_drho_by_dt = nfem.make_element("drho_by_dt", []) element_phi = nfem.make_element("phi", []) element_J = nfem.make_element("J", [2]) mwe_sigma = nfem.make_mwe("mwe_sigma", [(1, element_sigma)]) mwe_drho_by_dt = nfem.make_mwe("mwe_drho_by_dt", [(1, element_drho_by_dt)]) mwe_phi = nfem.make_mwe("mwe_phi", [(1, element_phi)]) mwe_J = nfem.make_mwe("mwe_J", [(1, element_J)]) diffop_laplace = nfem.diffop("-<d/dxj drho_by_dt|sigma|d/dxj phi>, j:2") diffop_J = nfem.diffop("<J(k)|sigma|d/dxk phi>, k:2") def fun_sigma0(dof_name_indices, position): return sigma0 field_sigma = nfem.make_field(mwe_sigma, fun_sigma0) def fun_sigma0(dof_name_indices, position): return sigma0 # Later on, we will modify this field:
#def fun_M0(dof_name_indices,pos): # r=math.sqrt(pos[0]*pos[0]+pos[1]*pos[1]+pos[2]*pos[2]) # if dof_name_indices[1][0] == 0 and r < 2.9: # return 1.0 # else: # return 0.0 def fun_M0(dof_name_indices,pos): if dof_name_indices[1][0] == 0: return 1.0 else: return 0.0 diffop_laplace=nfem.diffop("-<d/dxj rho_M||d/dxj phi_M>, j:3") diffop_div_M=nfem.diffop("<rho_M||d/dxj M(j)>, j:3") diffop_grad_phi=nfem.diffop("<H(j)||d/dxj phi_M>, j:3") log.info("OK 2!") #This is " $\ laplace -phi = =rho_M$ prematrix_laplace=nfem.prematrix(diffop_laplace,mwe_rho_M,mwe_phi_M) prematrix_div_M=nfem.prematrix(diffop_div_M,mwe_rho_M,mwe_M,ignore_jumps=False) prematrix_grad_phi=nfem.prematrix(diffop_grad_phi,mwe_H,mwe_phi_M) log.info("OK 3!") solve_bem=nfem.laplace_solver_bem(prematrix_laplace,inside_regions=[1]) log.info("OK 4!")
##### Making the elements... ##### empty_element=ocaml.empty_element; # conductivity (scalar) element_sigma = nfem.make_element("sigma",[]); element_drho_by_dt= nfem.make_element("drho_by_dt",[]); element_phi = nfem.make_element("phi",[]); element_J = nfem.make_element("J",[2]); mwe_sigma = nfem.make_mwe("mwe_sigma", [(1,element_sigma)]) mwe_drho_by_dt = nfem.make_mwe("mwe_drho_by_dt",[(1,element_drho_by_dt)]) mwe_phi = nfem.make_mwe("mwe_phi", [(1,element_phi)]) mwe_J = nfem.make_mwe("mwe_J", [(1,element_J)]) diffop_laplace=nfem.diffop("-<d/dxj drho_by_dt|sigma|d/dxj phi>, j:2") diffop_J=nfem.diffop("<J(k)|sigma|d/dxk phi>, k:2") # Initial conductivity is spatially constant: def fun_sigma0(dof_name_indices,position): return sigma0 # Later on, we will modify this field: field_sigma=nfem.make_field(mwe_sigma,fun_sigma0) # Dirichlet Boundary Conditions on our sample: def laplace_dbc(coords): if(abs(coords[1]) > (2.5-0.05)):
initial_settling_steps = 50, max_relaxation = 4, # callback=(my_function, N), # max_steps=677 max_steps=500 ) nfem.set_default_mesh(the_mesh) element_M = nfem.make_element("M",[3]) element_H = nfem.make_element("H",[3]) mwe_M = nfem.make_mwe("mwe_M", [(1,element_M)]) mwe_H = nfem.make_mwe("mwe_H", [(1,element_H)]) diffop_v_laplace = nfem.diffop("-<d/dxj H(k) || d/dxj M(k)>, j:3, k:3") # Note that this magnetization is "mostly zero": def fun_M0(dof_name_indices,position): if dof_name_indices[1][0]==1: # y-direction x=position[0] return 1.0/(1.0+(x*x/4.0)) else: return 0.0 field_M=nfem.make_field(mwe_M,fun_M0) prematrix_v_laplace=nfem.prematrix(diffop_v_laplace,mwe_H,mwe_M) v_laplace=nfem.prematrix_applicator(prematrix_v_laplace)
# density = density, initial_settling_steps=50, max_relaxation=4, # callback=(my_function, N), # max_steps=677 max_steps=500) nfem.set_default_mesh(the_mesh) element_M = nfem.make_element("M", [3]) element_H = nfem.make_element("H", [3]) mwe_M = nfem.make_mwe("mwe_M", [(1, element_M)]) mwe_H = nfem.make_mwe("mwe_H", [(1, element_H)]) diffop_v_laplace = nfem.diffop("-<d/dxj H(k) || d/dxj M(k)>, j:3, k:3") # Note that this magnetization is "mostly zero": def fun_M0(dof_name_indices, position): if dof_name_indices[1][0] == 1: # y-direction x = position[0] return 1.0 / (1.0 + (x * x / 4.0)) else: return 0.0 field_M = nfem.make_field(mwe_M, fun_M0) prematrix_v_laplace = nfem.prematrix(diffop_v_laplace, mwe_H, mwe_M)
nfem.set_default_dimension(2) nfem.set_default_order(1) thickness2d=0.4 # Initial magnetization is spatially constant: # (We use the same M0 for both cases!) def fun_M0(dof_name_indices,pos): m=[0.0,1.0,0.0] return m[dof_name_indices[1][0]] # Note that we can easily also use the 3d differential operators for # the 2d problems... diffop_laplace=nfem.diffop("-<d/dxj rho_M||d/dxj phi_M>, j:3") diffop_div_M=nfem.diffop("<rho_M||d/dxj M(j)>, j:3") diffop_grad_phi=nfem.diffop("<H(j)||d/dxj phi_M>, j:3") ##### Creating the mesh ##### # For now, we use a very very simple mesh... double_disc_2d = nmesh.union([nmesh.ellipsoid([3.0,3.0], transform=[("shift",[-1.0,0.0])]), nmesh.ellipsoid([3.0,3.0], transform=[("shift",[1.0,0.0])])]) double_disc_3d = nmesh.union([nmesh.conic([-1.0,0.0,thickness2d*0.5],3.0,[-1.0,0.0,-thickness2d*0.5],3.0), nmesh.conic([ 1.0,0.0,thickness2d*0.5],3.0,[ 1.0,0.0,-thickness2d*0.5],3.0)]) density = "density=1.;"
# callback=(my_function, N), # max_steps=677 max_steps=500 ) nfem.set_default_mesh(the_mesh) element_M = nfem.make_element("M",[3]) element_M2 = nfem.make_element("M2",[3],ord=2) element_H = nfem.make_element("H",[3]) mwe_M = nfem.make_mwe("mwe_M", [(1,element_M)]) mwe_M2 = nfem.make_mwe("mwe_M2", [(1,element_M2)]) mwe_H = nfem.make_mwe("mwe_H", [(1,element_H)]) diffop_v_laplace = nfem.diffop("-<d/dxj H(k) || d/dxj M(k)>, j:3, k:3") print "Made MWEs" sys.stdout.flush() # Note that this magnetization is "mostly zero": def fun_M0(dof_name_indices,position): if dof_name_indices[1][0]==1: # y-direction x=position[0] return 1.0/(1.0+(x*x/4.0)) else: return 0.0 # MMM field_M2=nfem.make_field(mwe_M2,fun_M0)
def setup(self): '''This function should be called after the method 'set' to setup the simulation (create the fields, the operators and so on)''' # Should not do initializizations more than once if self.is_ready: return mwe_m, field_m = self.new_mwe_and_field("m", [3], initial_values=self.initial_mag) mwe_h_total, field_h_total = self.new_mwe_and_field("h_total", [3]) if self.features["include_demag"]: self.new_field("h_demag", indices=[3]) if self.features["include_exchange"]: self.new_field("h_exch", indices=[3]) if self.features["external_field"]: h0 = self.features["external_field"] self.new_field("h_ext", indices=[3], initial_values=h0) # The demag field if self.features["include_demag"]: if self.mesh.dim != 3: raise "Sorry, the demag-calculation is implemented only for 3-D space." mwe_h_demag = self.mwes["h_demag"] field_h_demag = self.fields["h_demag"] mwe_scalar = self.new_mwe("scalar") mwe_rho_m = nfem.mwe_sibling(mwe_scalar, "mwe_rho_m", "renamed_scalar", [("scalar", "rho_m")]) mwe_phi_m = nfem.mwe_sibling(mwe_scalar, "mwe_phi_m", "renamed_scalar", [("scalar", "phi_m")]) field_div_m = nfem.make_field(mwe_rho_m) field_phi_m = nfem.make_field(mwe_phi_m) diffop_div_m_str = "%f <rho_m||d/dxj m(j)>, j:3" % self.m_sat print diffop_div_m_str compute_div_m = \ nfem.diffop_applicator(diffop_div_m_str, mwe_rho_m, mwe_m, interface_coeffs=[(-2,-2,1.0)], petsc_name="mumag_div_m") prematrix_laplace = \ nfem.prematrix("-<d/dxj rho_m||d/dxj phi_m>, j:3", mwe_rho_m, mwe_phi_m) solve_bem = \ nfem.laplace_solver_bem(prematrix_laplace, inside_regions=self.where) compute_grad_phi = \ nfem.diffop_applicator("<h_demag(j)||d/dxj phi_m>, j:3", mwe_h_demag, mwe_phi_m, result="field") cofield_div_m = compute_div_m(self.fields["m"]) solve_bem(cofield_div_m, target=field_phi_m) compute_grad_phi(field_phi_m, target=field_h_demag) def calculate_h_demag(): compute_div_m(self.fields["m"], target=cofield_div_m) solve_bem(cofield_div_m, target=field_phi_m) compute_grad_phi(field_phi_m, target=field_h_demag) self.calculate_h_demag = calculate_h_demag # Now we add the exchange and demag fields if needed if self.features["include_exchange"]: if not self.features["exchange_coupling"]: raise "You want to include exchange interaction, " + \ "but you did not specify the exchange coupling constant!" ec = self.features["exchange_coupling"] if ec < 0.0: raise "Error: you specified a negative exchange coupling constant." mwe_h_exch = self.mwes["h_exch"] field_h_exch = self.fields["h_exch"] exch_factor = -2.0*ec/self.m_sat_mu0 op_str = "%f <d/dxi h_exch(j) || d/dxi m(j)>, i:%d, j:3" % (exch_factor, self.mesh.dim) op_h_exch = nfem.diffop(op_str) p = nfem.prematrix(op_h_exch, mwe_h_exch, mwe_m, ignore_jumps=True) compute_h_exch = nfem.prematrix_applicator(p) h_exch_cofield = compute_h_exch(field_m) nfem.cofield_to_field(h_exch_cofield, target=field_h_exch) def calculate_h_exch(): compute_h_exch(field_m, target=h_exch_cofield) nfem.cofield_to_field(h_exch_cofield, target=field_h_exch) self.calculate_h_exch = calculate_h_exch # Create the C-functions which performs the different parts # of the computation some_names = ["m", "h_total"] some_mwes = self.mwe_list(some_names) some_fields = self.field_list(some_names) if self.uniaxial_anis: args = ["m_sat_mu0", "axis_x", "axis_y", "axis_z", "k1", "k2"] c_uniaxial = nfem.site_wise_applicator(args, ccode_uniaxial, field_mwes=some_mwes) def calculate_uniaxial_anis(): for ua in self.uniaxial_anis: axis, k1, k2 = ua axis_x, axis_y, axis_z = axis args_values = [self.m_sat_mu0, axis_x, axis_y, axis_z, k1, k2] c_uniaxial(args_values, fields=some_fields) self.calculate_uniaxial_anis = calculate_uniaxial_anis if self.cubic_anis: args = ["m_sat_mu0", "axis1_x", "axis1_y", "axis1_z", "axis2_x", "axis2_y", "axis2_z", "k1", "k2", "k3"] c_cubic = nfem.site_wise_applicator(args, ccode_cubic, field_mwes=some_mwes) def calculate_cubic_anis(): for ca in self.cubic_anis: axis1, axis2, k1, k2, k3 = ca axis1_x, axis1_y, axis1_z = axis1 axis2_x, axis2_y, axis2_z = axis2 args_values = [self.m_sat_mu0, axis1_x, axis1_y, axis1_z, axis2_x, axis2_y, axis2_z, k1, k2, k3] c_cubic(args_values, fields=some_fields) self.calculate_cubic_anis = calculate_cubic_anis more_names = ["h_total", "h_ext", "h_demag", "h_exch"] more_mwes = self.mwe_list(more_names) more_fields = self.field_list(more_names) add_fields = nfem.site_wise_applicator([], ccode_add_fields, field_mwes=more_mwes) def add_ext_demag_exch(): add_fields([], fields=more_fields) self.add_ext_demag_exch = add_ext_demag_exch if self.features["calculate_energy"]: swa_calculate_energy = \ nfem.site_wise_applicator(["energy"], ccode_calculate_energy, field_mwes=[mwe_m],cofield_mwes=[mwe_h_total]) cofield_h_total = nfem.field_to_cofield(field_h_total) def calculate_energy(): nfem.field_to_cofield(field_h_total, target=cofield_h_total) energy = swa_calculate_energy([0.0], fields=[field_m], cofields=[cofield_h_total]) return -self.m_sat_mu0*energy[0] self.__calculate_energy = calculate_energy self.is_ready = True
def setup(self): '''This function should be called after the method 'set' to setup the simulation (create the fields, the operators and so on)''' # Should not do initializizations more than once if self.is_ready: return mwe_m, field_m = self.new_mwe_and_field( "m", [3], initial_values=self.initial_mag) mwe_h_total, field_h_total = self.new_mwe_and_field("h_total", [3]) if self.features["include_demag"]: self.new_field("h_demag", indices=[3]) if self.features["include_exchange"]: self.new_field("h_exch", indices=[3]) if self.features["external_field"]: h0 = self.features["external_field"] self.new_field("h_ext", indices=[3], initial_values=h0) # The demag field if self.features["include_demag"]: if self.mesh.dim != 3: raise "Sorry, the demag-calculation is implemented only for 3-D space." mwe_h_demag = self.mwes["h_demag"] field_h_demag = self.fields["h_demag"] mwe_scalar = self.new_mwe("scalar") mwe_rho_m = nfem.mwe_sibling(mwe_scalar, "mwe_rho_m", "renamed_scalar", [("scalar", "rho_m")]) mwe_phi_m = nfem.mwe_sibling(mwe_scalar, "mwe_phi_m", "renamed_scalar", [("scalar", "phi_m")]) field_div_m = nfem.make_field(mwe_rho_m) field_phi_m = nfem.make_field(mwe_phi_m) diffop_div_m_str = "%f <rho_m||d/dxj m(j)>, j:3" % self.m_sat print diffop_div_m_str compute_div_m = \ nfem.diffop_applicator(diffop_div_m_str, mwe_rho_m, mwe_m, interface_coeffs=[(-2,-2,1.0)], petsc_name="mumag_div_m") prematrix_laplace = \ nfem.prematrix("-<d/dxj rho_m||d/dxj phi_m>, j:3", mwe_rho_m, mwe_phi_m) solve_bem = \ nfem.laplace_solver_bem(prematrix_laplace, inside_regions=self.where) compute_grad_phi = \ nfem.diffop_applicator("<h_demag(j)||d/dxj phi_m>, j:3", mwe_h_demag, mwe_phi_m, result="field") cofield_div_m = compute_div_m(self.fields["m"]) solve_bem(cofield_div_m, target=field_phi_m) compute_grad_phi(field_phi_m, target=field_h_demag) def calculate_h_demag(): compute_div_m(self.fields["m"], target=cofield_div_m) solve_bem(cofield_div_m, target=field_phi_m) compute_grad_phi(field_phi_m, target=field_h_demag) self.calculate_h_demag = calculate_h_demag # Now we add the exchange and demag fields if needed if self.features["include_exchange"]: if not self.features["exchange_coupling"]: raise "You want to include exchange interaction, " + \ "but you did not specify the exchange coupling constant!" ec = self.features["exchange_coupling"] if ec < 0.0: raise "Error: you specified a negative exchange coupling constant." mwe_h_exch = self.mwes["h_exch"] field_h_exch = self.fields["h_exch"] exch_factor = -2.0 * ec / self.m_sat_mu0 op_str = "%f <d/dxi h_exch(j) || d/dxi m(j)>, i:%d, j:3" % ( exch_factor, self.mesh.dim) op_h_exch = nfem.diffop(op_str) p = nfem.prematrix(op_h_exch, mwe_h_exch, mwe_m, ignore_jumps=True) compute_h_exch = nfem.prematrix_applicator(p) h_exch_cofield = compute_h_exch(field_m) nfem.cofield_to_field(h_exch_cofield, target=field_h_exch) def calculate_h_exch(): compute_h_exch(field_m, target=h_exch_cofield) nfem.cofield_to_field(h_exch_cofield, target=field_h_exch) self.calculate_h_exch = calculate_h_exch # Create the C-functions which performs the different parts # of the computation some_names = ["m", "h_total"] some_mwes = self.mwe_list(some_names) some_fields = self.field_list(some_names) if self.uniaxial_anis: args = ["m_sat_mu0", "axis_x", "axis_y", "axis_z", "k1", "k2"] c_uniaxial = nfem.site_wise_applicator(args, ccode_uniaxial, field_mwes=some_mwes) def calculate_uniaxial_anis(): for ua in self.uniaxial_anis: axis, k1, k2 = ua axis_x, axis_y, axis_z = axis args_values = [ self.m_sat_mu0, axis_x, axis_y, axis_z, k1, k2 ] c_uniaxial(args_values, fields=some_fields) self.calculate_uniaxial_anis = calculate_uniaxial_anis if self.cubic_anis: args = [ "m_sat_mu0", "axis1_x", "axis1_y", "axis1_z", "axis2_x", "axis2_y", "axis2_z", "k1", "k2", "k3" ] c_cubic = nfem.site_wise_applicator(args, ccode_cubic, field_mwes=some_mwes) def calculate_cubic_anis(): for ca in self.cubic_anis: axis1, axis2, k1, k2, k3 = ca axis1_x, axis1_y, axis1_z = axis1 axis2_x, axis2_y, axis2_z = axis2 args_values = [ self.m_sat_mu0, axis1_x, axis1_y, axis1_z, axis2_x, axis2_y, axis2_z, k1, k2, k3 ] c_cubic(args_values, fields=some_fields) self.calculate_cubic_anis = calculate_cubic_anis more_names = ["h_total", "h_ext", "h_demag", "h_exch"] more_mwes = self.mwe_list(more_names) more_fields = self.field_list(more_names) add_fields = nfem.site_wise_applicator([], ccode_add_fields, field_mwes=more_mwes) def add_ext_demag_exch(): add_fields([], fields=more_fields) self.add_ext_demag_exch = add_ext_demag_exch if self.features["calculate_energy"]: swa_calculate_energy = \ nfem.site_wise_applicator(["energy"], ccode_calculate_energy, field_mwes=[mwe_m],cofield_mwes=[mwe_h_total]) cofield_h_total = nfem.field_to_cofield(field_h_total) def calculate_energy(): nfem.field_to_cofield(field_h_total, target=cofield_h_total) energy = swa_calculate_energy([0.0], fields=[field_m], cofields=[cofield_h_total]) return -self.m_sat_mu0 * energy[0] self.__calculate_energy = calculate_energy self.is_ready = True
max_relaxation=4, # callback=(my_function, N), # max_steps=677 max_steps=500) nfem.set_default_mesh(the_mesh) element_M = nfem.make_element("M", [3]) element_M2 = nfem.make_element("M2", [3], ord=2) element_H = nfem.make_element("H", [3]) mwe_M = nfem.make_mwe("mwe_M", [(1, element_M)]) mwe_M2 = nfem.make_mwe("mwe_M2", [(1, element_M2)]) mwe_H = nfem.make_mwe("mwe_H", [(1, element_H)]) diffop_v_laplace = nfem.diffop("-<d/dxj H(k) || d/dxj M(k)>, j:3, k:3") print "Made MWEs" sys.stdout.flush() # Note that this magnetization is "mostly zero": def fun_M0(dof_name_indices, position): if dof_name_indices[1][0] == 1: # y-direction x = position[0] return 1.0 / (1.0 + (x * x / 4.0)) else: return 0.0 # MMM