def get_context(): """Set up context for classical (NS) solver""" V0 = C2CBasis(params.N[0], domain=(0, params.L[0])) V1 = C2CBasis(params.N[1], domain=(0, params.L[1])) V2 = R2CBasis(params.N[2], domain=(0, params.L[2])) T = TensorProductSpace(comm, (V0, V1, V2), **{'threads': params.threads}) VT = VectorTensorProductSpace([T]*3) kw = {'padding_factor': 1.5 if params.dealias == '3/2-rule' else 1, 'dealias_direct': params.dealias == '2/3-rule'} V0p = C2CBasis(params.N[0], domain=(0, params.L[0]), **kw) V1p = C2CBasis(params.N[1], domain=(0, params.L[1]), **kw) V2p = R2CBasis(params.N[2], domain=(0, params.L[2]), **kw) Tp = TensorProductSpace(comm, (V0p, V1p, V2p), **{'threads': params.threads}) VTp = VectorTensorProductSpace([Tp]*3) float, complex, mpitype = datatypes(params.precision) FFT = T # For compatibility - to be removed # Mesh variables X = T.local_mesh(True) K = T.local_wavenumbers(scaled=True) K2 = K[0]*K[0] + K[1]*K[1] + K[2]*K[2] # Set Nyquist frequency to zero on K that is, from now on, used for odd derivatives Kx = T.local_wavenumbers(scaled=True, eliminate_highest_freq=True) K_over_K2 = np.zeros((3,)+VT.local_shape()) for i in range(3): K_over_K2[i] = K[i] / np.where(K2==0, 1, K2) # Velocity and pressure U = Array(VT, False) U_hat = Array(VT) P = Array(T, False) P_hat = Array(T) # Primary variable u = U_hat # RHS array dU = Array(VT) curl = Array(VT, False) Source = Array(VT) # Possible source term initialized to zero work = work_arrays() hdf5file = NSWriter({"U":U[0], "V":U[1], "W":U[2], "P":P}, chkpoint={"current":{"U":U, "P":P}, "previous":{}}, filename=params.h5filename+".h5") return config.AttributeDict(locals())
def test_curl(typecode): K0 = Basis(N[0], 'F', dtype=typecode.upper()) K1 = Basis(N[1], 'F', dtype=typecode.upper()) K2 = Basis(N[2], 'F', dtype=typecode) T = TensorProductSpace(comm, (K0, K1, K2), dtype=typecode) X = T.local_mesh(True) K = T.local_wavenumbers() Tk = VectorTensorProductSpace(T) u = TrialFunction(Tk) v = TestFunction(Tk) U = Array(Tk) U_hat = Function(Tk) curl_hat = Function(Tk) curl_ = Array(Tk) # Initialize a Taylor Green vortex U[0] = np.sin(X[0]) * np.cos(X[1]) * np.cos(X[2]) U[1] = -np.cos(X[0]) * np.sin(X[1]) * np.cos(X[2]) U[2] = 0 U_hat = Tk.forward(U, U_hat) Uc = U_hat.copy() U = Tk.backward(U_hat, U) U_hat = Tk.forward(U, U_hat) assert allclose(U_hat, Uc) divu_hat = project(div(U_hat), T) divu = Array(T) divu = T.backward(divu_hat, divu) assert allclose(divu, 0) curl_hat[0] = 1j * (K[1] * U_hat[2] - K[2] * U_hat[1]) curl_hat[1] = 1j * (K[2] * U_hat[0] - K[0] * U_hat[2]) curl_hat[2] = 1j * (K[0] * U_hat[1] - K[1] * U_hat[0]) curl_ = Tk.backward(curl_hat, curl_) w_hat = Function(Tk) w_hat = inner(v, curl(U_hat), output_array=w_hat) A = inner(v, u) for i in range(3): w_hat[i] = A[i].solve(w_hat[i]) w = Array(Tk) w = Tk.backward(w_hat, w) #from IPython import embed; embed() assert allclose(w, curl_) u_hat = Function(Tk) u_hat = inner(v, U, output_array=u_hat) for i in range(3): u_hat[i] = A[i].solve(u_hat[i]) uu = Array(Tk) uu = Tk.backward(u_hat, uu) assert allclose(u_hat, U_hat)
def test_curl2(): # Test projection of curl K0 = FunctionSpace(N[0], 'C', bc=(0, 0)) K1 = FunctionSpace(N[1], 'F', dtype='D') K2 = FunctionSpace(N[2], 'F', dtype='d') K3 = FunctionSpace(N[0], 'C') T = TensorProductSpace(comm, (K0, K1, K2)) TT = TensorProductSpace(comm, (K3, K1, K2)) X = T.local_mesh(True) K = T.local_wavenumbers(False) Tk = VectorSpace(T) TTk = VectorSpace([T, T, TT]) U = Array(Tk) U_hat = Function(Tk) curl_hat = Function(TTk) curl_ = Array(TTk) # Initialize a Taylor Green vortex U[0] = np.sin(X[0]) * np.cos(X[1]) * np.cos(X[2]) * (1 - X[0]**2) U[1] = -np.cos(X[0]) * np.sin(X[1]) * np.cos(X[2]) * (1 - X[0]**2) U[2] = 0 U_hat = Tk.forward(U, U_hat) Uc = U_hat.copy() U = Tk.backward(U_hat, U) U_hat = Tk.forward(U, U_hat) assert allclose(U_hat, Uc) # Compute curl first by computing each term individually curl_hat[0] = 1j * (K[1] * U_hat[2] - K[2] * U_hat[1]) curl_[0] = T.backward( curl_hat[0], curl_[0]) # No x-derivatives, still in Dirichlet space dwdx_hat = project(Dx(U_hat[2], 0, 1), TT) # Need to use space without bc dvdx_hat = project(Dx(U_hat[1], 0, 1), TT) # Need to use space without bc dwdx = Array(TT) dvdx = Array(TT) dwdx = TT.backward(dwdx_hat, dwdx) dvdx = TT.backward(dvdx_hat, dvdx) curl_hat[1] = 1j * K[2] * U_hat[0] curl_hat[2] = -1j * K[1] * U_hat[0] curl_[1] = T.backward(curl_hat[1], curl_[1]) curl_[2] = T.backward(curl_hat[2], curl_[2]) curl_[1] -= dwdx curl_[2] += dvdx # Now do it with project w_hat = project(curl(U_hat), TTk) w = Array(TTk) w = TTk.backward(w_hat, w) assert allclose(w, curl_)
def get_context(): """Set up context for solver""" collapse_fourier = False if params.dealias == '3/2-rule' else True family = 'C' ST = FunctionSpace(params.N[0], family, bc=(0, 0), quad=params.Dquad) CT = FunctionSpace(params.N[0], family, quad=params.Dquad) CP = FunctionSpace(params.N[0], family, quad=params.Dquad) K0 = FunctionSpace(params.N[1], 'F', domain=(0, params.L[1]), dtype='D') K1 = FunctionSpace(params.N[2], 'F', domain=(0, params.L[2]), dtype='d') #CP.slice = lambda: slice(0, CP.N-2) constraints = ((3, 0, 0), (3, params.N[0] - 1, 0)) kw0 = { 'threads': params.threads, 'planner_effort': params.planner_effort["dct"], 'slab': (params.decomposition == 'slab'), 'collapse_fourier': collapse_fourier } FST = TensorProductSpace(comm, (ST, K0, K1), **kw0) # Dirichlet FCT = TensorProductSpace(comm, (CT, K0, K1), **kw0) # Regular Chebyshev N FCP = TensorProductSpace(comm, (CP, K0, K1), **kw0) # Regular Chebyshev N-2 VFS = VectorSpace(FST) VCT = VectorSpace(FCT) VQ = CompositeSpace([VFS, FCP]) mask = FST.get_mask_nyquist() if params.mask_nyquist else None # Padded kw = { 'padding_factor': 1.5 if params.dealias == '3/2-rule' else 1, 'dealias_direct': params.dealias == '2/3-rule' } if params.dealias == '3/2-rule': # Requires new bases due to planning and transforms on different size arrays STp = FunctionSpace(params.N[0], family, bc=(0, 0), quad=params.Dquad) CTp = FunctionSpace(params.N[0], family, quad=params.Dquad) else: STp, CTp = ST, CT K0p = FunctionSpace(params.N[1], 'F', dtype='D', domain=(0, params.L[1]), **kw) K1p = FunctionSpace(params.N[2], 'F', dtype='d', domain=(0, params.L[2]), **kw) FSTp = TensorProductSpace(comm, (STp, K0p, K1p), **kw0) FCTp = TensorProductSpace(comm, (CTp, K0p, K1p), **kw0) VFSp = VectorSpace(FSTp) VCp = CompositeSpace([FSTp, FCTp, FCTp]) float, complex, mpitype = datatypes("double") # Mesh variables X = FST.local_mesh(True) x0, x1, x2 = FST.mesh() K = FST.local_wavenumbers(scaled=True) # Solution variables UP_hat = Function(VQ) UP_hat0 = Function(VQ) U_hat, P_hat = UP_hat U_hat0, P_hat0 = UP_hat0 UP = Array(VQ) UP0 = Array(VQ) U, P = UP U0, P0 = UP0 # RK parameters a = (8. / 15., 5. / 12., 3. / 4.) b = (0.0, -17. / 60., -5. / 12.) # primary variable u = UP_hat H_hat = Function(VFS) dU = Function(VQ) hv = np.zeros((2, ) + H_hat.shape, dtype=np.complex) Source = Array( VFS) # Note - not using VQ. Only used for constant pressure gradient Sk = Function(VFS) K2 = K[1] * K[1] + K[2] * K[2] for i in range(3): K[i] = K[i].astype(float) work = work_arrays() u_dealias = Array(VFSp) curl_hat = Function(VCp) curl_dealias = Array(VCp) nu, dt, N = params.nu, params.dt, params.N up = TrialFunction(VQ) vq = TestFunction(VQ) ut, pt = up vt, qt = vq M = [] for rk in range(3): a0 = inner(vt, (2. / nu / dt / (a[rk] + b[rk])) * ut - div(grad(ut))) a1 = inner(vt, (2. / nu / (a[rk] + b[rk])) * grad(pt)) a2 = inner(qt, (2. / nu / (a[rk] + b[rk])) * div(ut)) M.append(BlockMatrix(a0 + a1 + a2)) # Collect all matrices if ST.family() == 'chebyshev': mat = config.AttributeDict( dict(AB=[ HelmholtzCoeff(N[0], 1., -(K2 - 2. / nu / dt / (a[rk] + b[rk])), 0, ST.quad) for rk in range(3) ], )) else: mat = config.AttributeDict( dict(ADD=inner_product((ST, 0), (ST, 2)), BDD=inner_product((ST, 0), (ST, 0)))) la = None hdf5file = CoupledRK3File(config.params.solver, checkpoint={ 'space': VQ, 'data': { '0': { 'UP': [UP_hat] } } }, results={ 'space': VFS, 'data': { 'U': [U] } }) del rk return config.AttributeDict(locals())
def get_context(): float, complex, mpitype = datatypes(params.precision) collapse_fourier = False if params.dealias == '3/2-rule' else True dim = len(params.N) dtype = lambda d: float if d == dim - 1 else complex V = [ Basis(params.N[i], 'F', domain=(0, params.L[i]), dtype=dtype(i)) for i in range(dim) ] kw0 = { 'threads': params.threads, 'planner_effort': params.planner_effort['fft'] } T = TensorProductSpace(comm, V, dtype=float, slab=(params.decomposition == 'slab'), collapse_fourier=collapse_fourier, **kw0) VT = VectorTensorProductSpace(T) VM = MixedTensorProductSpace([T] * 2 * dim) mask = T.mask_nyquist() if params.mask_nyquist else None kw = { 'padding_factor': 1.5 if params.dealias == '3/2-rule' else 1, 'dealias_direct': params.dealias == '2/3-rule' } Vp = [ Basis(params.N[i], 'F', domain=(0, params.L[i]), dtype=dtype(i), **kw) for i in range(dim) ] Tp = TensorProductSpace(comm, Vp, dtype=float, slab=(params.decomposition == 'slab'), collapse_fourier=collapse_fourier, **kw0) VTp = VectorTensorProductSpace(Tp) VMp = MixedTensorProductSpace([Tp] * 2 * dim) # Mesh variables X = T.local_mesh(True) K = T.local_wavenumbers(scaled=True) for i in range(dim): X[i] = X[i].astype(float) K[i] = K[i].astype(float) K2 = np.zeros(T.shape(True), dtype=float) for i in range(dim): K2 += K[i] * K[i] # Set Nyquist frequency to zero on K that is, from now on, used for odd derivatives Kx = T.local_wavenumbers(scaled=True, eliminate_highest_freq=True) for i in range(dim): Kx[i] = Kx[i].astype(float) K_over_K2 = np.zeros(VT.shape(True), dtype=float) for i in range(dim): K_over_K2[i] = K[i] / np.where(K2 == 0, 1, K2) UB = Array(VM) P = Array(T) curl = Array(VT) UB_hat = Function(VM) P_hat = Function(T) dU = Function(VM) Source = Array(VM) ub_dealias = Array(VMp) ZZ_hat = np.zeros((3, 3) + Tp.shape(True), dtype=complex) # Work array # Create views into large data structures U = UB[:3] U_hat = UB_hat[:3] B = UB[3:] B_hat = UB_hat[3:] # Primary variable u = UB_hat hdf5file = MHDFile(config.params.solver, checkpoint={ 'space': VM, 'data': { '0': { 'UB': [UB_hat] } } }, results={ 'space': VM, 'data': { 'UB': [UB] } }) return config.AttributeDict(locals())
def get_context(): """Set up context for solver""" # Get points and weights for Chebyshev weighted integrals assert params.Dquad == params.Bquad collapse_fourier = False if params.dealias == '3/2-rule' else True ST = Basis(params.N[0], 'C', bc=(0, 0), quad=params.Dquad) SB = Basis(params.N[0], 'C', bc='Biharmonic', quad=params.Bquad) CT = Basis(params.N[0], 'C', quad=params.Dquad) ST0 = Basis(params.N[0], 'C', bc=(0, 0), quad=params.Dquad) # For 1D problem K0 = Basis(params.N[1], 'F', domain=(0, params.L[1]), dtype='D') K1 = Basis(params.N[2], 'F', domain=(0, params.L[2]), dtype='d') kw0 = {'threads': params.threads, 'planner_effort': params.planner_effort["dct"], 'slab': (params.decomposition == 'slab'), 'collapse_fourier': collapse_fourier} FST = TensorProductSpace(comm, (ST, K0, K1), **kw0) # Dirichlet FSB = TensorProductSpace(comm, (SB, K0, K1), **kw0) # Biharmonic FCT = TensorProductSpace(comm, (CT, K0, K1), **kw0) # Regular Chebyshev VFS = VectorTensorProductSpace([FSB, FST, FST]) VFST = VectorTensorProductSpace([FST, FST, FST]) VUG = MixedTensorProductSpace([FSB, FST]) VCT = VectorTensorProductSpace(FCT) mask = FST.get_mask_nyquist() if params.mask_nyquist else None # Padded kw = {'padding_factor': 1.5 if params.dealias == '3/2-rule' else 1, 'dealias_direct': params.dealias == '2/3-rule'} if params.dealias == '3/2-rule': # Requires new bases due to planning and transforms on different size arrays STp = Basis(params.N[0], 'C', bc=(0, 0), quad=params.Dquad) SBp = Basis(params.N[0], 'C', bc='Biharmonic', quad=params.Bquad) CTp = Basis(params.N[0], 'C', quad=params.Dquad) else: STp, SBp, CTp = ST, SB, CT K0p = Basis(params.N[1], 'F', dtype='D', domain=(0, params.L[1]), **kw) K1p = Basis(params.N[2], 'F', dtype='d', domain=(0, params.L[2]), **kw) FSTp = TensorProductSpace(comm, (STp, K0p, K1p), **kw0) FSBp = TensorProductSpace(comm, (SBp, K0p, K1p), **kw0) FCTp = TensorProductSpace(comm, (CTp, K0p, K1p), **kw0) VFSp = VectorTensorProductSpace([FSBp, FSTp, FSTp]) float, complex, mpitype = datatypes("double") # Mesh variables X = FST.local_mesh(True) x0, x1, x2 = FST.mesh() K = FST.local_wavenumbers(scaled=True) # Solution variables U = Array(VFS) U0 = Array(VFS) U_hat = Function(VFS) U_hat0 = Function(VFS) g = Function(FST) # primary variable u = (U_hat, g) H_hat = Function(VFST) H_hat0 = Function(VFST) H_hat1 = Function(VFST) dU = Function(VFS) hv = Function(FSB) hg = Function(FST) Source = Array(VFS) Sk = Function(VFS) K2 = K[1]*K[1]+K[2]*K[2] K4 = K2**2 K_over_K2 = np.zeros((2,)+g.shape) for i in range(2): K_over_K2[i] = K[i+1] / np.where(K2 == 0, 1, K2) for i in range(3): K[i] = K[i].astype(float) work = work_arrays() u_dealias = Array(VFSp) u0_hat = np.zeros((2, params.N[0]), dtype=complex) h0_hat = np.zeros((2, params.N[0]), dtype=complex) w = np.zeros((params.N[0], ), dtype=complex) w1 = np.zeros((params.N[0], ), dtype=complex) nu, dt, N = params.nu, params.dt, params.N alfa = K2[0] - 2.0/nu/dt # Collect all matrices mat = config.AttributeDict( dict(CDD=inner_product((ST, 0), (ST, 1)), AB=HelmholtzCoeff(N[0], 1., -(K2 - 2.0/nu/dt), 0, ST.quad), AC=BiharmonicCoeff(N[0], nu*dt/2., (1. - nu*dt*K2), -(K2 - nu*dt/2.*K4), 0, SB.quad), # Matrices for biharmonic equation CBD=inner_product((SB, 0), (ST, 1)), ABB=inner_product((SB, 0), (SB, 2)), BBB=inner_product((SB, 0), (SB, 0)), SBB=inner_product((SB, 0), (SB, 4)), # Matrices for Helmholtz equation ADD=inner_product((ST, 0), (ST, 2)), BDD=inner_product((ST, 0), (ST, 0)), BBD=inner_product((SB, 0), (ST, 0)), CDB=inner_product((ST, 0), (SB, 1)), ADD0=inner_product((ST0, 0), (ST0, 2)), BDD0=inner_product((ST0, 0), (ST0, 0)),)) la = config.AttributeDict( dict(HelmholtzSolverG=Helmholtz(mat.ADD, mat.BDD, -np.ones((1, 1, 1)), (K2+2.0/nu/dt)), BiharmonicSolverU=Biharmonic(mat.SBB, mat.ABB, mat.BBB, -nu*dt/2.*np.ones((1, 1, 1)), (1.+nu*dt*K2), (-(K2 + nu*dt/2.*K4))), HelmholtzSolverU0=Helmholtz(mat.ADD0, mat.BDD0, np.array([-1.]), np.array([2./nu/dt])), TDMASolverD=TDMA(inner_product((ST, 0), (ST, 0))))) hdf5file = KMMFile(config.params.solver, checkpoint={'space': VFS, 'data': {'0': {'U': [U_hat]}, '1': {'U': [U_hat0]}}}, results={'space': VFS, 'data': {'U': [U]}}) return config.AttributeDict(locals())
def get_context(): """Set up context for solver""" # Get points and weights for Chebyshev weighted integrals assert params.Dquad == params.Bquad collapse_fourier = False if params.dealias == '3/2-rule' else True ST = Basis(params.N[0], 'C', bc=(0, 0), quad=params.Dquad) CT = Basis(params.N[0], 'C', quad=params.Dquad) CP = Basis(params.N[0], 'C', quad=params.Dquad) K0 = Basis(params.N[1], 'F', domain=(0, params.L[1]), dtype='D') K1 = Basis(params.N[2], 'F', domain=(0, params.L[2]), dtype='d') CP.slice = lambda: slice(0, CT.N) kw0 = {'threads': params.threads, 'planner_effort': params.planner_effort["dct"], 'slab': (params.decomposition == 'slab'), 'collapse_fourier': collapse_fourier} FST = TensorProductSpace(comm, (ST, K0, K1), **kw0) # Dirichlet FCT = TensorProductSpace(comm, (CT, K0, K1), **kw0) # Regular Chebyshev N FCP = TensorProductSpace(comm, (CP, K0, K1), **kw0) # Regular Chebyshev N-2 VFS = VectorTensorProductSpace(FST) VCT = VectorTensorProductSpace(FCT) VQ = MixedTensorProductSpace([VFS, FCP]) mask = FST.get_mask_nyquist() if params.mask_nyquist else None # Padded kw = {'padding_factor': 1.5 if params.dealias == '3/2-rule' else 1, 'dealias_direct': params.dealias == '2/3-rule'} if params.dealias == '3/2-rule': # Requires new bases due to planning and transforms on different size arrays STp = Basis(params.N[0], 'C', bc=(0, 0), quad=params.Dquad) CTp = Basis(params.N[0], 'C', quad=params.Dquad) else: STp, CTp = ST, CT K0p = Basis(params.N[1], 'F', dtype='D', domain=(0, params.L[1]), **kw) K1p = Basis(params.N[2], 'F', dtype='d', domain=(0, params.L[2]), **kw) FSTp = TensorProductSpace(comm, (STp, K0p, K1p), **kw0) FCTp = TensorProductSpace(comm, (CTp, K0p, K1p), **kw0) VFSp = VectorTensorProductSpace(FSTp) VCp = MixedTensorProductSpace([FSTp, FCTp, FCTp]) float, complex, mpitype = datatypes("double") constraints = ((3, 0, 0), (3, params.N[0]-1, 0)) # Mesh variables X = FST.local_mesh(True) x0, x1, x2 = FST.mesh() K = FST.local_wavenumbers(scaled=True) # Solution variables UP_hat = Function(VQ) UP_hat0 = Function(VQ) U_hat, P_hat = UP_hat U_hat0, P_hat0 = UP_hat0 UP = Array(VQ) UP0 = Array(VQ) U, P = UP U0, P0 = UP0 # primary variable u = UP_hat H_hat = Function(VFS) H_hat0 = Function(VFS) H_hat1 = Function(VFS) dU = Function(VQ) Source = Array(VFS) # Note - not using VQ. Only used for constant pressure gradient Sk = Function(VFS) K2 = K[1]*K[1]+K[2]*K[2] for i in range(3): K[i] = K[i].astype(float) work = work_arrays() u_dealias = Array(VFSp) curl_hat = Function(VCp) curl_dealias = Array(VCp) nu, dt, N = params.nu, params.dt, params.N up = TrialFunction(VQ) vq = TestFunction(VQ) ut, pt = up vt, qt = vq alfa = 2./nu/dt a0 = inner(vt, (2./nu/dt)*ut-div(grad(ut))) a1 = inner(vt, (2./nu)*grad(pt)) a2 = inner(qt, (2./nu)*div(ut)) M = BlockMatrix(a0+a1+a2) # Collect all matrices mat = config.AttributeDict( dict(CDD=inner_product((ST, 0), (ST, 1)), AB=HelmholtzCoeff(N[0], 1., alfa-K2, 0, ST.quad),)) la = None hdf5file = CoupledFile(config.params.solver, checkpoint={'space': VQ, 'data': {'0': {'UP': [UP_hat]}, '1': {'UP': [UP_hat0]}}}, results={'space': VFS, 'data': {'U': [U]}}) return config.AttributeDict(locals())
def get_context(): """Set up context for classical (NS) solver""" float, complex, mpitype = datatypes(params.precision) collapse_fourier = False if params.dealias == '3/2-rule' else True dim = len(params.N) dtype = lambda d: float if d == dim - 1 else complex V = [ Basis(params.N[i], 'F', domain=(0, params.L[i]), dtype=dtype(i)) for i in range(dim) ] kw0 = { 'threads': params.threads, 'planner_effort': params.planner_effort['fft'] } T = TensorProductSpace(comm, V, dtype=float, slab=(params.decomposition == 'slab'), collapse_fourier=collapse_fourier, **kw0) VT = VectorTensorProductSpace(T) # Different bases for nonlinear term, either 2/3-rule or 3/2-rule kw = { 'padding_factor': 1.5 if params.dealias == '3/2-rule' else 1, 'dealias_direct': params.dealias == '2/3-rule' } Vp = [ Basis(params.N[i], 'F', domain=(0, params.L[i]), dtype=dtype(i), **kw) for i in range(dim) ] Tp = TensorProductSpace(comm, Vp, dtype=float, slab=(params.decomposition == 'slab'), collapse_fourier=collapse_fourier, **kw0) VTp = VectorTensorProductSpace(Tp) # Mesh variables X = T.local_mesh(True) K = T.local_wavenumbers(scaled=True) for i in range(dim): X[i] = X[i].astype(float) K[i] = K[i].astype(float) K2 = np.zeros(T.shape(True), dtype=float) for i in range(dim): K2 += K[i] * K[i] # Set Nyquist frequency to zero on K that is, from now on, used for odd derivatives Kx = T.local_wavenumbers(scaled=True, eliminate_highest_freq=True) for i in range(dim): Kx[i] = Kx[i].astype(float) K_over_K2 = np.zeros(VT.shape(True), dtype=float) for i in range(dim): K_over_K2[i] = K[i] / np.where(K2 == 0, 1, K2) # Velocity and pressure. Use ndarray view for efficiency U = Array(VT) U_hat = Function(VT) P = Array(T) P_hat = Function(T) u_dealias = Array(VTp) # Primary variable u = U_hat # RHS array dU = Function(VT) curl = Array(VT) Source = Function(VT) # Possible source term initialized to zero work = work_arrays() hdf5file = NSFile(config.params.solver, checkpoint={ 'space': VT, 'data': { '0': { 'U': [U_hat] } } }, results={ 'space': VT, 'data': { 'U': [U], 'P': [P] } }) return config.AttributeDict(locals())
def get_context(): """Set up context for solver""" # Get points and weights for Chebyshev weighted integrals ST = ShenDirichletBasis(params.N[0], quad=params.Dquad) SB = ShenBiharmonicBasis(params.N[0], quad=params.Bquad) CT = Basis(params.N[0], quad=params.Dquad) ST0 = ShenDirichletBasis(params.N[0], quad=params.Dquad, plan=True) # For 1D problem K0 = C2CBasis(params.N[1], domain=(0, params.L[1])) K1 = R2CBasis(params.N[2], domain=(0, params.L[2])) #CT = ST.CT # Chebyshev transform FST = TensorProductSpace(comm, (ST, K0, K1), **{ 'threads': params.threads, 'planner_effort': params.planner_effort["dct"] }) # Dirichlet FSB = TensorProductSpace(comm, (SB, K0, K1), **{ 'threads': params.threads, 'planner_effort': params.planner_effort["dct"] }) # Biharmonic FCT = TensorProductSpace(comm, (CT, K0, K1), **{ 'threads': params.threads, 'planner_effort': params.planner_effort["dct"] }) # Regular Chebyshev VFS = VectorTensorProductSpace([FSB, FST, FST]) # Padded STp = ShenDirichletBasis(params.N[0], quad=params.Dquad) SBp = ShenBiharmonicBasis(params.N[0], quad=params.Bquad) CTp = Basis(params.N[0], quad=params.Dquad) K0p = C2CBasis(params.N[1], padding_factor=1.5, domain=(0, params.L[1])) K1p = R2CBasis(params.N[2], padding_factor=1.5, domain=(0, params.L[2])) FSTp = TensorProductSpace( comm, (STp, K0p, K1p), **{ 'threads': params.threads, 'planner_effort': params.planner_effort["dct"] }) FSBp = TensorProductSpace( comm, (SBp, K0p, K1p), **{ 'threads': params.threads, 'planner_effort': params.planner_effort["dct"] }) FCTp = TensorProductSpace( comm, (CTp, K0p, K1p), **{ 'threads': params.threads, 'planner_effort': params.planner_effort["dct"] }) VFSp = VectorTensorProductSpace([FSBp, FSTp, FSTp]) VFSp = VFS FCTp = FCT FSTp = FST FSBp = FSB Nu = params.N[0] - 2 # Number of velocity modes in Shen basis Nb = params.N[0] - 4 # Number of velocity modes in Shen biharmonic basis u_slice = slice(0, Nu) v_slice = slice(0, Nb) float, complex, mpitype = datatypes("double") # Mesh variables X = FST.local_mesh(True) x0, x1, x2 = FST.mesh() K = FST.local_wavenumbers(scaled=True) # Solution variables U = Array(VFS, False) U0 = Array(VFS, False) U_hat = Array(VFS) U_hat0 = Array(VFS) g = Array(FST) # primary variable u = (U_hat, g) H_hat = Array(VFS) H_hat0 = Array(VFS) H_hat1 = Array(VFS) dU = Array(VFS) hv = Array(FST) hg = Array(FST) Source = Array(VFS, False) Sk = Array(VFS) K2 = K[1] * K[1] + K[2] * K[2] K_over_K2 = np.zeros((2, ) + g.shape) for i in range(2): K_over_K2[i] = K[i + 1] / np.where(K2 == 0, 1, K2) work = work_arrays() nu, dt, N = params.nu, params.dt, params.N K4 = K2**2 kx = K[0][:, 0, 0] alfa = K2[0] - 2.0 / nu / dt # Collect all matrices mat = config.AttributeDict( dict( CDD=inner_product((ST, 0), (ST, 1)), AB=HelmholtzCoeff(kx, -1.0, -alfa, ST.quad), AC=BiharmonicCoeff(kx, nu * dt / 2., (1. - nu * dt * K2[0]), -(K2[0] - nu * dt / 2. * K4[0]), quad=SB.quad), # Matrices for biharmonic equation CBD=inner_product((SB, 0), (ST, 1)), ABB=inner_product((SB, 0), (SB, 2)), BBB=inner_product((SB, 0), (SB, 0)), SBB=inner_product((SB, 0), (SB, 4)), # Matrices for Helmholtz equation ADD=inner_product((ST, 0), (ST, 2)), BDD=inner_product((ST, 0), (ST, 0)), BBD=inner_product((SB, 0), (ST, 0)), CDB=inner_product((ST, 0), (SB, 1)), ADD0=inner_product((ST0, 0), (ST0, 2)), BDD0=inner_product((ST0, 0), (ST0, 0)), )) # Collect all linear algebra solvers #la = config.AttributeDict(dict( #HelmholtzSolverG = Helmholtz(N[0], np.sqrt(K2[0]+2.0/nu/dt), ST), #BiharmonicSolverU = Biharmonic(N[0], -nu*dt/2., 1.+nu*dt*K2[0], #-(K2[0] + nu*dt/2.*K4[0]), quad=SB.quad, #solver="cython"), #HelmholtzSolverU0 = Helmholtz(N[0], np.sqrt(2./nu/dt), ST), #TDMASolverD = TDMA(inner_product((ST, 0), (ST, 0))) #) #) mat.ADD.axis = 0 mat.BDD.axis = 0 mat.SBB.axis = 0 la = config.AttributeDict( dict(HelmholtzSolverG=Helmholtz(mat.ADD, mat.BDD, -np.ones( (1, 1, 1)), (K2[0] + 2.0 / nu / dt)[np.newaxis, :, :]), BiharmonicSolverU=Biharmonic( mat.SBB, mat.ABB, mat.BBB, -nu * dt / 2. * np.ones( (1, 1, 1)), (1. + nu * dt * K2[0])[np.newaxis, :, :], (-(K2[0] + nu * dt / 2. * K4[0]))[np.newaxis, :, :]), HelmholtzSolverU0=old_Helmholtz(N[0], np.sqrt(2. / nu / dt), ST), TDMASolverD=TDMA(inner_product((ST, 0), (ST, 0))))) hdf5file = KMMWriter({ "U": U[0], "V": U[1], "W": U[2] }, chkpoint={ 'current': { 'U': U }, 'previous': { 'U': U0 } }, filename=params.solver + ".h5", mesh={ "x": x0, "y": x1, "z": x2 }) return config.AttributeDict(locals())
def get_context(): """Set up context for solver""" # Get points and weights for Chebyshev weighted integrals assert params.Dquad == params.Bquad collapse_fourier = False if params.dealias == '3/2-rule' else True ST = Basis(params.N[2], 'C', bc=(0, 0), quad=params.Dquad) SB = Basis(params.N[2], 'C', bc='Biharmonic', quad=params.Bquad) CT = Basis(params.N[2], 'C', quad=params.Dquad) ST0 = Basis(params.N[2], 'C', bc=(0, 0), quad=params.Dquad) # For 1D problem K0 = Basis(params.N[0], 'F', domain=(0, params.L[0]), dtype='D') K1 = Basis(params.N[1], 'F', domain=(0, params.L[1]), dtype='d') kw0 = {'threads':params.threads, 'planner_effort':params.planner_effort["dct"], 'slab': (params.decomposition == 'slab'), 'collapse_fourier': collapse_fourier} FST = TensorProductSpace(comm, (K0, K1, ST), axes=(2, 0, 1), **kw0) # Dirichlet FSB = TensorProductSpace(comm, (K0, K1, SB), axes=(2, 0, 1), **kw0) # Biharmonic FCT = TensorProductSpace(comm, (K0, K1, CT), axes=(2, 0, 1), **kw0) # Regular Chebyshev VFS = MixedTensorProductSpace([FST, FST, FSB]) VFST = MixedTensorProductSpace([FST, FST, FST]) VUG = MixedTensorProductSpace([FST, FSB]) # Padded kw = {'padding_factor': 1.5 if params.dealias == '3/2-rule' else 1, 'dealias_direct': params.dealias == '2/3-rule'} if params.dealias == '3/2-rule': # Requires new bases due to planning and transforms on different size arrays STp = Basis(params.N[2], 'C', bc=(0, 0), quad=params.Dquad) SBp = Basis(params.N[2], 'C', bc='Biharmonic', quad=params.Bquad) CTp = Basis(params.N[2], 'C', quad=params.Dquad) else: STp, SBp, CTp = ST, SB, CT K0p = Basis(params.N[0], 'F', dtype='D', domain=(0, params.L[0]), **kw) K1p = Basis(params.N[1], 'F', dtype='d', domain=(0, params.L[1]), **kw) FSTp = TensorProductSpace(comm, (K0p, K1p, STp), axes=(2, 0, 1), **kw0) FSBp = TensorProductSpace(comm, (K0p, K1p, SBp), axes=(2, 0, 1), **kw0) FCTp = TensorProductSpace(comm, (K0p, K1p, CTp), axes=(2, 0, 1), **kw0) VFSp = MixedTensorProductSpace([FSTp, FSTp, FSBp]) Nu = params.N[2]-2 # Number of velocity modes in Shen basis Nb = params.N[2]-4 # Number of velocity modes in Shen biharmonic basis u_slice = slice(0, Nu) v_slice = slice(0, Nb) float, complex, mpitype = datatypes("double") # Mesh variables X = FST.local_mesh(True) x0, x1, x2 = FST.mesh() K = FST.local_wavenumbers(scaled=True) # Solution variables U = Array(VFS) U0 = Array(VFS) U_hat = Function(VFS) U_hat0 = Function(VFS) g = Function(FST) # primary variable u = (U_hat, g) H_hat = Function(VFST) H_hat0 = Function(VFST) H_hat1 = Function(VFST) dU = Function(VUG) hv = Function(FST) hg = Function(FST) Source = Array(VFS) Sk = Function(VFS) K2 = K[0]*K[0]+K[1]*K[1] K4 = K2**2 # Set Nyquist frequency to zero on K that is used for odd derivatives in nonlinear terms Kx = FST.local_wavenumbers(scaled=True, eliminate_highest_freq=True) K_over_K2 = np.zeros((2,)+g.shape) for i in range(2): K_over_K2[i] = K[i] / np.where(K2 == 0, 1, K2) work = work_arrays() u_dealias = Array(VFSp) u0_hat = np.zeros((2, params.N[2]), dtype=complex) h0_hat = np.zeros((2, params.N[2]), dtype=complex) w = np.zeros((params.N[2], ), dtype=complex) w1 = np.zeros((params.N[2], ), dtype=complex) nu, dt, N = params.nu, params.dt, params.N # Collect all matrices mat = config.AttributeDict( dict(CDD=inner_product((ST, 0), (ST, 1)), CTD=inner_product((CT, 0), (ST, 1)), BTT=inner_product((CT, 0), (CT, 0)), AB=HelmholtzCoeff(N[2], 1.0, -(K2 - 2.0/nu/dt), 2, ST.quad), AC=BiharmonicCoeff(N[2], nu*dt/2., (1. - nu*dt*K2), -(K2 - nu*dt/2.*K4), 2, SB.quad), # Matrices for biharmonic equation CBD=inner_product((SB, 0), (ST, 1)), ABB=inner_product((SB, 0), (SB, 2)), BBB=inner_product((SB, 0), (SB, 0)), SBB=inner_product((SB, 0), (SB, 4)), # Matrices for Helmholtz equation ADD=inner_product((ST, 0), (ST, 2)), BDD=inner_product((ST, 0), (ST, 0)), BBD=inner_product((SB, 0), (ST, 0)), CDB=inner_product((ST, 0), (SB, 1)), ADD0=inner_product((ST0, 0), (ST0, 2)), BDD0=inner_product((ST0, 0), (ST0, 0)))) la = config.AttributeDict( dict(HelmholtzSolverG=Helmholtz(mat.ADD, mat.BDD, -np.ones((1, 1, 1)), (K2+2.0/nu/dt)), BiharmonicSolverU=Biharmonic(mat.SBB, mat.ABB, mat.BBB, -nu*dt/2.*np.ones((1, 1, 1)), (1.+nu*dt*K2), (-(K2 + nu*dt/2.*K4))), HelmholtzSolverU0=Helmholtz(mat.ADD0, mat.BDD0, np.array([-1.]), np.array([2./nu/dt])), TDMASolverD=TDMA(inner_product((ST, 0), (ST, 0))))) hdf5file = KMMFile(config.params.solver, checkpoint={'space': VFS, 'data': {'0': {'U': [U_hat]}, '1': {'U': [U_hat0]}}}, results={'space': VFS, 'data': {'U': [U]}}) return config.AttributeDict(locals())
def get_context(): """Set up context for solver""" # Get points and weights for Chebyshev weighted integrals assert params.Dquad == params.Bquad ST = Basis(params.N[0], 'C', bc=(0, 0), quad=params.Dquad) SB = Basis(params.N[0], 'C', bc='Biharmonic', quad=params.Bquad) CT = Basis(params.N[0], 'C', quad=params.Dquad) ST0 = Basis(params.N[0], 'C', bc=(0, 0), quad=params.Dquad) # For 1D problem K0 = Basis(params.N[1], 'F', domain=(0, params.L[1]), dtype='D') K1 = Basis(params.N[2], 'F', domain=(0, params.L[2]), dtype='d') kw0 = { 'threads': params.threads, 'planner_effort': params.planner_effort["dct"] } FST = TensorProductSpace(comm, (ST, K0, K1), axes=(0, 1, 2), collapse_fourier=False, **kw0) # Dirichlet FSB = TensorProductSpace(comm, (SB, K0, K1), axes=(0, 1, 2), collapse_fourier=False, **kw0) # Biharmonic FCT = TensorProductSpace(comm, (CT, K0, K1), axes=(0, 1, 2), collapse_fourier=False, **kw0) # Regular Chebyshev VFS = MixedTensorProductSpace([FSB, FST, FST]) VUG = MixedTensorProductSpace([FSB, FST]) # Padded kw = { 'padding_factor': 1.5 if params.dealias == '3/2-rule' else 1, 'dealias_direct': params.dealias == '2/3-rule' } if params.dealias == '3/2-rule': # Requires new bases due to planning and transforms on different size arrays STp = Basis(params.N[0], 'C', bc=(0, 0), quad=params.Dquad) SBp = Basis(params.N[0], 'C', bc='Biharmonic', quad=params.Bquad) CTp = Basis(params.N[0], 'C', quad=params.Dquad) else: STp, SBp, CTp = ST, SB, CT K0p = Basis(params.N[1], 'F', dtype='D', domain=(0, params.L[1]), **kw) K1p = Basis(params.N[2], 'F', dtype='d', domain=(0, params.L[2]), **kw) FSTp = TensorProductSpace(comm, (STp, K0p, K1p), axes=(0, 1, 2), collapse_fourier=False, **kw0) FSBp = TensorProductSpace(comm, (SBp, K0p, K1p), axes=(0, 1, 2), collapse_fourier=False, **kw0) FCTp = TensorProductSpace(comm, (CTp, K0p, K1p), axes=(0, 1, 2), collapse_fourier=False, **kw0) VFSp = MixedTensorProductSpace([FSBp, FSTp, FSTp]) Nu = params.N[0] - 2 # Number of velocity modes in Shen basis Nb = params.N[0] - 4 # Number of velocity modes in Shen biharmonic basis u_slice = slice(0, Nu) v_slice = slice(0, Nb) float, complex, mpitype = datatypes("double") # Mesh variables X = FST.local_mesh(True) x0, x1, x2 = FST.mesh() K = FST.local_wavenumbers(scaled=True) # Solution variables U = Array(VFS) U0 = Array(VFS) U_hat = Function(VFS) U_hat0 = Function(VFS) g = Function(FST) # primary variable u = (U_hat, g) H_hat = Function(VFS) H_hat0 = Function(VFS) H_hat1 = Function(VFS) dU = Function(VUG) hv = Function(FST) hg = Function(FST) Source = Array(VFS) Sk = Function(VFS) K2 = K[1] * K[1] + K[2] * K[2] K4 = K2**2 # Set Nyquist frequency to zero on K that is used for odd derivatives in nonlinear terms Kx = FST.local_wavenumbers(scaled=True, eliminate_highest_freq=True) K_over_K2 = np.zeros((2, ) + g.shape) for i in range(2): K_over_K2[i] = K[i + 1] / np.where(K2 == 0, 1, K2) work = work_arrays() nu, dt, N = params.nu, params.dt, params.N alfa = K2[0] - 2.0 / nu / dt # Collect all matrices mat = config.AttributeDict( dict( CDD=inner_product((ST, 0), (ST, 1)), AB=HelmholtzCoeff(N[0], 1.0, -(K2 - 2.0 / nu / dt), ST.quad), AC=BiharmonicCoeff(N[0], nu * dt / 2., (1. - nu * dt * K2), -(K2 - nu * dt / 2. * K4), quad=SB.quad), # Matrices for biharmonic equation CBD=inner_product((SB, 0), (ST, 1)), ABB=inner_product((SB, 0), (SB, 2)), BBB=inner_product((SB, 0), (SB, 0)), SBB=inner_product((SB, 0), (SB, 4)), # Matrices for Helmholtz equation ADD=inner_product((ST, 0), (ST, 2)), BDD=inner_product((ST, 0), (ST, 0)), BBD=inner_product((SB, 0), (ST, 0)), CDB=inner_product((ST, 0), (SB, 1)), ADD0=inner_product((ST0, 0), (ST0, 2)), BDD0=inner_product((ST0, 0), (ST0, 0)), )) ## Collect all linear algebra solvers #la = config.AttributeDict(dict( #HelmholtzSolverG = old_Helmholtz(N[0], np.sqrt(K2[0]+2.0/nu/dt), ST), #BiharmonicSolverU = old_Biharmonic(N[0], -nu*dt/2., 1.+nu*dt*K2[0], #-(K2[0] + nu*dt/2.*K4[0]), quad=SB.quad, #solver="cython"), #HelmholtzSolverU0 = old_Helmholtz(N[0], np.sqrt(2./nu/dt), ST), #TDMASolverD = TDMA(inner_product((ST, 0), (ST, 0))) #) #) mat.ADD.axis = 0 mat.BDD.axis = 0 mat.SBB.axis = 0 la = config.AttributeDict( dict(HelmholtzSolverG=Helmholtz(mat.ADD, mat.BDD, -np.ones( (1, 1, 1)), (K2[0] + 2.0 / nu / dt)[np.newaxis, :, :]), BiharmonicSolverU=Biharmonic( mat.SBB, mat.ABB, mat.BBB, -nu * dt / 2. * np.ones( (1, 1, 1)), (1. + nu * dt * K2[0])[np.newaxis, :, :], (-(K2[0] + nu * dt / 2. * K4[0]))[np.newaxis, :, :]), HelmholtzSolverU0=Helmholtz(mat.ADD0, mat.BDD0, np.array([-1.]), np.array([2. / nu / dt])), TDMASolverD=TDMA(inner_product((ST, 0), (ST, 0))))) hdf5file = KMMWriter({ "U": U[0], "V": U[1], "W": U[2] }, chkpoint={ 'current': { 'U': U }, 'previous': { 'U': U0 } }, filename=params.solver + ".h5", mesh={ "x": x0, "y": x1, "z": x2 }) return config.AttributeDict(locals())
N = int(sys.argv[-2]) N = [N, N + 1, N + 2] #N = (14, 15, 16) SD = FunctionSpace(N[1], family=family, bc=(a, b)) K1 = FunctionSpace(N[0], family='F', dtype='D') K2 = FunctionSpace(N[2], family='F', dtype='d') subcomms = Subcomm(MPI.COMM_WORLD, [0, 0, 1]) T = TensorProductSpace(subcomms, (K1, SD, K2), axes=(1, 0, 2)) u = TrialFunction(T) v = TestFunction(T) # Get manufactured right hand side fe = div(grad(u)).tosympy(basis=ue) K = T.local_wavenumbers() # Get f on quad points fj = Array(T, buffer=fe) # Compute right hand side of Poisson equation f_hat = inner(v, fj) # Get left hand side of Poisson equation matrices = inner(v, div(grad(u))) # Create Helmholtz linear algebra solver H = Solver(*matrices) # Solve and transform to real space u_hat = Function(T) # Solution spectral space
def get_context(): """Set up context for classical (NS) solver""" float, complex, mpitype = datatypes(params.precision) collapse_fourier = False if params.dealias == '3/2-rule' else True dim = len(params.N) dtype = lambda d: float if d == dim-1 else complex V = [Basis(params.N[i], 'F', domain=(0, params.L[i]), dtype=dtype(i)) for i in range(dim)] kw0 = {'threads': params.threads, 'planner_effort': params.planner_effort['fft']} T = TensorProductSpace(comm, V, dtype=float, slab=(params.decomposition == 'slab'), collapse_fourier=collapse_fourier, **kw0) VT = VectorTensorProductSpace(T) # Different bases for nonlinear term, either 2/3-rule or 3/2-rule kw = {'padding_factor': 1.5 if params.dealias == '3/2-rule' else 1, 'dealias_direct': params.dealias == '2/3-rule'} Vp = [Basis(params.N[i], 'F', domain=(0, params.L[i]), dtype=dtype(i), **kw) for i in range(dim)] Tp = TensorProductSpace(comm, Vp, dtype=float, slab=(params.decomposition == 'slab'), collapse_fourier=collapse_fourier, **kw0) VTp = VectorTensorProductSpace(Tp) # Mesh variables X = T.local_mesh(True) K = T.local_wavenumbers(scaled=True) for i in range(dim): X[i] = X[i].astype(float) K[i] = K[i].astype(float) K2 = np.zeros(T.shape(True), dtype=float) for i in range(dim): K2 += K[i]*K[i] # Set Nyquist frequency to zero on K that is, from now on, used for odd derivatives Kx = T.local_wavenumbers(scaled=True, eliminate_highest_freq=True) for i in range(dim): Kx[i] = Kx[i].astype(float) K_over_K2 = np.zeros(VT.shape(True), dtype=float) for i in range(dim): K_over_K2[i] = K[i] / np.where(K2 == 0, 1, K2) # Velocity and pressure. Use ndarray view for efficiency U = Array(VT) U_hat = Function(VT) P = Array(T) P_hat = Function(T) u_dealias = Array(VTp) # Primary variable u = U_hat # RHS array dU = Function(VT) curl = Array(VT) Source = Function(VT) # Possible source term initialized to zero work = work_arrays() hdf5file = NSFile(config.params.solver, checkpoint={'space': VT, 'data': {'0': {'U': [U_hat]}}}, results={'space': VT, 'data': {'U': [U], 'P': [P]}}) return config.AttributeDict(locals())
def get_context(): float, complex, mpitype = datatypes(params.precision) collapse_fourier = False if params.dealias == '3/2-rule' else True dim = len(params.N) dtype = lambda d: float if d == dim-1 else complex V = [Basis(params.N[i], 'F', domain=(0, params.L[i]), dtype=dtype(i)) for i in range(dim)] kw0 = {'threads': params.threads, 'planner_effort': params.planner_effort['fft']} T = TensorProductSpace(comm, V, dtype=float, slab=(params.decomposition == 'slab'), collapse_fourier=collapse_fourier, **kw0) VT = VectorTensorProductSpace(T) VM = MixedTensorProductSpace([T]*2*dim) kw = {'padding_factor': 1.5 if params.dealias == '3/2-rule' else 1, 'dealias_direct': params.dealias == '2/3-rule'} Vp = [Basis(params.N[i], 'F', domain=(0, params.L[i]), dtype=dtype(i), **kw) for i in range(dim)] Tp = TensorProductSpace(comm, Vp, dtype=float, slab=(params.decomposition == 'slab'), collapse_fourier=collapse_fourier, **kw0) VTp = VectorTensorProductSpace(Tp) VMp = MixedTensorProductSpace([Tp]*2*dim) # Mesh variables X = T.local_mesh(True) K = T.local_wavenumbers(scaled=True) for i in range(dim): X[i] = X[i].astype(float) K[i] = K[i].astype(float) K2 = np.zeros(T.shape(True), dtype=float) for i in range(dim): K2 += K[i]*K[i] # Set Nyquist frequency to zero on K that is, from now on, used for odd derivatives Kx = T.local_wavenumbers(scaled=True, eliminate_highest_freq=True) for i in range(dim): Kx[i] = Kx[i].astype(float) K_over_K2 = np.zeros(VT.shape(True), dtype=float) for i in range(dim): K_over_K2[i] = K[i] / np.where(K2 == 0, 1, K2) UB = Array(VM) P = Array(T) curl = Array(VT) UB_hat = Function(VM) P_hat = Function(T) dU = Function(VM) Source = Array(VM) ub_dealias = Array(VMp) ZZ_hat = np.zeros((3, 3) + Tp.shape(True), dtype=complex) # Work array # Create views into large data structures U = UB[:3] U_hat = UB_hat[:3] B = UB[3:] B_hat = UB_hat[3:] # Primary variable u = UB_hat hdf5file = MHDFile(config.params.solver, checkpoint={'space': VM, 'data': {'0': {'UB': [UB_hat]}}}, results={'space': VM, 'data': {'UB': [UB]}}) return config.AttributeDict(locals())