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""" 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(): """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 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())
gn = Array(FY, buffer=neumann_condition) evaluate_x_bndry = FX.evaluate_basis_all(-1) project_g = inner(gn, v_bndry) bndry_integral = np.outer(evaluate_x_bndry, project_g) rhs -= bndry_integral Sol = sf.la.SolverGeneric2ND(mat) u_hat = Function(T) u_hat = Sol(rhs, u_hat) u_ana = Array(T, buffer=ua) l2_error = np.linalg.norm(u_hat.backward() - u_ana) print(l2_error) xx, yy = T.mesh() X, Y = np.meshgrid(xx.squeeze(), yy.squeeze()) fig = plt.figure() ax = fig.add_subplot(1, 2, 1, projection='3d') ax.plot_surface(X, Y, np.transpose(u_ana)) ax.set_xlabel('x') ax.set_ylabel('y') ax = fig.add_subplot(1, 2, 2, projection='3d') ax.plot_surface(X, Y, np.transpose(u_hat.backward())) ax.set_xlabel('x') ax.set_ylabel('y')