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Conatus
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Conatus
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Conatus 0.1.1 · CPU supported, GPU (CUDA 12) in beta

Getting started

  • Installation
  • Tutorials
    • Getting started in ten minutes
    • 0. Getting started: convection between two plates
    • 1. A first eigenvalue problem: Orr–Sommerfeld
    • 2. A first initial-value problem: Rayleigh–Bénard 2D, CPU then GPU
    • 3. Symmetries and symmetry subspaces
    • 4. Nonlinear boundary-value problems and continuation: Bratu
    • 5. Invariant solutions: Kuramoto–Sivashinsky, L = 22
    • 8. Polar geometry: a drum, a pipe, two rotating cylinders
    • 10. Bifurcations: branch switching, cycles, codimension 2, normal forms
    • 11. Record, query, reproduce: the run registry
    • 12. Chaos and ensembles: Lyapunov spectrum, covariant vectors, Poincaré map, basins
    • 13. Where a global mode is born, and what the data say about it
    • 14. Coming from Dedalus
    • 15. Covariant Lyapunov vectors of Kuramoto–Sivashinsky: tangencies and the physical modes
    • 16. Lagrangian tracers and a numerical dye

Using Conatus

  • User guide
    • Geometries
    • Spherical shells
    • Channels between two surfaces
    • Equations
    • Boundary conditions
    • Ready problems
    • Units and conventions
    • Simulations and time steppers
    • Resolution
    • GPU
    • Diagnostics and visualization
    • Particles and dye of a simulation
    • Input and output
    • The Studio
    • Pilot a run from a script or an agent
    • For AI agents
    • Notebooks
    • Dynamics
      • Eigenvalues and stability
      • Onset of convection
      • Non-modal analysis
      • Invariant solutions
      • Continuation and bifurcations
      • Floquet analysis
      • Eigenvalues in a region
      • Chaos and ensembles
      • Invariant manifolds and slices
      • Symmetry subspaces
      • Adjoints and sensitivity
      • Tangent, adjoint and optimal perturbations
      • Data-driven analysis
    • explain() and the Methods paragraph
    • Numerical uncertainty
    • The run registry
    • Reproducibility and provenance
    • Checking an installation
    • Errors and what they mean
    • Experimental features
    • Coming from Dedalus
    • The expert layer
    • IR and operators
    • Bases and domains
    • Tau terms by hand
  • Gallery: fluids everywhere
    • Weakly nonlinear theory derived from the IR: Landau and Ginzburg–Landau coefficients
    • Rayleigh–Bénard onset in 3D: the nonlinear Boussinesq equations, linearized by the IR
    • Onset of rotating Rayleigh–Bénard convection on the f-plane (Chandrasekhar 1961, Ch. III)
    • Salt fingers: stationary double-diffusive onset in a layer with free walls (Stern 1960; Baines & Gill 1969, J. Fluid Mech. 37, 289-306)
    • Phase-space geometry in three steps
    • Womersley flow in a plane channel: exact profile (LBVP and IVP) and Floquet stability (Hill)
    • Turing instability of the Brusselator (Prigogine & Lefever 1968)
    • Complex Ginzburg–Landau equation: Benjamin–Feir–Newell and Eckhaus instabilities of plane waves
    • Swift–Hohenberg: onset of rolls, weakly nonlinear amplitude, roll branch by continuation, 2D rolls
    • Kelvin–Helmholtz instability of the tanh mixing layer (Michalke 1964), inviscid and viscous
    • Non-modal stability of plane Poiseuille flow: transient growth and the continuous adjoint
    • Wavemaker and base-flow sensitivity of Orszag’s Tollmien-Schlichting mode (plane Poiseuille, Re = 1e4, alpha = 1), then the steady-forcing sensitivity
    • Stratified Kelvin–Helmholtz: Taylor–Goldstein equation for the tanh/tanh layer (Hazel 1972)
  • API reference
    • User layer: import conatus as cn
      • conatus.Box
      • conatus.Channel
      • conatus.Disk
      • conatus.Annulus
      • conatus.Pipe
      • conatus.Sphere
      • conatus.Ball
      • conatus.Shell
      • conatus.TaylorCouette
      • conatus.MappedBox
      • conatus.periodic
      • conatus.walls
      • conatus.line
      • conatus.half_line
      • conatus.between
      • conatus.no_slip
      • conatus.free_slip
      • conatus.navier_slip
      • conatus.Model
      • conatus.model.Simulation
      • conatus.model.Linearization
      • conatus.model.Compiled
      • conatus.problems.channel
      • conatus.problems.channel_evp
      • conatus.problems.plane_couette
      • conatus.problems.plane_couette_evp
      • conatus.problems.rayleigh_benard
      • conatus.problems.rayleigh_benard_evp
      • conatus.problems.taylor_couette
      • conatus.problems.taylor_couette_evp
      • conatus.problems.pipe
      • conatus.problems.pipe_evp
      • conatus.problems.kuramoto_sivashinsky
      • conatus.problems.kolmogorov
      • conatus.problems.swift_hohenberg
      • conatus.problems.rotating_shell_convection
      • conatus.problems.rotating_shell_convection_evp
      • conatus.problems.Ready
      • conatus.runs.track
      • conatus.runs.record
      • conatus.runs.find
      • conatus.runs.get
      • conatus.runs.compare
      • conatus.runs.lineage
      • conatus.runs.reproduce
      • conatus.runs.to_dataframe
      • conatus.runs.export
      • conatus.runs.explain
      • conatus.runs.Run
      • conatus.runs.RunList
      • conatus.runs.Registry
      • conatus.series
      • conatus.spectrum
      • conatus.profile
      • conatus.view
      • conatus.time_average
      • conatus.uncertainty
      • conatus.StopRun
      • conatus.doctor
      • conatus.from_dedalus
      • conatus.parse_equation
      • conatus.parse_expr
      • conatus.box
      • conatus.contour.count
      • conatus.contour.beyn
      • conatus.contour.CountResult
      • conatus.contour.BeynResult
      • conatus.contour.RegionEVPResult
    • Expert layer: conatus.expert
      • Expert layer by module
        • conatus.expert.Check
        • conatus.expert.VerificationReport
        • conatus.expert.verify
        • conatus.expert.CartesianCoordinates
        • conatus.expert.PolarCoordinates
        • conatus.expert.CylindricalCoordinates
        • conatus.expert.S2Coordinates
        • conatus.expert.SphericalCoordinates
        • conatus.expert.RealFourier
        • conatus.expert.ComplexFourier
        • conatus.expert.Jacobi
        • conatus.expert.Chebyshev
        • conatus.expert.ChebyshevT
        • conatus.expert.ChebyshevU
        • conatus.expert.ChebyshevV
        • conatus.expert.Legendre
        • conatus.expert.Ultraspherical
        • conatus.expert.DiskBasis
        • conatus.expert.AnnulusBasis
        • conatus.expert.SphereBasis
        • conatus.expert.ShellBasis
        • conatus.expert.BallBasis
        • conatus.expert.Hermite
        • conatus.expert.Laguerre
        • conatus.expert.CompoundChebyshev
        • conatus.expert.Domain
        • conatus.expert.Field
        • conatus.expert.VectorField
        • conatus.expert.TensorField
        • conatus.expert.Parameter
        • conatus.expert.dot
        • conatus.expert.cross
        • conatus.expert.outer
        • conatus.expert.conj
        • conatus.expert.comp
        • conatus.expert.diff
        • conatus.expert.grad
        • conatus.expert.div
        • conatus.expert.lap
        • conatus.expert.curl
        • conatus.expert.dt
        • conatus.expert.integ
        • conatus.expert.interp
        • conatus.expert.lift
        • conatus.expert.unit_vector
        • conatus.expert.exp
        • conatus.expert.log
        • conatus.expert.sin
        • conatus.expert.cos
        • conatus.expert.tanh
        • conatus.expert.sqrt
        • conatus.expert.absolute
        • conatus.expert.sign
        • conatus.expert.Problem
        • conatus.expert.IVP
        • conatus.expert.LBVP
        • conatus.expert.EVP
        • conatus.expert.NLBVP
        • conatus.expert.NonlinearLHSError
        • conatus.expert.ProblemError
        • conatus.expert.RankReport
        • conatus.expert.EVEN
        • conatus.expert.ODD
        • conatus.expert.Reflection
        • conatus.expert.SymmetrySubspace
        • conatus.expert.SymmetryError
        • conatus.expert.SymmetryBreakingError
        • conatus.expert.ShiftReflect
        • conatus.expert.AzimuthalMFold
        • conatus.expert.EquatorialParity
        • conatus.expert.MappedChebyshev
        • conatus.expert.RationalMap
        • conatus.expert.TanhMap
        • conatus.expert.TanMap
        • conatus.expert.parse_equation
        • conatus.expert.parse_expr
        • conatus.expert.ChannelBaseFlow
        • conatus.expert.channel
        • conatus.expert.UnitSystem
        • conatus.expert.convert
        • conatus.expert.Energy
        • conatus.expert.ChannelUnits
        • conatus.expert.DiscretizationError
        • conatus.expert.LBVPSolution
        • conatus.expert.Plan
        • conatus.expert.RankError
        • conatus.expert.discretize
        • conatus.expert.FieldData
        • conatus.expert.grid
        • conatus.expert.EVPResult
        • conatus.expert.solve_dense
        • conatus.expert.solve_sparse
        • conatus.expert.eigenvalues
        • conatus.expert.ParametricEVP
        • conatus.expert.CriticalPoint
        • conatus.expert.critical
        • conatus.expert.NewtonSolver
        • conatus.expert.NLBVPSolution
        • conatus.expert.NewtonNotConverged
        • conatus.expert.PeriodicNewtonSolver
        • conatus.expert.linearize
        • conatus.expert.InnerProduct
        • conatus.expert.CFL
        • conatus.expert.EmbeddedError
        • conatus.expert.TauWatch
        • conatus.expert.IVPSolver
        • conatus.expert.SCHEMES
        • conatus.expert.SpectralError
        • conatus.expert.FlowMap
        • conatus.expert.VJPSuspended
        • conatus.expert.revolve_cost
        • conatus.expert.FourierOps
        • conatus.expert.NewtonKrylovHookstep
        • conatus.expert.Equilibrium
        • conatus.expert.equilibrium_eigenvalues
        • conatus.expert.find_equilibrium
        • conatus.expert.find_travelling_wave
        • conatus.expert.find_relative_periodic_orbit
        • conatus.expert.floquet_multipliers
        • conatus.expert.symmetry_breaking_check
        • conatus.expert.EdgeTracker
        • conatus.expert.ThresholdBisection
        • conatus.expert.ContinuationSettings
        • conatus.expert.NLBVPContinuation
        • conatus.expert.KSDomainContinuation
        • conatus.expert.HillBlocks
        • conatus.expert.hill_from_plan
        • conatus.expert.secant_root
        • conatus.expert.exponents_dense
        • conatus.expert.HillGPU
        • conatus.expert.CertifiedRoot
        • conatus.expert.SecantRoot
        • conatus.expert.shell_floquet
        • conatus.expert.floquet_exponents
        • conatus.expert.optimal_gain
        • conatus.expert.periodic_operator
        • conatus.expert.energy_factor
        • conatus.expert.gain
        • conatus.expert.propagator
        • conatus.expert.Y
        • conatus.expert.compare_adjoints
        • conatus.expert.max_growth
        • conatus.expert.numerical_abscissa
        • conatus.expert.parallel_shear_flow
        • conatus.expert.state_space
        • conatus.expert.CHANNEL_SYSTEMS
        • conatus.expert.laminar_poiseuille
        • conatus.expert.methods
        • conatus.expert.ConatusError
        • conatus.expert.EquationError
        • conatus.expert.UndeclaredVariableError
        • conatus.expert.ParameterError
        • conatus.expert.BoundaryConditionError
        • conatus.expert.EquationSyntaxError
        • conatus.expert.ResolutionError
        • conatus.expert.CoordinateError
        • conatus.expert.OptionError
        • conatus.expert.InputTypeError
        • conatus.expert.DtypeError
        • conatus.expert.TensorError
        • conatus.expert.ConvergenceError
        • conatus.expert.NumericalError
        • conatus.expert.UnderResolvedWarning
        • conatus.expert.IllPosedWarning
        • conatus.expert.InitialDataWarning
        • conatus.expert.BackendError
        • conatus.expert.MissingDependencyError
        • conatus.expert.MissingFileError
        • conatus.expert.UnsupportedError
        • conatus.expert.AmbiguousNameError
        • conatus.expert.ResolutionWarning
        • conatus.expert.CorrectnessWarning
        • conatus.expert.BaseStateWarning
        • conatus.expert.GroupWarning
        • conatus.expert.DefaultChoiceWarning
        • conatus.expert.ExperimentalWarning
        • conatus.expert.gpu_available
        • conatus.expert.gpu_report
        • conatus.expert.ir_system
        • conatus.expert.ode_problem
        • conatus.expert.continue_equilibria
        • conatus.expert.normal_form
        • conatus.expert.CollocationMesh
        • conatus.expert.PeriodicOrbitProblem
        • conatus.expert.continue_orbits
        • conatus.expert.branch_switch
        • conatus.expert.continue_codim2
        • conatus.expert.amplitude_equation
        • conatus.expert.ginzburg_landau
        • conatus.expert.cos_mode_observable
        • conatus.expert.FirstFourierModeSlice
        • conatus.expert.find_rpo_in_slice
        • conatus.expert.slice_equilibrium_check
        • conatus.expert.PoincareSection
        • conatus.expert.first_return_map
        • conatus.expert.globalize
        • conatus.expert.unstable_manifold
        • conatus.expert.find_connection
        • conatus.expert.scan_connection
        • conatus.expert.ecs_system
        • conatus.expert.base_flow_sensitivity
        • conatus.expert.ginzburg_landau_exact
        • conatus.expert.linear_ginzburg_landau
        • conatus.expert.structural_sensitivity
        • conatus.expert.DMD
        • conatus.expert.DataInnerProduct
        • conatus.expert.SPOD
        • conatus.expert.dmd
        • conatus.expert.edmd
        • conatus.expert.monomials
        • conatus.expert.pod
        • conatus.expert.rbf
        • conatus.expert.spod
        • conatus.expert.kaplan_yorke
        • conatus.expert.lyapunov_spectrum
        • conatus.expert.poincare_section
        • conatus.expert.Ensemble
        • conatus.expert.ensemble_fate
        • conatus.expert.proportion_ci
        • conatus.expert.CountResult
        • conatus.expert.BeynResult
        • conatus.expert.RegionEVPResult

About

  • Principles
  • Mathematics
    • Spectral discretisation and the tau method
    • Curvilinear geometries: regular bases
    • Implicit–explicit time stepping
    • Eigenproblems, residuals and the physical adjoint
    • Invariant solutions: Newton–Krylov–hookstep
    • Continuation and bifurcations
    • Floquet–Hill analysis of time-periodic flows
    • Non-modal analysis: transient growth
    • Lyapunov exponents, covariant vectors and ensembles
    • Symmetry subspaces, slices and phase-space geometry
  • Citing Conatus
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conatus.expert.ProblemError¶

conatus.expert.ProblemError¶

alias of EquationError

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