11 March 2009 ICVT, Universit¨ at Stuttgart MAX-PLANCK-INSTITUT TECHNISCHER SYSTEME MAGDEBURG DYNAMIK KOMPLEXER O O T T V O N G U E R I C K E U N IV E R S I T Ä T M A G D E B U R G DIANA — A short introduction Michael Krasnyk Max Planck Institute for Dynamics of Complex Technical Systems, PSPD group Otto-von-Guericke-University, IFAT
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11 March 2009ICVT, Universitat Stuttgart
MAX−PLANCK−INSTITUT
TECHNISCHER SYSTEMEMAGDEBURG
DYNAMIK KOMPLEXER
O
O
TTV
ON
GU
ERIC
KE UNIVERSITÄT
MA
GD
EBU
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DIANA — A short introduction
Michael Krasnyk
Max Planck Institute for Dynamics of Complex Technical Systems, PSPD groupOtto-von-Guericke-University, IFAT
O
O
TTV
ON
GU
ER
ICKE UNIVERSITÄ
TM
AG
DE
BURG
Motivation
High demand for first principle modeling of chemical processes
Complexity of processes and models
Structure of implemented models
Goals of computer-based modeling
computer-aided process engineering
systematical modeling approaches
reusable and transparent models
Physically motivated concepts for structuring of balance based models
Dynamic solvers find solutions of the Cauchy problem ϕ(t, x0, ν), such that
f (t, ϕ, ϕ, ν) ≡ 0, s.t. ϕ(t0, x0, ν) = x0
Dynamic simulation is presented by the following solvers
IDASolver and DASPKSolver for implicit DAE systemswith differential index 1 (libraries ida.so and daspk.so)
OdessaSolver for ODE systems with ∂f /∂x = I (library odessa.so)
The linear systems in the integrators are solved by the direct dense LAPACK orsparse UMFPACK linear algebra solvers
For integrating a DAE initial-value problem, an important requirement is that thepair of vectors x0 and x0 are both initialized to satisfy the DAE residual
f (t0, x0, x0, ν) = 0
For semi-explicit differential index-one systems, IDA provides a routine thatcomputes consistent initial conditions from a user’s initial guess
Interface methodsGetParameters method returns collections of solver parameters
Solve method starts the solution of an ESO that is associated with the solver
GetSolution method returns the solution vector x
Solver parametersStart parameter specifies the start of a new simulation (True) or continuationof the current one (False)
CalcIC parameter controls whether consistent initial conditions are computed atthe initial time (True) or not (False)
T is the current value of the independent variable t
T0 is the starting value of the independent variable
Tend is the final value of the independent variable
Intermediate parameter with the True value tells the solver to take one internalstep and to return the solution at the point reached by that step, otherwiseintegration proceeds to the parameter value Tend without interruption
VerboseLevel controls a verbosity level of the solver
LASolver specifies whether the dense or sparse linear algebra solver will be used
Interface methodsSolve method solves a nonlinear task f (x , ν) = 0 for constant parameter νContinuate method performs a continuation with respect to parameter νAdd/RemoveFreeParameter method adds or removes λ to the nonlinear system
Continuation solver parametersParametrization parameter specifies the parametrization type (PseudoArclengthor Local)Predictor is the predictor type (Tangent or Chord)
StepSize is the current step size σ(k)
InitialStepSize is the initial step size σ(1)
InitialDirection is the initial direction of a continuationMinStepSize is the minimal step size σmin
MaxStepSize The is the maximal step size σmax
MaxStepsAmount is the maximal number of steps kmax
Tol relative tolerance in the argument spaceSteady-state continuation solver parameters
StabilityCheck, Stability parameters specify local stability check and stabilityof the current pointConditionCheck check for limit point SteadyStateZCE or Hopf point SteadyStateZREconditions
Singularity analysis solver parametersConditionCheck check for zeros of test functions (SingularityG[x|xx|p|xp])Gx,Gxx,Gp,Gxp values of test function derivativesConditionEquations set of adjoint test function equations
Nelder-Mead downhill simplex method implementation by D. E. Shaw
Gradient Based Methods
routine L-BFGS-B
Limited-memory quasi-Newton code for large-scale bound-constrained or un-constrained optimization by C. Zhu and J. Nocedal.
IPOpt
Package for large-scale nonlinear optimization of continuous systems, imple-ments a primal-dual interior point method, and uses line searches based onFilter methods and Hessian approximation using BFGS update.
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