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Author: Strogies, Nikolai × Type: Report ×

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Now showing 1 - 5 of 5
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    A Bayesian approach to parameter identification in gas networks
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2018) Hajian, Soheil; Hintermüller, Michael; Schillings, Claudia; Strogies, Nikolai
    The inverse problem of identifying the friction coefficient in an isothermal semilinear Euler system is considered. Adopting a Bayesian approach, the goal is to identify the distribution of the quantity of interest based on a finite number of noisy measurements of the pressure at the boundaries of the domain. First well-posedness of the underlying non-linear PDE system is shown using semigroup theory, and then Lipschitz continuity of the solution operator with respect to the friction coefficient is established. Based on the Lipschitz property, well-posedness of the resulting Bayesian inverse problem for the identification of the friction coefficient is inferred. Numerical tests for scalar and distributed parameters are performed to validate the theoretical results.
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    Consequences of uncertain friction for the transport of natural gas through passive networks of pipelines
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2018) Heitsch, Holger; Strogies, Nikolai
    Assuming a pipe-wise constant structure of the friction coefficient in the modeling of natural gas transport through a passive network of pipes via semilinear systems of balance laws with associated linear coupling and boundary conditions, uncertainty in this parameter is quantified by a Markov chain Monte Carlo method. Here, information on the prior distribution is obtained from practitioners. The results are applied to the problem of validating technical feasibility under random exit demand in gas transport networks. In particular, the impact of quantified uncertainty to the probability level of technical feasible exit demand situations is studied by two example networks of small and medium size. The gas transport of the network is modeled by stationary solutions that are steady states of the time dependent semilinear problems.
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    Dissipative and non-dissipative evolutionary quasi-variational inequalities with gradient constraints
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2017) Hintermüller, Michael; Rautenberg, Carlos N.; Strogies, Nikolai
    Evolutionary quasi-variational inequality (QVI) problems of dissipative and non-dissipative nature with pointwise constraints on the gradient are studied. A semi-discretization in time is employed for the study of the problems and the derivation of a numerical solution scheme, respectively. Convergence of the discretization procedure is proven and properties of the original infinite dimensional problem, such as existence, extra regularity and non-decrease in time, are derived. The proposed numerical solver reduces to a finite number of gradient-constrained convex optimization problems which can be solved rather efficiently. The paper ends with a report on numerical tests obtained by a variable splitting algorithm involving different nonlinearities and types of constraints.
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    Parameter identification in a semilinear hyperbolic system
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Egger, Herbert; Kugler, Thomas; Strogies, Nikolai
    We consider the identification of a nonlinear friction law in a one-dimensional damped wave equation from additional boundary measurements. Well-posedness of the governing semilinear hyperbolic system is established via semigroup theory and contraction arguments. We then investigate the inverse problem of recovering the unknown nonlinear damping law from additional boundary measurements of the pressure drop along the pipe. This coefficient inverse problem is shown to be ill-posed and a variational regularization method is considered for its stable solution. We prove existence of minimizers for the Tikhonov functional and discuss the convergence of the regularized solutions under an approximate source condition. The meaning of this condition and some arguments for its validity are discussed in detail and numerical results are presented for illustration of the theoretical findings.
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    On the consistency of Runge-Kutta methods up to order three applied to the optimal control of scalar conservation laws
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2017) Hintermüller, Michael; Strogies, Nikolai
    Higher-order Runge-Kutta (RK) time discretization methods for the optimal control of scalar conservation laws are analyzed and numerically tested. The hyperbolic nature of the state system introduces specific requirements on discretization schemes such that the discrete adjoint states associated with the control problem converge as well. Moreover, conditions on the RK-coefficients are derived that coincide with those characterizing strong stability preserving Runge-Kutta methods. As a consequence, the optimal order for the adjoint state is limited, e.g., to two even in the case where the conservation law is discretized by a third-order method. Finally, numerical tests for controlling Burgers equation validate the theoretical results.