Browsing by Author "Mehrmann, Volker"

Now showing 1 - 9 of 9
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    Discretization of Inherent ODEs and the Geometric Integration of DAEs with Symmetries
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2022) Kunkel, Peter; Mehrmann, Volker
    Discretization methods for differential-algebraic equations (DAEs) are considered that are based on the integration of an associated inherent ordinary differential equation (ODE). This allows to make use of any discretization scheme suitable for the numerical integration of ODEs. For DAEs with symmetries it is shown that the inherent ODE can be constructed in such a way that it inherits the symmetry properties of the given DAE and geometric properties of its flow. This in particular allows the use of geometric integration schemes with a numerical flow that has analogous geometric properties.
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    Formal adjoints of linear DAE operators and their role in optimal control
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2011) Kunkel, Peter; Mehrmann, Volker
    For regular strangeness-free linear differential-algebraic equations (DAEs) the definition of an adjoint DAE is straightforward. This definition can be formally extended to general linear DAEs. In this paper, we analyze the properties of the formal adjoints and their implications in solving linear-quadratic optimal control problems with DAE constraints.
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    Linear and Nonlinear Eigenproblems for PDEs
    (Zürich : EMS Publ. House, 2009) Mehrmann, Volker; Osborn, John; Xu, Jinchao
    The workshop discussed the numerical solution of linear and nonlinear eigenvalue problems for partial differential equations. It included the theoretical analysis the development of new (adaptive) methods, the iterative solution of the algebraic problems as well as the application in many areas of science and engineering.
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    Local and Global Canonical Forms for Differential-Algebraic Equations with Symmetries
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2022) Kunkel, Peter; Mehrmann, Volker
    Linear time-varying differential-algebraic equations with symmetries are studied. The structures that we address are self-adjoint and skew-adjoint systems. Local and global canonical forms under congruence are presented and used to classify the geometric properties of the flow associated with the differential equation as symplectic or generalized orthogonal flow. As applications, the results are applied to the analysis of dissipative Hamiltonian systems arising from circuit simulation and incompressible flow.
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    Mini-Workshop: Dimensional Reduction of Large-Scale Systems
    (Oberwolfach-Walke : Mathematisches Forschungsinstitut Oberwolfach, 2003) Mehrmann, Volker; Golub, Gene; Sorensen, Danny C.
    [no abstract available]
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    Mini-Workshop: Mathematics of Dissipation – Dynamics, Data and Control (hybrid meeting)
    (Zürich : EMS Publ. House, 2021) Mehrmann, Volker; Scherpen, Jacquelien M.A.; Schwenninger, Felix L.
    Dissipation of energy --- as well as its sibling the increase of entropy --- are fundamental facts inherent to any physical system. The concept of dissipativity has been extended to a more general system theoretic setting via port-Hamiltonian systems and this framework is a driver of innovations in many of areas of science and technology. The particular strength of the approach lies in the modularity of modeling, the strong geometric, analytic and algebraic properties and the very good approximation properties.
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    Nichtnegative Matrizen, M-Matrizen und deren Verallgemeinerungen
    (Oberwolfach-Walke : Mathematisches Forschungsinstitut Oberwolfach, 2000) Mehrmann, Volker; Schneider, Hans
    [no abstract available]
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    Numerical Solution of PDE Eigenvalue Problems
    (Zürich : EMS Publ. House, 2013) Mehrmann, Volker; Xu, Jinchao
    This workshop brought together researchers from many different areas of numerical analysis, scientific computing and application areas, ranging from quantum mechanics, acoustic field computation to material science, working on eigenvalue problems for partial differential equations. Major challenges and new research directions were identified and the interdisciplinary cooperation was strengthened through a very lively workshop with many discussions.
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    Self-adjoint differential-algebraic equations
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2011) Kunkel, Peter; Mehrmann, Volker; Scholz, Lena
    Motivated from linear-quadratic optimal control problems for differential-algebraic equations (DAEs), we study the functional analytic properties of the operator associated with the necessary optimality boundary value problem and show that it is associated with a self-conjugate operator and a self-adjoint pair of matrix functions. We then study general self-adjoint pairs of matrix valued functions and derive condensed forms under orthogonal congruence transformations that preserve the self-adjointness. We analyze the relationship between self-adjoint DAEs and Hamiltonian systems with symplectic flows. We also show how to extract self-adjoint and Hamiltonian reduced systems from derivative arrays.