The Experts below are selected from a list of 9612 Experts worldwide ranked by ideXlab platform

Heiko K Weichelt - One of the best experts on this subject based on the ideXlab platform.

  • efficient solution of large scale Algebraic riccati equations associated with index 2 daes via the inexact low rank newton adi method
    Applied Numerical Mathematics, 2020
    Co-Authors: Peter Benner, Matthias Heinkenschloss, Jens Saak, Heiko K Weichelt
    Abstract:

    Abstract This paper extends the algorithm of Benner et al. (2016) [10] to Riccati equations associated with Hessenberg index-2 Differential Algebratic Equation (DAE) systems. Such DAE systems arise, e.g., from semi-discretized, linearized (around steady state) Navier-Stokes equations. The solution of the associated Riccati equation is important, e.g., to compute feedback laws that stabilize the Navier-Stokes equations. Challenges in the numerical solution of the Riccati equation arise from the large-scale of the underlying systems and the Algebraic Constraint in the DAE system. These challenges are met by a careful extension of the inexact low-rank Newton-ADI method to the case of DAE systems. A main ingredient in the extension to the DAE case is the projection onto the manifold described by the Algebraic Constraints. In the algorithm, the equations are never explicitly projected, but the projection is only applied as needed. Numerical experience indicates that the algorithmic choices for the control of inexactness and line-search can help avoid subproblems with matrices that are only marginally stable. The performance of the algorithm is illustrated on a large-scale Riccati equation associated with the stabilization of Navier-Stokes flow around a cylinder.

  • efficient solution of large scale Algebraic riccati equations associated with index 2 daes via the inexact low rank newton adi method
    arXiv: Numerical Analysis, 2018
    Co-Authors: Peter Benner, Matthias Heinkenschloss, Jens Saak, Heiko K Weichelt
    Abstract:

    This paper extends the algorithm of Benner, Heinkenschloss, Saak, and Weichelt: An inexact low-rank Newton-ADI method for large-scale Algebraic Riccati equations, Applied Numerical Mathematics Vol. 108 (2016), pp. 125-142, this https URL to Riccati equations associated with Hessenberg index-2 Differential Algebraic Equation (DAE) systems. Such DAE systems arise, e.g., from semi-discretized, linearized (around steady state) Navier-Stokes equations. The solution of the associated Riccati equation is important, e.g., to compute feedback laws that stabilize the Navier-Stokes equations. Challenges in the numerical solution of the Riccati equation arise from the large-scale of the underlying systems, the Algebraic Constraint in the DAE system, and the fact that matrices arising in some subproblems may only be marginally stable. These challenges are met by a careful extension of the inexact low-rank Newton-ADI method to the case of DAE systems. A main ingredient in the extension to the DAE case is the projection onto the manifold of the Algebraic Constraints. In the algorithm, the equations are never explicitly projected, but the projection is only applied as needed. The performance of the algorithm is illustrated on a large-scale Riccati equation associated with the stabilization of Navier-Stokes flow around a cylinder.

Peter Benner - One of the best experts on this subject based on the ideXlab platform.

  • efficient solution of large scale Algebraic riccati equations associated with index 2 daes via the inexact low rank newton adi method
    Applied Numerical Mathematics, 2020
    Co-Authors: Peter Benner, Matthias Heinkenschloss, Jens Saak, Heiko K Weichelt
    Abstract:

    Abstract This paper extends the algorithm of Benner et al. (2016) [10] to Riccati equations associated with Hessenberg index-2 Differential Algebratic Equation (DAE) systems. Such DAE systems arise, e.g., from semi-discretized, linearized (around steady state) Navier-Stokes equations. The solution of the associated Riccati equation is important, e.g., to compute feedback laws that stabilize the Navier-Stokes equations. Challenges in the numerical solution of the Riccati equation arise from the large-scale of the underlying systems and the Algebraic Constraint in the DAE system. These challenges are met by a careful extension of the inexact low-rank Newton-ADI method to the case of DAE systems. A main ingredient in the extension to the DAE case is the projection onto the manifold described by the Algebraic Constraints. In the algorithm, the equations are never explicitly projected, but the projection is only applied as needed. Numerical experience indicates that the algorithmic choices for the control of inexactness and line-search can help avoid subproblems with matrices that are only marginally stable. The performance of the algorithm is illustrated on a large-scale Riccati equation associated with the stabilization of Navier-Stokes flow around a cylinder.

  • efficient solution of large scale Algebraic riccati equations associated with index 2 daes via the inexact low rank newton adi method
    arXiv: Numerical Analysis, 2018
    Co-Authors: Peter Benner, Matthias Heinkenschloss, Jens Saak, Heiko K Weichelt
    Abstract:

    This paper extends the algorithm of Benner, Heinkenschloss, Saak, and Weichelt: An inexact low-rank Newton-ADI method for large-scale Algebraic Riccati equations, Applied Numerical Mathematics Vol. 108 (2016), pp. 125-142, this https URL to Riccati equations associated with Hessenberg index-2 Differential Algebraic Equation (DAE) systems. Such DAE systems arise, e.g., from semi-discretized, linearized (around steady state) Navier-Stokes equations. The solution of the associated Riccati equation is important, e.g., to compute feedback laws that stabilize the Navier-Stokes equations. Challenges in the numerical solution of the Riccati equation arise from the large-scale of the underlying systems, the Algebraic Constraint in the DAE system, and the fact that matrices arising in some subproblems may only be marginally stable. These challenges are met by a careful extension of the inexact low-rank Newton-ADI method to the case of DAE systems. A main ingredient in the extension to the DAE case is the projection onto the manifold of the Algebraic Constraints. In the algorithm, the equations are never explicitly projected, but the projection is only applied as needed. The performance of the algorithm is illustrated on a large-scale Riccati equation associated with the stabilization of Navier-Stokes flow around a cylinder.

Ahmed A Shabana - One of the best experts on this subject based on the ideXlab platform.

  • Integration of Geometry and Analysis for Vehicle System Applications: Continuum-Based Leaf Spring and Tire Assembly
    2020
    Co-Authors: Yiguan Liu, Brian Tinsley, Ahmed A Shabana
    Abstract:

    The development of new and complex vehicle models using the absolute nodal coordinate formulation (ANCF) and multibody systems (MBS) algorithms is discussed in this paper. It is shown how a continuum-based finite element (FE) leaf spring and tire assembly can be developed at a preprocessing stage and integrated with MBS algorithms, allowing for the elimination of dependent variables before the start of the dynamic simulations. Leaf springs, which are important elements in the suspension system of large vehicles, are discretized using ANCF FEs and are integrated with ANCF tire meshes to develop new models with significant details. To this end, the concept of the ANCF reference node (ANCF-RN) is used in order to systematically assemble the vehicle model using linear Algebraic Constraint equations that can be applied at a preprocessing stage. These Algebraic Constraint equations define new FE connectivity conditions that include the leaf spring shackle/chassis assembly, tire flexible tread/rigid rim assembly, tire/axle assembly, and revolute joints between different vehicle components. The approach presented in this paper allows for using both gradient deficient and fully parameterized ANCF FEs to develop the new models. In order to develop accurate leaf spring models, the prestress of the leaves and the contact forces between leaves are taken into consideration in the ANCF models developed in this investigation. Numerical results are presented in order to demonstrate the use of the computational framework described in this paper to build continuum-based leaf spring/tire assembly that can be integrated with complex vehicle models. The results of this paper also demonstrate the feasibility of developing a CAD (computer-aided design)/analysis system in which the geometry and analysis mesh of a complete vehicle can be developed in one step, thereby avoiding the incompatibility and costly process of using different codes in the flexible MBS analysis

  • a total lagrangian ancf liquid sloshing approach for multibody system applications
    Journal of Computational and Nonlinear Dynamics, 2015
    Co-Authors: Cheng Wei, Liang Wang, Ahmed A Shabana
    Abstract:

    The objective of this investigation is to develop a total Lagrangian non-incremental liquid sloshing solution procedure based on the finite element (FE) absolute nodal coordinate formulation (ANCF). The proposed liquid sloshing modeling approach can be used to avoid the difficulties of integrating most of fluid dynamics formulations, which are based on the Eulerian approach, with multibody system (MBS) dynamics formulations, which are based on a total Lagrangian approach. The proposed total Lagrangian FE fluid dynamics formulation, which can be systematically integrated with computational MBS algorithms, differs significantly from the conventional FE or finite volume methods which are based on an Eulerian representation that employs the velocity field of a fixed control volume in the region of interest. The ANCF fluid equations are expressed in terms of displacement and gradient coordinates of material points, allowing for straight forward implementation of kinematic Constraint equations and for the systematic modeling of the interaction of the fluid with the external environment or with rigid and flexible bodies. The fluid incompressibility conditions and surface traction forces are considered and derived directly from the Navier Stokes equations. Two ANCF brick elements, one is obtained using an incomplete polynomial representation and the other is obtained from a B-spline volume representation, are used. The new approach ensures the continuity of the displacement gradients at the nodal points and allows for imposing higher degree of continuity across the element interface by applying Algebraic Constraint equations that can be used to eliminate dependent variables and reduce the model dimensionality. Regardless of the magnitude of the fluid displacement, the fluid has a constant mass matrix, leading to zero Coriolis and centrifugal forces. The analysis presented in this paper demonstrates the feasibility of developing an efficient non-incremental total Lagrangian approach for modeling sloshing problems in MBS system applications in which the bodies can experience large displacements including finite rotations. Several examples are presented in order to shed light on the potential of using the ANCF liquid sloshing formulation developed in this study.Copyright © 2015 by ASME

  • A comparative study of joint formulations: application to multibody system tracked vehicles
    Nonlinear Dynamics, 2013
    Co-Authors: Michael Wallin, Ahmed K. Aboubakr, Paramsothy Jayakumar, Michael D. Letherwood, David J. Gorsich, Ashraf Hamed, Ahmed A Shabana
    Abstract:

    This paper is focused on the dynamic formulation of mechanical joints using different approaches that lead to different models with different numbers of degrees of freedom. Some of these formulations allow for capturing the joint deformations using a discrete elastic model while the others are continuum-based and capture joint deformation modes that cannot be captured using the discrete elastic joint models. Specifically, three types of joint formulations are considered in this investigation; the ideal , compliant discrete element , and compliant continuum-based joint models . The ideal joint formulation , which does not allow for deformation degrees of freedom in the case of rigid body or small deformation analysis, requires introducing a set of Algebraic Constraint equations that can be handled in computational multibody system (MBS) algorithms using two fundamentally different approaches: constrained dynamics approach and penalty method. When the constrained dynamics approach is used, the Constraint equations must be satisfied at the position, velocity, and acceleration levels. The penalty method, on the other hand, ensures that the Algebraic equations are satisfied at the position level only. In the compliant discrete element joint formulation , no Constraint conditions are used; instead the connectivity conditions between bodies are enforced using forces that can be defined in their most general form in MBS algorithms using bushing elements that allow for the definition of general nonlinear forces and moments. The new compliant continuum-based joint formulation , which is based on the finite element (FE) absolute nodal coordinate formulation (ANCF), has several advantages: (1) It captures modes of joint deformations that cannot be captured using the compliant discrete joint models; (2) It leads to linear connectivity conditions, thereby allowing for the elimination of the dependent variables at a preprocessing stage; (3) It leads to a constant inertia matrix in the case of chain like structure; and (4) It automatically captures the deformation of the bodies using distributed inertia and elasticity. The formulations of these three different joint models are compared in order to shed light on the fundamental differences between them. Numerical results of a detailed tracked vehicle model are presented in order to demonstrate the implementation of some of the formulations discussed in this investigation.

  • uniqueness of the geometric representation in large rotation finite element formulations
    Journal of Computational and Nonlinear Dynamics, 2010
    Co-Authors: Ahmed A Shabana
    Abstract:

    Several finite element formulations used in the analysis of large rotation and large deformation problems employ independent interpolations for the displacement and rotation fields. As explained in this paper, three rotations defined as field variables can be sufficient to define a space curve that represents the element centerline. The frame defined by the rotations can differ from the Frenet frame of the space curve defined by the same rotation field and, therefore, such a rotation-based representation can provide measure of twist shear deformations and captures the rotation of the beam about its axis. However, the space curve defined using the rotation interpolation has a geometry that can significantly differ from the geometry defined by an independent displacement interpolation. Furthermore, the two different space curves defined by the two different interpolations can differ by a rigid body motion. Therefore, in these formulations, the uniqueness of the kinematic representation is an issue unless nonlinear Algebraic Constraint equations are used to establish relationships between the two independent displacement and rotation interpolations. Nonetheless, significant geometric and kinematic differences between two independent space curves cannot always be reduced by using restoring elastic forces. Because of the nonuniqueness of such a finite element representation, imposing continuity on higher derivatives such as the curvature vector is not straight forward as in the case of the absolute nodal coordinate formulation (ANCF) that defines unique displacement and rotation fields. ANCF finite elements allow for imposing curvature continuity without increasing the order of the interpolation or the number of nodal coordinates, as demonstrated in this paper. Furthermore, the relationship between ANCF finite elements and the B-spline representation used in computational geometry can be established, allowing for a straight forward integration of computer aided design and analysis.

  • integration of b spline geometry and ancf finite element analysis
    Nonlinear Dynamics, 2010
    Co-Authors: Peng Lan, Ahmed A Shabana
    Abstract:

    The goal of this investigation is to introduce a new computer procedure for the integration of B-spline geometry and the absolute nodal coordinate formulation (ANCF) finite element analysis. The procedure is based on developing a linear transformation that can be used to transform systematically the B-spline representation to an ANCF finite element mesh preserving the same geometry and the same degree of continuity. Such a linear transformation that relates the B-spline control points and the finite element position and gradient coordinates will facilitate the integration of computer aided design and analysis (ICADA). While ANCF finite elements automatically ensure the continuity of the position and gradient vectors at the nodal points, the B-spline representation allows for imposing a higher degree of continuity by decreasing the knot multiplicity. As shown in this investigation, a higher degree of continuity can be systematically achieved using ANCF finite elements by imposing linear Algebraic Constraint equations that can be used to eliminate nodal variables. The analysis presented in this study shows that continuity of the curvature vector and its derivative which corresponds in the cubic B-spline representation to zero knot multiplicity can be systematically achieved using ANCF finite elements. In this special case, as the knot multiplicity reduces to zero, the recurrence B-spline formula causes two segments to automatically blend together forming one cubic segment defined on a larger domain. Similarly in this special case, the Algebraic Constraint equations required for the C 3 continuity convert two ANCF cubic finite elements to one finite element, demonstrating the strong relationship between the B-spline representation and the ANCF finite element representation. For the same order of interpolation, higher degree of continuity at the finite element interface can lead to a coarser mesh and to a lower dimensional model. Using the B-spline/ANCF finite element transformation developed in this paper, the equations of motion of a finite element mesh that represents exactly the B-spline geometry can be developed. Because of the linearity of the transformation developed in this investigation, all the ANCF finite element desirable features are preserved; including the constant mass matrix that can be used to develop an optimum sparse matrix structure of the nonlinear multibody system dynamic equations.

L I Xiaoxiang - One of the best experts on this subject based on the ideXlab platform.

  • Algebraic Constraint based view rendering
    Computer Engineering, 2002
    Co-Authors: L I Xiaoxiang
    Abstract:

    A new technique for the image rendering based on Algebraic Constraint is proposed. It is used to render novel view from two reference image of different location. By studying the geometry relationship among the corresponding points on three different projective planes, the tri-linear tensor constraining the corresponding points of different view is obtained. From this tensor the corresponding relationship between images can be obtained and the novel view is thus obtained. Comparing with other image re-projection methods, this method needs only two reference images and the implementation is easy and quick. The satisfying results are given in the experiment.

Alexander M. Alekseenko - One of the best experts on this subject based on the ideXlab platform.

  • Constraint-Preserving Boundary Conditions for the Linearized Baumgarte-Shapiro-Shibata-Nakamura Formulation
    Hindawi Limited, 2008
    Co-Authors: Alexander M. Alekseenko
    Abstract:

    We derive two sets of explicit homogeneous Algebraic Constraint-preserving boundary conditions for the second-order in time reduction of the linearized Baumgarte-Shapiro-Shibata-Nakamura (BSSN) system. Our second-order reduction involves components of the linearized extrinsic curvature only. An initial-boundary value problem for the original linearized BSSN system is formulated and the existence of the solution is proved using the properties of the reduced system. A treatment is proposed for the full nonlinear BSSN system to construct Constraint-preserving boundary conditions without invoking the second order in time reduction. Energy estimates on the principal part of the BSSN system (which is first order in temporal and second order in spatial derivatives) are obtained. Generalizations to the case of nonhomogeneous boundary data are proposed

  • Research Article Constraint-Preserving Boundary Conditions for the Linearized Baumgarte-Shapiro-Shibata-Nakamura Formulation
    2008
    Co-Authors: Alexander M. Alekseenko
    Abstract:

    We derive two sets of explicit homogeneous Algebraic Constraint-preserving boundary conditions for the second-order in time reduction of the linearized Baumgarte-Shapiro-Shibata-Nakamura BSSN system. Our second-order reduction involves components of the linearized extrinsic curvature only. An initial-boundary value problem for the original linearized BSSN system is formulated and the existence of the solution is proved using the properties of the reduced system. A treatment is proposed for the full nonlinear BSSN system to construct Constraint-preserving boundary conditions without invoking the second order in time reduction. Energy estimates on the principal part of the BSSN system which is first order in temporal and second order in spatial derivatives are obtained. Generalizations to the case of nonhomogeneous boundary data are proposed. Copyright q 2008 Alexander M. Alekseenko. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1