[01161] Error-Controlled Adaptive Algorithms in Full-Order and Reduced-Order Model Simulations
Session Time & Room : 1C (Aug.21, 13:20-15:00) @E604
Type : Proposal of Minisymposium
Abstract : Controlling numerical errors is of high importance in simulation of various science and engineering problems, e.g., solids, fluids, and air. In full-order model simulations, the discretization error between the continuous solution and the discrete one plays a central role. In reduced-order model simulations, approximation errors during the reduction process is pivotal. Recent research advancements in both these domains have been on development of error-controlled adaptive algorithms, which is the focus of this minisymposium.
Organizer(s) : Kapil Ahuja, Marc C. Steinbach, and Thomas Wick
01161 (1/1) : 1C @E604 [Chair: Bernhard Endtmayer]
[01786] Modeling and multigoal-oriented a posteriori error control for heated material processing using a generalized Boussinesq modell
Format : Talk at Waseda University
Author(s) :
Sven Beuchler (IfAM, Leibniz University Hanover)
Bernhard Endtmayer (IfAM, Leibniz University Hanover)
Johannes Lankeit (IfAM, Leibniz University Hanover)
Thomas Wick (IfAM, Leibniz University Hanover)
Abstract : In this presentation, we develop a posteriori error control for a generalized Boussinesq model. The stationary Navier-
Stokes equations with temperature dependent viscosity are coupled with a stationary heat equation. We use the dual-
weighted residual method in which an adjoint problem is utilized to obtain sensitivity measures with
respect to several goal functionals. The error localization is done with the help of a partition-
of-unity in a weak formulation. The resulting error estimators are used within an adaptive algorithm. Finally, numerical examples are presented.
[04451] Error-Controlled Local Interpolation of Moment Matching Reduced Order Models for Vibroacoustics
Format : Talk at Waseda University
Author(s) :
Harikrishnan K. Sreekumar (Technische Universität Braunschweig, Institut für Akustik)
Ulrich Römer (Technische Universität Braunschweig, Institut für Dynamik und Schwingungen)
Matthias Bollhöfer (Technische Universität Braunschweig, Institut für Numerische Mathematik)
Christopher Blech (Technische Universität Braunschweig, Institut für Akustik)
Sabine C. Langer (Technische Universität Braunschweig, Institut für Akustik)
Abstract : Surrogate modeling for high-dimensional parametric problems is computationally challenging and therefore demands techniques to capture the essential features with the least effort. To this end, we present an adaptive error-controlled strategy to drive accurate modeling at two levels: moment matching reduced-order models approximating the frequency response and sparse grid interpolation for parametric approximation. We compare dimension-adaptive and spatially-adaptive refinement strategies with respect to convergence, demonstrated using problems from vibroacoustics.
[04671] Advances in A Posteriori Error Estimation and Adaptive Model Order Reduction
Format : Talk at Waseda University
Author(s) :
Sridhar Chellappa (Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg)
Lihong Feng (Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg)
Peter Benner (MPI for Dynamics of Complex Technical Systems, Magdeburg)
Abstract : Reduced-order models (ROMs) play an important role in applications such as engineering design, control, optimization, etc. which require reliable simulations of large-scale systems in real-time. We discuss our recent work on a posteriori error estimation and adaptivity. The objective of this work is to reduce the training cost for ROM. We discuss several new error estimators and illustrate their use in adaptive basis enrichment and adaptive parameter sampling. The benefits of the adaptive methods are demonstrated on several numerical examples.
[05257] Stable Linear Solves in Parametric Model Order Reduction
Format : Online Talk on Zoom
Author(s) :
Kapil Ahuja (Indian Institute of Technology Indore (IIT Indore))
Navneet Pratap Singh (Bennett University)
Abstract : We study stability of class of algorithms for model order reduction (MOR) of parametric linear dynamical systems, with respect to inexact linear solves. Our most novel contribution is achieving backward stable MOR algorithms. To achieve this, we first adapt the underlying linear solver such that it satisfies orthogonalities required for stability. Next, we demonstrate that by suitably using a recycling variant of the solver, these orthogonalities can be satisfied without any code changes and cheaply.
