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New methods for finite element model updating problems

AIAA JOURNAL 2006年第6期44卷 1310-1316页

作者： Kuo, Yuen-Cheng Lin, Wen-Wei Xu, Shufang Natl Univ Kaohsiung Dept Appl Math Kaohsiung 811 Taiwan Natl Tsing Hua Univ Dept Math Hsinchu 300 Taiwan Peking Univ Sch Math Sci Beijing 100871 Peoples R China

We consider two finite element model updating problems, which incorporate the measured modal data into the analytical finite element model, producing an adjusted model on the (mass) damping and stiffness, that closely matches the experimental modal data. We develop two efficient numerical algorithms for solving these problems. The new algorithms are direct methods that require O(nk(2)) and O(nk(2) + k(6)) flops, respectively, and employ sparse matrix techniques when the analytic model is sparse. Here n is the dimension of the coefficient matrices defining the analytical model, and k is the number of measured eigenpairs.

关键词： Finite Element Modeling numerical algorithms Lagrange Multipliers Proportional Damping Boeing Distributed Parameter System Frequency Response Functions Conjugate Gradient Method Gaussian Elimination Structural Dynamics

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Evaluation of high-order spectral volume method for benchmark computational aeroacoustic problems

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AIAA JOURNAL 2005年第2期43卷 337-348页

作者： Wang, ZJ Michigan State Univ Dept Mech Engn E Lansing MI 48824 USA

A time-accurate, high-order finite volume method named spectral volume (SV) method has been developed recently for conservation laws on unstructured grids and successfully demonstrated for Euler equations. In this paper, the SV method is evaluated for several benchmark problems in computational aeroacoustics (CAA) to demonstrate its potential for CAA applications. Both one-dimensional and two-dimensional problems are tested in the evaluation. It is shown that the higher-order SV schemes can achieve the same accuracy at a much lower cost than the lower-order ones.

关键词： Finite Volume Method Euler Equations Computational Aeroacoustics Unstructured Grid Riemann Problem Shape Functions Flow Conditions DG Method numerical algorithms Specific Heat

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TIME-DEPENDENT WAVE ENVELOPE FINITE-DIFFERENCE ANALYSIS OF SOUND-PROPAGATION

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AIAA JOURNAL 1986年第1期24卷 32-38页

作者： BAUMEISTER, KJ NASA Lewis Research Center Cleveland Ohio

A transient finite difference wave envelope formulation is presented for sound propagation without steady flow. Before the finite difference equations are formulated, the governing wave equation is first transformed to a form whose solution tends not to oscillate along the propagation direction. This transformation reduces the required number of grid points by an order of magnitude. Physically, the transformed pressure represents the amplitude of the conventional sound wave. The derivation for the wave envelope transient wave equation and appropriate boundary conditions are presented as well as the difference equations and stability requirements. To illustrate the method, example solutions are presented for sound propagation in a straight hard-wall duct and in a two-dimensional, straight soft-wall duct. The numerical results are in good agreement with exact analytical results. © 1986 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.

关键词： Acoustic Propagation Turbofan Engines Finite Difference Approximation numerical Analysis Mach Number Nacelles numerical algorithms Harmonic Oscillation Aerospace Engineering Radiation Pattern

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Thermomechanical formulation of ductile damage coupled to nonlinear isotropic hardening and multiplicative viscoplasticity

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JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 2016年 91卷 334-358页

作者： Soyarslan, C. Bargmann, S. Hamburg Univ Technol Inst Continuum Mech & Mat Mech D-21073 Hamburg Germany Helmholtz Zentrum Geesthacht Inst Mat Res D-21502 Geesthacht Germany

In this paper, we present a thermomechanical framework which makes use of the internal variable theory of thermodynamics for damage-coupled finite viscoplasticity with nonlinear isotropic hardening. Damage evolution, being an irreversible process, generates heat. In addition to its direct effect on material's strength and stiffness, it causes deterioration of the heat conduction. The formulation, following the footsteps of Simo and Miehe (1992), introduces inelastic entropy as an additional state variable. Given a temperature dependent damage dissipation potential, we show that the evolution of inelastic entropy assumes a split form relating to plastic and damage parts, respectively. The solution of the thermomechanical problem is based on the so-called isothermal split. This allows the use of the model in 2D and 3D example problems involving geometrical imperfection triggered necking in an axisymmetric bar and thermally triggered necking of a 3D rectangular bar. (C) 2016 The Authors. Published by Elsevier Ltd.

关键词： Damage coupled elastoplasticity Thermomechanical coupling Finite strain Finite elements numerical algorithms Return map

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Variational Data Assimilation Technique in Mathematical Modeling of Ocean Dynamics

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PURE AND APPLIED GEOPHYSICS 2012年第3期169卷 555-578页

作者： Agoshkov, V. I. Zalesny, V. B. RAS Inst Numer Math Moscow 199333 Russia

Problems of the variational data assimilation for the primitive equation ocean model constructed at the Institute of numerical Mathematics, Russian Academy of Sciences are considered. The model has a flexible computational structure and consists of two parts: a forward prognostic model, and its adjoint analog. The numerical algorithm for the forward and adjoint models is constructed based on the method of multicomponent splitting. The method includes splitting with respect to physical processes and space coordinates. numerical experiments are performed with the use of the Indian Ocean and the World Ocean as examples. These numerical examples support the theoretical conclusions and demonstrate the rationality of the approach using an ocean dynamics model with an observed data assimilation procedure.

关键词： Variational data assimilation ocean dynamics mathematical models numerical algorithms adjoint equations multicomponent splitting World ocean circulation

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Free surface lattice Boltzmann with enhanced bubble model

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2014年第2期67卷 331-339页

作者： Anderl, Daniela Bogner, Simon Rauh, Cornelia Ruede, Ulrich Delgado, Antonio Univ Erlangen Nurnberg Lehrstuhl Stromungsmech D-91058 Erlangen Germany Univ Erlangen Nurnberg Lehrstuhl Syst Simulat D-91058 Erlangen Germany

This paper presents an enhancement to the free surface lattice Boltzmann method (FSLBM) for the simulation of bubbly flows including rupture and breakup of bubbles. The FSLBM uses a volume of fluid approach to reduce the problem of a liquid-gas two-phase flow to a single-phase free surface simulation. In bubbly flows compression effects leading to an increase or decrease of pressure in the suspended bubbles cannot be neglected. Therefore, the free surface simulation is augmented by a bubble model that supplies the missing information by tracking the topological changes of the free surface in the flow. The new model presented here is capable of handling the effects of bubble breakup and coalesce without causing a significant computational overhead. Thus, the enhanced bubble model extends the applicability of the FSLBM to a new range of practically relevant problems, like bubble formation and development in chemical reactors or foaming processes. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： Lattice Boltzmann Free surface Volume of fluid Interface capturing Bubbly flow numerical algorithms

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A Low Complexity Scaling Method for the Lanczos Kernel in Fixed-Point Arithmetic

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IEEE TRANSACTIONS ON COMPUTERS 2015年第2期64卷 303-315页

作者： Jerez, Juan Luis Constantinides, George A. Kerrigan, Eric C. Univ London Imperial Coll Sci Technol & Med Dept Elect & Elect Engn London SW7 2AZ England Univ London Imperial Coll Sci Technol & Med Dept Aeronaut London SW7 2AZ England

We consider the problem of enabling fixed-point implementation of linear algebra kernels on low-cost embedded systems, as well as motivating more efficient computational architectures for scientific applications. Fixed-point arithmetic presents additional design challenges compared to floating-point arithmetic, such as having to bound peak values of variables and control their dynamic ranges. algorithms for solving linear equations or finding eigenvalues are typically nonlinear and iterative, making solving these design challenges a nontrivial task. For these types of algorithms, the bounding problem cannot be automated by current tools. We focus on the Lanczos iteration, the heart of well-known methods such as conjugate gradient and minimum residual. We show how one can modify the algorithm with a low-complexity scaling procedure to allow us to apply standard linear algebra to derive tight analytical bounds on all variables of the process, regardless of the properties of the original matrix. It is shown that the numerical behavior of fixed-point implementations of the modified problem can be chosen to be at least as good as a floating-point implementation, if necessary. The approach is evaluated on field-programmable gate array (FPGA) platforms, highlighting orders of magnitude potential performance and efficiency improvements by moving form floating-point to fixed-point computation.

关键词： Computer arithmetic computations on matrices numerical algorithms design aids

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Development of closed-loop tail-sizing criteria for a High Speed Civil Transport

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JOURNAL OF AIRCRAFT 1997年第5期34卷 658-664页

作者： Kaminer, II Howard, RM Buttrill, CS NASA LANGLEY RES CTRDYNAM & CONTROL BRANCHHAMPTONVA 23681

A study was conducted to determine the closed-loop tail-sizing criteria for a High Speed Civil Transport using a newly developed integrated aircraft/controller design methodology. The key idea is to cast closed loop requirements as linear matrix inequalities, for which efficient numerical solvers are available, In particular, the effects of certain feedback specifications, and of actuator amplitude and rate constraints on the maximum allowable e.g. travel for a given set of tail sizes are studied, A constant gain slate feedback controller Is designed as a part of the tail-sizing process.

关键词： High Speed Civil Transport Closed Loop Transfer Function Supersonic Aircraft Damping Ratio Angle of Attack Federal Aviation Regulation numerical algorithms Aircraft Dynamics Aerodynamic Center Stability Augmentation

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General matrix pencil techniques for the solution of algebraic Riccati equations: A unified approach

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 1997年第8期42卷 1085-1097页

作者： Ionescu, V Oara, C Weiss, M TECH UNIV EINDHOVEN FAC APPL PHYS NL-5600 MB EINDHOVEN NETHERLANDS

We present a unified theory of matrix pencil techniques for solving both continuous and discrete-time algebraic Riccati equations (ARE's) under fairly general conditions on the coefficient matrices, The theory applies to a large class of ARE's and Riccati-like equations arising from the singular H-infinity- and H-2- control problems, singular linear quadratic control, the ii-block Nehari problem, or from singular J-spectral factorizations. The underlying concept is the so-called proper deflating subspace of a (possibly singular) matrix pencil in terms of which necessary and sufficient conditions for the solvability of Riccati equations are given, It is shown that these conditions can be checked and the solutions computed by a numerically sound algorithm.

关键词： matrix pencils numerical algorithms Riccati equations spectral factorizations

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Petascale large eddy simulation of jet engine noise based on the truncated SPIKE algorithm

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PARALLEL COMPUTING 2014年第9期40卷 496-511页

作者： Situ, Yingchong Martha, Chandra S. Louis, Matthew E. Li, Zhiyuan Sameh, Ahmed H. Blaisdell, Gregory A. Lyrintzis, Anastasios S. Purdue Univ Dept Comp Sci W Lafayette IN 47907 USA Purdue Univ Sch Aeronaut & Astronaut W Lafayette IN 47907 USA

With the emergence of petascale computing platforms, high-fidelity computational aeroacoustics (CAA) simulation has become a feasible, robust and accurate tool that complements theoretical and empirical approaches in the prediction of sound levels generated by aircraft airframes and engines. Differentiating itself from the broader discipline of computational fluid dynamics, CAA is particularly challenging as it demands high accuracy, good spectral resolution, and low dispersion and diffusion errors from the underlying numerical methods. Large eddy simulation based on space-implicit high-order compact finite difference schemes has been shown to meet such stringent requirements. In this paper, we discuss a new, scalable parallelization scheme with a three-dimensional computational space partitioning. Unlike many traditional multiblock computational fluid dynamics (CFD) methods, our partitioning is non-overlapping. We use the truncated SPIKE algorithm to solve the governing equations accurately and limit one-sided biased differentiation to just the physical boundaries. We present experimental performance data collected on Kraken and Ranger, two near-petascale computing platforms. (C) 2014 Elsevier B.V. All rights reserved.

关键词： Computational fluid dynamics Large eddy simulation Finite difference methods Parallel algorithms Linear systems numerical algorithms

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