Charbel Farhat

Bio: Charbel Farhat is an academic researcher from Stanford University. The author has contributed to research in topics: Finite element method & Domain decomposition methods. The author has an hindex of 82, co-authored 413 publications receiving 24495 citations. Previous affiliations of Charbel Farhat include Duke University & NASA Headquarters.

A method of finite element tearing and interconnecting and its parallel solution algorithm

Abstract: A novel domain decomposition approach for the parallel finite element solution of equilibrium equations is presented. The spatial domain is partitioned into a set of totally disconnected subdomains, each assigned to an individual processor. Lagrange multipliers are introduced to enforce compatibility at the interface nodes. In the static case, each floating subdomain induces a local singularity that is resolved in two phases. First, the rigid body modes are eliminated in parallel from each local problem and a direct scheme is applied concurrently to all subdomains in order to recover each partial local solution. Next, the contributions of these modes are related to the Lagrange multipliers through an orthogonality condition. A parallel conjugate projected gradient algorithm is developed for the solution of the coupled system of local rigid modes components and Lagrange multipliers, which completes the solution of the problem. When implemented on local memory multiprocessors, this proposed method of tearing and interconnecting requires less interprocessor communications than the classical method of substructuring. It is also suitable for parallel/vector computers with shared memory. Moreover, unlike parallel direct solvers, it exhibits a degree of parallelism that is not limited by the bandwidth of the finite element system of equations.

FETI‐DP: a dual–primal unified FETI method—part I: A faster alternative to the two‐level FETI method

Abstract: The FETI method and its two-level extension (FETI-2) are two numerically scalable domain decomposition methods with Lagrange multipliers for the iterative solution of second-order solid mechanics and fourth-order beam, plate and shell structural problems, respectively.The FETI-2 method distinguishes itself from the basic or one-level FETI method by a second set of Lagrange multipliers that are introduced at the subdomain cross-points to enforce at each iteration the exact continuity of a subset of the displacement field at these specific locations. In this paper, we present a dual–primal formulation of the FETI-2 concept that eliminates the need for that second set of Lagrange multipliers, and unifies all previously developed one-level and two-level FETI algorithms into a single dual–primal FETI-DP method. We show that this new FETI-DP method is numerically scalable for both second-order and fourth-order problems. We also show that it is more robust and more computationally efficient than existing FETI solvers, particularly when the number of subdomains and/or processors is very large. Copyright © 2001 John Wiley & Sons, Ltd.

Interpolation Method for Adapting Reduced-Order Models and Application to Aeroelasticity

Abstract: Reduced-order models are usually thought of as computationally inexpensive mathematical representations that offer the potential for near real-time analysis. Although most reduced-order models can operate in near real-time, their construction can be computationally expensive, as it requires accumulating a large number of system responses to input excitations. Furthermore, reduced-order models usually lack robustness with respect to parameter changes and therefore must often be rebuilt for each parameter variation. Together, these two issues underline the need for a fast and robust method for adapting precomputed reduced-order models to new sets of physical or modeling parameters. To this effect, this paper presents an interpolation method based on the Grassmann manifold and its tangent space at a point that is applicable to structural, aerodynamic, aeroelastic, and many other reduced-order models based on projection schemes. This method is illustrated here with the adaptation of computational-fluid-dynamics-based aeroelastic reduced-order models of complete fighter configurations to new values of the freestream Mach number. Good correlations with results obtained from direct reduced-order model reconstruction, high-fidelity nonlinear and linear simulations are reported, thereby highlighting the potential of the proposed reduced-order model adaptation method for near real-time aeroelastic predictions using precomputed reduced-order model databases.

Iterative Methods for Sparse Linear Systems

Abstract: Preface 1. Background in linear algebra 2. Discretization of partial differential equations 3. Sparse matrices 4. Basic iterative methods 5. Projection methods 6. Krylov subspace methods Part I 7. Krylov subspace methods Part II 8. Methods related to the normal equations 9. Preconditioned iterations 10. Preconditioning techniques 11. Parallel implementations 12. Parallel preconditioners 13. Multigrid methods 14. Domain decomposition methods Bibliography Index.

Damage identification and health monitoring of structural and mechanical systems from changes in their vibration characteristics: A literature review

Abstract: This report contains a review of the technical literature concerning the detection, location, and characterization of structural damage via techniques that examine changes in measured structural vibration response. The report first categorizes the methods according to required measured data and analysis technique. The analysis categories include changes in modal frequencies, changes in measured mode shapes (and their derivatives), and changes in measured flexibility coefficients. Methods that use property (stiffness, mass, damping) matrix updating, detection of nonlinear response, and damage detection via neural networks are also summarized. The applications of the various methods to different types of engineering problems are categorized by type of structure and are summarized. The types of structures include beams, trusses, plates, shells, bridges, offshore platforms, other large civil structures, aerospace structures, and composite structures. The report describes the development of the damage-identification methods and applications and summarizes the current state-of-the-art of the technology. The critical issues for future research in the area of damage identification are also discussed.

A summary review of vibration-based damage identification methods

Abstract: This paper provides an overview of methods to detect, locate, and characterize damage in structural and mechanical systems by examining changes in measured vibration response. Research in vibration-based damage identification has been rapidly expanding over the last few years. The basic idea behind this technology is that modal parameters (notably frequencies, mode shapes, and modal damping) are functions of the physical properties of the structure (mass, damping, and stiffness). Therefore, changes in the physical properties will cause detectable changes in the modal properties. The motivation for the development of this technology is presented. The methods are categorized according to various criteria such as the level of damage detection provided, model-based versus non-model-based methods, and linear versus nonlinear methods. The methods are also described in general terms including difficulties associated with their implementation and their fidelity. Past, current, and future-planned applications of this technology to actual engineering systems are summarized. The paper concludes with a discussion of critical issues for future research in the area of vibration-based damage identification.

Numerical solution of saddle point problems

Abstract: Large linear systems of saddle point type arise in a wide variety of applications throughout computational science and engineering. Due to their indefiniteness and often poor spectral properties, such linear systems represent a significant challenge for solver developers. In recent years there has been a surge of interest in saddle point problems, and numerous solution techniques have been proposed for this type of system. The aim of this paper is to present and discuss a large selection of solution methods for linear systems in saddle point form, with an emphasis on iterative methods for large and sparse problems.