Efficient Newton-Krylov solver for aerodynamic computations

Pueyo, Alberto; Zingg, David W.

doi:10.2514/3.14077

Cited by 27 publications

(46 citation statements)

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“…Many studies on numbering techniques for ILU preconditioners appear in the literature, cf., e.g., [18,36] and references therein. For ILU methods, in many applications, a reverse Cuthill-McKee ordering algorithm [17] provides good results [6,29,34,35]. The PBGS preconditioner can be significantly improved by reordering techniques that should be such that one approximately follows the directions in which information is propagated.…”

Section: Methodsmentioning

confidence: 99%

Iterative Solvers for Discretized Stationary Euler Equations

Pollul

Reusken

2010

Notes on Numerical Fluid Mechanics and Multidisciplinary Design

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In this paper we treat subjects which are relevant in the context of iterative methods in implicit time integration for compressible flow simulations. We present a novel renumbering technique, some strategies for choosing the time step in the implicit time integration, and a novel implementation of a matrix-free evaluation for matrix-vector products. For the linearized compressible Euler equations, we present various comparative studies within the QUADFLOW package concerning preconditioning techniques, ordering methods, time stepping strategies, and different implementations of the matrix-vector product. The main goal is to improve efficiency and robustness of the iterative method used in the flow solver.

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Section: Methodsmentioning

confidence: 99%

Iterative Solvers for Discretized Stationary Euler Equations

Pollul

Reusken

2010

Notes on Numerical Fluid Mechanics and Multidisciplinary Design

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“…Among the fastest algorithms are the Newton-Krylov solvers (see Refs. [1][2][3][4]. For example, promising results are presented by Pueyo and Zingg,4 who used the preconditioned generalized minimum residual (GMRES) 5 Krylov subspace method in conjunction with an inexact Newton strategy.…”

Section: Introductionmentioning

confidence: 99%

“…[1][2][3][4]. For example, promising results are presented by Pueyo and Zingg,4 who used the preconditioned generalized minimum residual (GMRES) 5 Krylov subspace method in conjunction with an inexact Newton strategy. A critical component in this approach is a fast solution of the linear system at each Newton iteration, which is provided by the preconditioned GMRES algorithm.…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore, the same preconditioned GMRES algorithm is also used within a Newton-Krylov solver (see Ref. 4) for the solution of the ow eld equations.…”

Section: Introductionmentioning

confidence: 99%

“…We carefully linearize the twodimensional Navier-Stokes equations coupled with the SpalartAllmaras turbulence model. 23 We adopt the approach of Pueyo and Zingg 4 to solve the adjoint and ow-sensitivity equations using the GMRES algorithmin conjunctionwith a novel preconditionerbased on an approximation of the ow Jacobian matrix. Furthermore, the same preconditioned GMRES algorithm is also used within a Newton-Krylov solver (see Ref.…”

Section: Introductionmentioning

confidence: 99%

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Newton-Krylov algorithm for aerodynamic design using the Navier-Stokes equations

Nemec¹,

Zingg²

2002

AIAA Journal

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A Newton-Krylov algorithm is presented for two-dimensional Navier-Stokes aerodynamic shape optimization problems. The algorithm is applied to both the discrete-adjoint and the discrete ow-sensitivity methods for calculating the gradient of the objective function. The adjoint and ow-sensitivity equations are solved using a novel preconditioned generalized minimum residual (GMRES) strategy. Together with a complete linearization of the discretized Navier-Stokes and turbulence model equations, this results in an accurate and ef cient evaluation of the gradient. Furthermore, fast ow solutions are obtained using the same preconditioned GMRES strategy in conjunction with an inexact Newton approach. The performance of the new algorithm is demonstrated for several design examples, including inverse design, lift-constrained drag minimization, lift enhancement, and maximization of lift-to-drag ratio. In all examples, the norm of the gradient is reduced by several orders of magnitude, indicating that a local minimum has been obtained. By the use of the adjoint method, the gradient is obtained in from one-fth to one-half of the time required to converge a ow solution.

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The importance of structure in incomplete factorization preconditioners

Scott

Tůma

2010

Bit Numer Math

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In this paper, we consider level-based preconditioning, which is one of the basic approaches to incomplete factorization preconditioning of iterative methods. It is well-known that while structure-based preconditioners can be very useful, excessive memory demands can limit their usefulness. Here we present an improved strategy that considers the individual entries of the system matrix and restricts small entries to contributing to fewer levels of fill than the largest entries. Using symmetric positive-definite problems arising from a wide range of practical applications, we show that the use of variable levels of fill can yield incomplete Cholesky factorization preconditioners that are more efficient than those resulting from the standard level-based approach. The concept of level-based preconditioning, which is based on the structural properties of the system matrix, is then transferred to the numerical incomplete decomposition. In particular, the structure of the incomplete factorization determined in the symbolic factorization phase is explicitly used in the numerical factorization phase. Further numerical results demonstrate that our level-based approach can lead to much sparser but efficient incomplete factorization preconditioners.

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Efficient Newton-Krylov solver for aerodynamic computations

Cited by 27 publications

References 0 publications

Iterative Solvers for Discretized Stationary Euler Equations

Iterative Solvers for Discretized Stationary Euler Equations

Newton-Krylov algorithm for aerodynamic design using the Navier-Stokes equations

The importance of structure in incomplete factorization preconditioners

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