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.

/pdf/iterative-methods-for-sparse-linear-systems-34ozhpwq89.pdf

Iterative Methods for Sparse Linear Systems

http://www.inf.ufes.br/~luciac/comcie/JFNK-Knoll.pdf

Jacobian-free Newton-Krylov methods: a survey of approaches and applications

Optimal design methods involving the solution of an adjoint system of equations are an active area of research in computational fluid dynamics, particularly for aeronautical applications. This paper presents an introduction to the subject, emphasising the simplicity of the ideas when viewed in the context of linear algebra. Detailed discussions also include the extension to p.d.e.'s, the construction of the adjoint p.d.e. and its boundary conditions, and the physical significance of the adjoint solution. The paper concludes with examples of the use of adjoint methods for optimising the design of business jets.

/pdf/an-introduction-to-the-adjoint-approach-to-design-2kv9evoz8u.pdf

An Introduction to the Adjoint Approach to Design

A fictitious domain approach to the direct numerical simulation of incompressible viscous flow past moving rigid bodies: application to particulate flow

http://lsec.cc.ac.cn/lcfd/DEWENO/paper/WENO_Tri.pdf

Weighted Essentially Non-oscillatory Schemes on Triangular Meshes

A locally refined rectangular grid finite element method: application to computational fluid dynamics and computational physics

We study parallel two-level overlapping Schwarz algorithms for solving nonlinear finite element problems, in particular, for the full potential equation of aerodynamics discretized in two dimensions with bilinear elements. The overall algorithm, Newton--Krylov--Schwarz (NKS), employs an inexact finite difference Newton method and a Krylov space iterative method, with a two-level overlapping Schwarz method as a preconditioner. We demonstrate that NKS, combined with a density upwinding continuation strategy for problems with weak shocks, is robust and economical for this class of mixed elliptic-hyperbolic nonlinear partial differential equations, with proper specification of several parameters. We study upwinding parameters, inner convergence tolerance, coarse grid density, subdomain overlap, and the level of fill-in in the incomplete factorization, and report their effect on numerical convergence rate, overall execution time, and parallel efficiency on a distributed-memory parallel computer.

/pdf/parallel-newton-krylov-schwarz-algorithms-for-the-transonic-x7ujujejbv.pdf

Parallel Newton--Krylov--Schwarz Algorithms for the Transonic Full Potential Equation

We study parallel two-level overlapping Schwarz algorithms for solving nonlinear finite element problems, in particular, for the full potential equation of aerodynamics discretized in two dimensions with bilinear elements. The overall algorithm, Newton-Krylov-Schwarz (NKS), employs an inexact finite-difference Newton method and a Krylov space iterative method, with a two-level overlapping Schwarz method as a preconditioner. We demonstrate that NKS, combined with a density upwinding continuation strategy for problems with weak shocks, is robust and economical for this class of mixed elliptic-hyperbolic nonlinear partial differential equations, with proper specification of several parameters. We study upwinding parameters, inner convergence tolerance, coarse grid density, subdomain overlap, and the level of fill-in in the incomplete factorization, and report their effect on numerical convergence rate, overall execution time, and parallel efficiency on a distributed-memory parallel computer.

Parallel newton-krylov-schwarz algorithms for the transonic full potential equation

Three model problems associated with aerodynamic drag minimizations are studied. These test cases have been proposed by the aerodynamic design optimization discussion group, and they include an inviscid NACA0012 nonlifting airfoil, a viscous RAE2822 lifting airfoil, and a viscous lifting wing based on the NASA Common Research Model. Various optimization methods are used, including MDOPT, TRANAIR, SYN83, and SYN107. The resulting designed and associated baseline geometries are cross analyzed by several computational fluid dynamics codes, including OVERFLOW, TRANAIR, GGNS, and FLO82. Pathological issues are unveiled in both of the simple airfoil model problems. Designed geometries for the inviscid symmetric test case exhibit strong tendencies to permit nonsymmetric flow solutions. Designed airfoils for the viscous lifting case also support nonunique solutions and hysteresis loops at or near the design point in Reynolds-averaged Navier–Stokes and integral boundary-layer method simulations. These results prov...

Study Based on the AIAA Aerodynamic Design Optimization Discussion Group Test Cases

Practical Design and Optimization in Computational Fluid Dynamics

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