Effective adjoint approaches for computational fluid dynamics

[1]  Joaquim R. R. A. Martins,et al.  A Jacobian-free approximate Newton-Krylov startup strategy for RANS simulations , 2019, J. Comput. Phys..

[2]  Joaquim R. R. A. Martins,et al.  Design optimization for self-propulsion of a bulk carrier hull using a discrete adjoint method , 2019, Computers & Fluids.

[3]  Joaquim R. R. A. Martins,et al.  Aerothermal optimization of a ribbed U-bend cooling channel using the adjoint method , 2019, International Journal of Heat and Mass Transfer.

[4]  Joaquim R. R. A. Martins,et al.  CFD discrete adjoint benchmarks , 2019 .

[5]  P. Sagaut,et al.  Shape Optimization Using the Adjoint Lattice Boltzmann Method for Aerodynamic Applications , 2019, AIAA Journal.

[6]  Joaquim R. R. A. Martins,et al.  Robust aerodynamic shape optimization—From a circle to an airfoil , 2019, Aerospace Science and Technology.

[7]  Joaquim R. R. A. Martins,et al.  OpenMDAO: an open-source framework for multidisciplinary design, analysis, and optimization , 2019, Structural and Multidisciplinary Optimization.

[8]  Joaquim R. R. A. Martins,et al.  High-Fidelity Design-Allocation Optimization of a Commercial Aircraft Maximizing Airline Profit , 2019, Journal of Aircraft.

[9]  Joaquim R. R. A. Martins,et al.  Aerodynamic Shape Optimization with Time Spectral Flutter Adjoint , 2019, AIAA Scitech 2019 Forum.

[10]  Dimitri J. Mavriplis,et al.  Discrete Adjoint Formulation for Turbulent Flow Problems with Transition Modelling on Unstructured Meshes , 2019, AIAA Scitech 2019 Forum.

[11]  Joaquim R. R. A. Martins,et al.  An Object-oriented Framework for Rapid Discrete Adjoint Development using OpenFOAM , 2019, AIAA Scitech 2019 Forum.

[12]  Joaquim R. R. A. Martins,et al.  Computational Modeling of Flutter Constraint for High-Fidelity Aerostructural Optimization , 2019, AIAA Scitech 2019 Forum.

[13]  Joaquim R. R. A. Martins,et al.  Impact of Morphing Trailing Edges on Mission Performance for the Common Research Model , 2019, Journal of Aircraft.

[14]  Joaquim R. R. A. Martins,et al.  RANS-Based Aerodynamic Shape Optimization of a Strut-Braced Wing with Overset Meshes , 2018, Journal of Aircraft.

[15]  Nicolas R. Gauger,et al.  High-Performance Derivative Computations using CoDiPack , 2017, ACM Trans. Math. Softw..

[16]  Joaquim R. R. A. Martins,et al.  Multimodality in aerodynamic wing design optimization , 2017 .

[17]  Markus Towara,et al.  Discrete adjoint optimization with OpenFOAM , 2019 .

[18]  Barry F. Smith,et al.  PETSc Users Manual , 2019 .

[19]  Joaquim R. R. A. Martins,et al.  Coupled aeropropulsive design optimisation of a boundary-layer ingestion propulsor , 2018, The Aeronautical Journal.

[20]  J. Martins,et al.  Multipoint high-fidelity CFD-based aerodynamic shape optimization of a 10 MW wind turbine , 2018, Wind Energy Science.

[21]  K. Giannakoglou,et al.  Multi-point aerodynamic shape optimization of cars based on continuous adjoint , 2018, Structural and Multidisciplinary Optimization.

[22]  Joaquim R. R. A. Martins,et al.  Design of a transonic wing with an adaptive morphing trailing edge via aerostructural optimization , 2018, Aerospace Science and Technology.

[23]  K. Giannakoglou,et al.  The continuous adjoint method for shape optimization in Conjugate Heat Transfer problems with turbulent incompressible flows , 2018, Applied Thermal Engineering.

[24]  Jens-Dominik Mueller,et al.  STAMPS: a Finite-Volume Solver Framework for Adjoint Codes Derived with Source-Transformation AD , 2018, 2018 Multidisciplinary Analysis and Optimization Conference.

[25]  Christian B Allen,et al.  Efficient Multi-Resolution Approaches for Exploration of External Aerodynamic Shape and Topology , 2018, 2018 Applied Aerodynamics Conference.

[26]  Graeme J. Kennedy,et al.  Application of a Time-Accurate Aeroelastic Coupling Framework to Flutter-Constrained Design Optimization , 2018, 2018 Multidisciplinary Analysis and Optimization Conference.

[27]  Joaquim R. R. A. Martins,et al.  Aerothermal Optimization of Internal Cooling Passages Using a Discrete Adjoint Method , 2018, 2018 Joint Thermophysics and Heat Transfer Conference.

[28]  Joaquim R. R. A. Martins,et al.  Trajectory Optimization of a Supersonic Aircraft with a Thermal Fuel Management System , 2018, 2018 Multidisciplinary Analysis and Optimization Conference.

[29]  Joaquim R. R. A. Martins,et al.  A Computational Architecture for Coupling Heterogeneous Numerical Models and Computing Coupled Derivatives , 2018, ACM Trans. Math. Softw..

[30]  Timothy R. Brooks,et al.  Benchmark Aerostructural Models for the Study of Transonic Aircraft Wings , 2018, AIAA Journal.

[31]  Athanasios Barlas,et al.  Computational fluid dynamics-based surrogate optimization of a wind turbine blade tip extension for maximising energy production , 2018, Journal of Physics: Conference Series.

[32]  Thomas D. Economon,et al.  Adjoint-based fluid dynamic design optimization in quasi-periodic unsteady flow problems using a harmonic balance method , 2018, J. Comput. Phys..

[33]  Joaquim R. R. A. Martins,et al.  An aerodynamic design optimization framework using a discrete adjoint approach with OpenFOAM , 2018 .

[34]  Joaquim R. R. A. Martins,et al.  On the influence of optimization algorithm and initial design on wing aerodynamic shape optimization , 2018 .

[35]  Cetin Batur Dilgen,et al.  Topology Optimization of Turbulent Flows , 2018 .

[36]  Joaquim R. R. A. Martins,et al.  Open-source coupled aerostructural optimization using Python , 2018 .

[37]  Ji-chao Li,et al.  Adjoint-Based Two-Step Optimization Method Using Proper Orthogonal Decomposition and Domain Decomposition , 2018 .

[38]  John T. Hwang,et al.  Large-Scale Multidisciplinary Optimization of an Electric Aircraft for On-Demand Mobility , 2018 .

[39]  Niklas Kühl,et al.  Adjoint volume-of-fluid approaches for the hydrodynamic optimisation of ships , 2018 .

[40]  C. Mader,et al.  Modeling Boundary Layer Ingestion Using a Coupled Aeropropulsive Analysis , 2018 .

[41]  Dimitri J. Mavriplis,et al.  Adjoint-Based Aeroacoustic Design-Optimization of Flexible Rotors in Forward Flight , 2017 .

[42]  Jens-Dominik Müller,et al.  Adjoint based design optimisation of an internal cooling channel U-bend for minimized pressure losses , 2017 .

[43]  Thomas D. Economon,et al.  Adjoint Formulation Investigations of Benchmark Aerodynamic Design Cases in SU2 , 2017 .

[44]  Joaquim R. R. A. Martins,et al.  Aerodynamic shape optimization of wind turbine blades using a Reynolds‐averaged Navier–Stokes model and an adjoint method , 2017 .

[45]  J. Martins,et al.  Buffet-Onset Constraint Formulation for Aerodynamic Shape Optimization , 2017 .

[46]  S. Timme,et al.  Robust and efficient adjoint solver for complex flow conditions , 2017 .

[47]  Yi-sheng Gao,et al.  Automatic differentiation based discrete adjoint method for aerodynamic design optimization on unstructured meshes , 2017 .

[48]  R. Liem,et al.  Expected drag minimization for aerodynamic design optimization based on aircraft operational data , 2017 .

[49]  Joaquim R. R. A. Martins,et al.  An efficient parallel overset method for aerodynamic shape optimization , 2017 .

[50]  Timothy R. Brooks,et al.  High-fidelity multipoint aerostructural optimization of a high aspect ratio tow-steered composite wing , 2017 .

[51]  Zhenping Feng,et al.  Study on continuous adjoint optimization with turbulence models for aerodynamic performance and heat transfer in turbomachinery cascades , 2017 .

[52]  Xin Yuan,et al.  An Efficient Unsteady Adjoint Optimization System for Multistage Turbomachinery , 2017 .

[53]  Andrew Ning,et al.  Integrated Design of Downwind Land-based Wind Turbines using Analytic Gradients , 2016 .

[54]  Ken Badcock,et al.  Enabling off-design linearised aerodynamics analysis using Krylov subspace recycling technique , 2016 .

[55]  Tim A. Albring,et al.  Efficient Aerodynamic Design using the Discrete Adjoint Method in SU2 , 2016 .

[56]  K. Giannakoglou,et al.  Continuous Adjoint Methods for Turbulent Flows, Applied to Shape and Topology Optimization: Industrial Applications , 2016 .

[57]  J. Alonso,et al.  SU2: An Open-Source Suite for Multiphysics Simulation and Design , 2016 .

[58]  Takayuki Yamada,et al.  Topology optimization in thermal-fluid flow using the lattice Boltzmann method , 2016, J. Comput. Phys..

[59]  Qiqi Wang,et al.  Least Squares Shadowing Sensitivity Analysis of Chaotic Flow Around a Two-Dimensional Airfoil , 2016 .

[60]  John T. Hwang,et al.  Multidisciplinary Design Optimization of Aircraft Configurations Part 1 : A modular coupled adjoint approach , 2016 .

[61]  Timothy R. Brooks,et al.  Multidisciplinary Design Optimization of Aircraft Configurations Part 2 : High-fidelity aerostructural optimization , 2016 .

[62]  Joaquim R. R. A. Martins,et al.  Aerodynamic Shape Optimization of Common Research Model Wing–Body–Tail Configuration , 2016 .

[63]  J. Martins,et al.  Multipoint Aerodynamic Shape Optimization Investigations of the Common Research Model Wing , 2015 .

[64]  Joaquim R. R. A. Martins,et al.  High-Fidelity Hydrodynamic Shape Optimization of a 3-D Hydrofoil , 2015 .

[65]  K. Giannakoglou,et al.  The continuous adjoint approach to the k–ω SST turbulence model with applications in shape optimization , 2015 .

[66]  Marcus Meyer,et al.  Stabilisation of discrete steady adjoint solvers , 2015, J. Comput. Phys..

[67]  Yang Wang,et al.  Fixed point discrete adjoint of SIMPLE-like solvers , 2015 .

[68]  Thomas A. Reist,et al.  Drag Minimization Based on the Navier–Stokes Equations Using a Newton–Krylov Approach , 2015 .

[69]  D. P. Young,et al.  Study Based on the AIAA Aerodynamic Design Optimization Discussion Group Test Cases , 2015 .

[70]  Joaquim R. R. A. Martins,et al.  Aerodynamic Shape Optimization Investigations of the Common Research Model Wing Benchmark , 2015 .

[71]  Joaquim R. R. A. Martins,et al.  Multimission Aircraft Fuel-Burn Minimization via Multipoint Aerostructural Optimization , 2015 .

[72]  Joaquim R. R. A. Martins,et al.  Aerodynamic Design Optimization Studies of a Blended-Wing-Body Aircraft , 2014 .

[73]  Joaquim R. R. A. Martins,et al.  A parallel finite-element framework for large-scale gradient-based design optimization of high-performance structures , 2014 .

[74]  Jeffrey P. Thomas,et al.  Discrete Adjoint Method for Aeroelastic Design Optimization , 2014 .

[75]  C. Othmer.  Adjoint methods for car aerodynamics , 2014 .

[76]  Graeme J. Kennedy,et al.  Scalable Parallel Approach for High-Fidelity Steady-State Aeroelastic Analysis and Adjoint Derivative Computations , 2014 .

[77]  Joaquim R. R. A. Martins,et al.  Multipoint High-Fidelity Aerostructural Optimization of a Transport Aircraft Configuration , 2014 .

[78]  Jens-Dominik Müller,et al.  CAD‐based shape optimisation with CFD using a discrete adjoint , 2014 .

[79]  Jacques Peter,et al.  Gradient-Based Aerodynamic Optimization with the elsA Software , 2014 .

[80]  P. Luchini,et al.  Adjoint Equations in Stability Analysis , 2014, 2404.17304.

[81]  J. Martins,et al.  Benchmarking Optimization Algorithms for Wing Aerodynamic Design Optimization , 2014 .

[82]  John T. Hwang,et al.  Review and Unification of Methods for Computing Derivatives of Multidisciplinary Computational Models , 2013 .

[83]  B. Lockwood,et al.  Gradient-based methods for uncertainty quantification in hypersonic flows , 2013 .

[84]  C. Mader,et al.  Stability-Constrained Aerodynamic Shape Optimization of Flying Wings , 2013 .

[85]  Cody A. Paige,et al.  Automatic Differentiation Adjoint of the Reynolds-Averaged Navier-Stokes Equations with a Turbulence Model , 2013 .

[86]  Jeffrey P. Thomas,et al.  Discrete Adjoint Method for Nonlinear Aeroelastic Sensitivities for Compressible and Viscous Flows , 2013 .

[87]  Laurent Hascoët,et al.  The Tapenade automatic differentiation tool: Principles, model, and specification , 2013, TOMS.

[88]  David A. Ham,et al.  Automated Derivation of the Adjoint of High-Level Transient Finite Element Programs , 2012, SIAM J. Sci. Comput..

[89]  Qiqi Wang,et al.  Forward and adjoint sensitivity computation of chaotic dynamical systems , 2012, J. Comput. Phys..

[90]  Uwe Naumann,et al.  A Discrete Adjoint Model for OpenFOAM , 2013, ICCS.

[91]  C. Mader,et al.  Derivatives for Time-Spectral Computational Fluid Dynamics Using an Automatic Differentiation Adjoint , 2012 .

[92]  Kai A. James,et al.  Structural and Multidisciplinary Optimization Manuscript No. Stress-constrained Topology Optimization with Design- Dependent Loading , 2022 .

[93]  J. Alonso,et al.  A Coupled-Adjoint Method for Aerodynamic and Aeroacoustic Optimization , 2012 .

[94]  Joaquim R. R. A. Martins,et al.  Extensions to the design structure matrix for the description of multidisciplinary design, analysis, and optimization processes , 2012, Structural and Multidisciplinary Optimization.

[95]  Anders Logg,et al.  Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book , 2012 .

[96]  Uwe Naumann,et al.  The Art of Differentiating Computer Programs - An Introduction to Algorithmic Differentiation , 2012, Software, environments, tools.

[97]  Boris Diskin,et al.  Discrete Adjoint-Based Design for Unsteady Turbulent Flows on Dynamic Overset Unstructured Grids , 2012 .

[98]  Eric Blades,et al.  A fast mesh deformation method using explicit interpolation , 2012, J. Comput. Phys..

[99]  C. Mader,et al.  Computation of Aircraft Stability Derivatives Using an Automatic Differentiation Adjoint Approach , 2011 .

[100]  Uri M. Ascher,et al.  A First Course in Numerical Methods , 2011 .

[101]  D. Darmofal,et al.  Review of Output-Based Error Estimation and Mesh Adaptation in Computational Fluid Dynamics , 2011 .

[102]  U. Naumann,et al.  dco/c++: Derivative Code by Overloading in C++ , 2011 .

[103]  Joel Brezillon,et al.  Investigation on Adjoint Based Gradient Computations for Realistic 3d Aero-Optimization , 2010 .

[104]  Joaquim R. R. A. Martins,et al.  A CAD-Free Approach to High-Fidelity Aerostructural Optimization , 2010 .

[105]  Jason E. Hicken,et al.  A Simplified and Flexible Variant of GCROT for Solving Nonsymmetric Linear Systems , 2010, SIAM J. Sci. Comput..

[106]  D. X. Wang,et al.  Adjoint Aerodynamic Design Optimization for Blades in Multistage Turbomachines—Part I: Methodology and Verification , 2010 .

[107]  Li He,et al.  Adjoint Aerodynamic Design Optimization for Blades in Multistage Turbomachines—Part II: Validation and Application , 2010 .

[108]  R. Dwight,et al.  Numerical sensitivity analysis for aerodynamic optimization: A survey of approaches , 2010 .

[109]  Jason E. Hicken,et al.  Aerodynamic Optimization Algorithm with Integrated Geometry Parameterization and Mesh Movement , 2010 .

[110]  R. Dwight,et al.  Efficient and robust algorithms for solution of the adjoint compressible Navier–Stokes equations with applications , 2009 .

[111]  C. Othmer.  A continuous adjoint formulation for the computation of topological and surface sensitivities of ducted flows , 2008 .

[112]  Jason E. Hicken,et al.  Parallel Newton-Krylov Solver for the Euler Equations Discretized Using Simultaneous-Approximation Terms , 2008 .

[113]  John C. Vassberg,et al.  Development of a Common Research Model for Applied CFD Validation Studies , 2008 .

[114]  M. Giles.  Collected Matrix Derivative Results for Forward and Reverse Mode Algorithmic Differentiation , 2008 .

[115]  David W. Zingg,et al.  Numerical aerodynamic optimization incorporating laminar-turbulent transition prediction , 2007 .

[116]  D. Mavriplis.  Discrete Adjoint-Based Approach for Optimization Problems on Three-Dimensional Unstructured Meshes , 2007 .

[117]  R. Dwight,et al.  Effect of Approximations of the Discrete Adjoint on Gradient-Based Optimization , 2006 .

[118]  J. Alonso,et al.  ADjoint: An Approach for the Rapid Development of Discrete Adjoint Solvers , 2006 .

[119]  P. Lallemand,et al.  Adjoint lattice Boltzmann equation for parameter identification , 2006 .

[120]  D. Mavriplis.  Multigrid Solution of the Discrete Adjoint for Optimization Problems on Unstructured Meshes , 2006 .

[121]  Andrea Walther,et al.  Differentiating Fixed Point Iterations with ADOL-C: Gradient Calculation for Fluid Dynamics , 2006, HPSC.

[122]  Georgi Kalitzin,et al.  Unsteady turbomachinery computations using massively parallel platforms , 2006 .

[123]  D. Ghate,et al.  Using Automatic Differentiation for Adjoint CFD Code Development , 2005 .

[124]  Alan Carle,et al.  Reducing reverse-mode memory requirements by using profile-driven checkpointing , 2005, Future Gener. Comput. Syst..

[125]  Jeffrey P. Thomas,et al.  Discrete Adjoint Approach for Modeling Unsteady Aerodynamic Design Sensitivities , 2005 .

[126]  Alex Pothen,et al.  What Color Is Your Jacobian? Graph Coloring for Computing Derivatives , 2005, SIAM Rev..

[127]  Jens-Dominik Müller,et al.  On the performance of discrete adjoint CFD codes using automatic differentiation , 2005 .

[128]  J. Alonso,et al.  A Coupled-Adjoint Sensitivity Analysis Method for High-Fidelity Aero-Structural Design , 2005 .

[129]  E. Nielsen,et al.  Efficient Construction of Discrete Adjoint Operators on Unstructured Grids Using Complex Variables , 2005 .

[130]  T. Pulliam,et al.  Adjoint Formulation for an Embedded-Boundary Cartesian Method , 2005 .

[131]  E. Nielsen,et al.  Using an Adjoint Approach to Eliminate Mesh Sensitivities in Computational Design , 2005 .

[132]  D. Darmofal,et al.  An implicit, exact dual adjoint solution method for turbulent flows on unstructured grids , 2004 .

[133]  Joaquim R. R. A. Martins,et al.  The complex-step derivative approximation , 2003, TOMS.

[134]  Yousef Saad,et al.  Iterative methods for sparse linear systems , 2003 .

[135]  M. Giles,et al.  Algorithm Developments for Discrete Adjoint Methods , 2003 .

[136]  A. Griewank,et al.  Piggyback Differentiation and Optimization , 2003 .

[137]  Erich Kaltofen,et al.  Computer Algebra Handbook : Foundations · Applications · Systems , 2003 .

[138]  Antony Jameson,et al.  Aerodynamic Shape Optimization Using the Adjoint Method , 2003 .

[139]  T. Pulliam,et al.  Multipoint and Multi-Objective Aerodynamic Shape Optimization , 2002 .

[140]  Joaquim R. R. A. Martins,et al.  High-Fidelity Aerostructural Design Optimization of a Supersonic Business Jet , 2002 .

[141]  M. Giles,et al.  Adjoint methods for PDEs: a posteriori error analysis and postprocessing by duality , 2002, Acta Numerica.

[142]  D. Zingg,et al.  Newton-Krylov Algorithm for Aerodynamic Design Using the Navier-Stokes Equations , 2002 .

[143]  M. Hafez,et al.  Frontiers of Computational Fluid Dynamics 2002 , 2001 .

[144]  R. M. Hicks,et al.  Single-Point and Multipoint Aerodynamic Shape Optimization of High-Speed Civil Transport , 2001 .

[145]  A. Iollo,et al.  An aerodynamic optimization method based on the inverse problem adjoint equations , 2001 .

[146]  Antony Jameson,et al.  A perspective on computational algorithms for aerodynamic analysis and design , 2001 .

[147]  S. Obayashi,et al.  Aerodynamic Optimization of Supersonic Transport Wing Using Unstructured Adjoint Method , 2001 .

[148]  Niles A. Pierce,et al.  An Introduction to the Adjoint Approach to Design , 2000 .

[149]  M. Giles.  On the iterative solution of adjoint equations , 2000 .

[150]  A. Jameson,et al.  A COMPARISON OF THE CONTINUOUS AND DISCRETE ADJOINT APPROACH TO AUTOMATIC AERODYNAMIC OPTIMIZATION , 2000 .

[151]  M. Allen,et al.  Sensitivity analysis of the climate of a chaotic system , 2000 .

[152]  Mark Drela,et al.  Pros & Cons of Airfoil Optimization , 1998 .

[153]  J. Eric,et al.  Aerodynamic Design Optimization on Unstructured Meshes Using the Navier-Stokes Equations , 1998 .

[154]  Jeffrey T. Onufer,et al.  A diagonalized diagonal dominant alternating direction implicit (D3ADI) scheme and subiteration correction , 1998 .

[155]  A. Jameson,et al.  Optimum Aerodynamic Design Using the Navier–Stokes Equations , 1997 .

[156]  E. Oran.  Frontiers in Computational Fluid Dynamics , 1997 .

[157]  P. Roe.  Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes , 1997 .

[158]  B. Mohammadi.  a New Optimal Shape Design Procedure for Inviscid and Viscous Turbulent Flows , 1997 .

[159]  M. J. Rimlinger,et al.  Constrained Multipoint Aerodynamic Shape Optimization Using an Adjoint Formulation and Parallel Computers , 1997 .

[160]  W. K. Anderson,et al.  Aerodynamic design optimization on unstructured grids with a continuous adjoint formulation , 1997 .

[161]  J. Peraire,et al.  Practical Three-Dimensional Aerodynamic Design and Optimization Using Unstructured Meshes , 1997 .

[162]  W. K. Anderson,et al.  Aerodynamic Design on Unstructured Grids for Turbulent , 1997 .

[163]  William Gropp,et al.  Efficient Management of Parallelism in Object-Oriented Numerical Software Libraries , 1997, SciTools.

[164]  A. Jameson,et al.  Aerodynamic Shape Optimization of Complex Aircraft Configurations via an Adjoint Formulation , 1996 .

[165]  F. Menter.  Two-equation eddy-viscosity turbulence models for engineering applications , 1994 .

[166]  Y. Marzouk,et al.  Large-Scale Inverse Problems and Quantification of Uncertainty , 1994 .

[167]  B. Christianson.  Reverse accumulation and attractive fixed points , 1994 .

[168]  P. A. Newman,et al.  An incremental strategy for calculating consistent discrete CFD sensitivity derivatives , 1992 .

[169]  Arthur C. Taylor,et al.  Observations on computational methodologies for use in large-scale, gradient-based, multidisciplinary design , 1992 .

[170]  P. Spalart.  A One-Equation Turbulence Model for Aerodynamic Flows , 1992 .

[171]  Eli Turkel,et al.  Effect of artificial viscosity on three-dimensional flow solutions , 1990 .

[172]  Antony Jameson,et al.  Aerodynamic design via control theory , 1988, J. Sci. Comput..

[173]  C. Rhie,et al.  Numerical Study of the Turbulent Flow Past an Airfoil with Trailing Edge Separation , 1983 .

[174]  A. Jameson,et al.  Numerical solution of the Euler equations by finite volume methods using Runge Kutta time stepping schemes , 1981 .

[175]  George M. Siouris,et al.  Applied Optimal Control: Optimization, Estimation, and Control , 1979, IEEE Transactions on Systems, Man, and Cybernetics.

[176]  B. V. Leer,et al.  Towards the ultimate conservative difference scheme V. A second-order sequel to Godunov's method , 1979 .

[177]  J. Arora,et al.  Efficient optimal design of structures by generalized steepest descent programming , 1976 .

[178]  O. Pironneau.  On optimum profiles in Stokes flow , 1973, Journal of Fluid Mechanics.

[179]  D. Spalding,et al.  A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows , 1972 .

[180]  J. Lions.  Optimal Control of Systems Governed by Partial Differential Equations , 1971 .

[181]  Arthur E. Bryson,et al.  Applied Optimal Control , 1969 .

[182]  J. N. Lyness,et al.  Numerical Differentiation of Analytic Functions , 1967 .