Prof. Michael Giles

Education

B.A.(Mathematics), Cambridge University, June 1981.
S.M.(Aeronautics), Massachusetts Institute of Technology, February 1983.
Thesis title: Asymptotic Analysis of Numerical Wave Propagation in Finite Difference Equations.
Ph.D.(Aeronautics), Massachusetts Institute of Technology, June 1985.
Thesis title: Newton Solution of Steady Two-Dimensional Transonic Flow.

Career

Undergraduate Engineering Apprentice,
Rolls-Royce Ltd., Derby
January 1978 - June 1981
Assistant Professor,
Dept. of Aeronautics and Astronautics, Massachusetts Institute of Technology,
July 1985 - June 1990
Associate Professor and Director of Computational Fluid Dynamics Laboratory,
Dept. of Aeronautics and Astronautics, Massachusetts Institute of Technology,
July 1990 - June 1992
Rolls-Royce Reader in Computational Fluid Dynamics
Oxford University Computing Laboratory,
July 1992 - June 1997
Professor of Computational Fluid Dynamics,
Oxford University Computing Laboratory,
July 1997 - June 2004
Professor of Scientific Computing,
Oxford University Computing Laboratory,
July 2004 - December 2007
Professor of Scientific Computing,
Oxford University Mathematical Institute,
January 2008 - present

Recent Administrative Duties

Director of the Rolls-Royce University Technology Centre for Computational Fluid Dynamics, 1992 - 2007.
Chairman of the Oxford Supercomputing Centre 1997-8 and 2003-6.
Co-Director of the Oxford Centre for Computational Finance, 2001 - 2007.
Founding member of the Oxford-Man Institute of Quantitative Finance, 2007 - present.

Recent Teaching

2002/2003

Numerical Computing -- second year Engineering and Computing Science
Numerically Intensive Computing for Finance -- MSc in Math Modelling and Scientific Computing
Numerically Intensive Computing for Finance -- MSc in Mathematical Finance

2003/2004

Numerical Computing -- second year Engineering and Computing Science
Numerically Intensive Computing for Finance -- MSc in Math Modelling and Scientific Computing
Numerically Intensive Computing for Finance -- MSc in Mathematical Finance

2004/2005

Numerically Intensive Computing for Finance -- MSc in Math Modelling and Scientific Computing
Numerically Intensive Computing for Finance -- MSc in Mathematical Finance

2005/2006 (one term on sabbatical)

Numerical Methods in Finance -- MSc in Mathematical Finance
Numerically Intensive Computing for Finance -- MSc in Math Modelling and Scientific Computing
Numerically Intensive Computing for Finance -- MSc in Mathematical Finance

2006/2007 (two terms on sabbatical / fellowship leave)

Numerical Methods in Finance -- MSc in Mathematical Finance
Numerical Computing -- second year Engineering and Computing Science
Numerically Intensive Computing for Finance -- MSc in Mathematical Finance

2007/2008 (three terms on sabbatical / fellowship leave)

Numerical Methods in Finance -- MSc in Mathematical Finance
Monte Carlo Methods -- MSc in Mathematical and Computational Finance
Numerically Intensive Computing for Finance -- MSc in Mathematical Finance

Student theses supervised

Dept. of Aeronautics and Astronautics, Massachusetts Institute of Technology

N. Brittain, S.M., "An investigation into the k-epsilon model of turbulence", 1986.

B. Krouthen, S.M., "A new investigation of hot streams in turbines" 1988.

D. Lindquist, S.M., "A comparison of numerical schemes on triangular and quadrilateral meshes", 1988.

S. Allmaras, PhD, "Coupled Euler/Navier-Stokes algorithm for 2D unsteady transonic shock/boundary-layer interaction", 1989.

M. Turner, PhD, "Design and analysis of three-dimensional internal flowfields using a two stream function formulation", 1990.

D. Lindquist, PhD, "Computation of unsteady transonic flowfields using shock capturing and the linear perturbation Euler equations", 1991.

A. Saxer, PhD, "A numerical analysis of 3D inviscid stator/rotor interactions using non-reflecting boundary conditions", 1991.

G. Fritsch, PhD, "An analytical and numerical study of the second-order effects of unsteadiness on the performance of turbomachines", 1991.

K. Isomura, PhD, "A numerical investigation of a flutter in a transonic fan", supervised jointly with Prof A. Epstein, 1996.
Oxford University Computing Laboratory

D. Burgess, DPhil, "Parallel computing for unstructured mesh algorithms", 1995.

G.N. Shrinivas, DPhil, "Three-dimensional design methods for turbomachinery applications", 1996.

A. Johnson, DPhil, "Parallelising implicit methods on unstructured grids", 1996.

N. Pierce, DPhil, "Preconditioned multigrid methods for compressible flow calculations on stretched meshes", 1997.

P. Moinier, DPhil, "Algorithm developments for an unstructured viscous flow solver", 1999.

M.C. Duta, DPhil, "The use of the adjoint method for the minimisation of forced vibration in turbomachinery", 2002.

A.L. Laird, DPhil, "A hybrid spectral discretisation and iterative solution methods for acoustic models in potential flow", 2004.

M.S. Campobasso, DPhil, "Effects of flow instabilities on the linear harmonic analysis of unsteady flow in turbomachinery", 2004.
Oxford University Mathematical Institute

K.E. Schmitz Abe, DPhil "Pricing exotic options using improved strong convergencee", 2007.

Research

(Note: in the text below, citations such as (4) refer to the journal and book publications listed subsequently.)

With an education in applied mathematics from Cambridge University and aeronautical engineering and computational methods from MIT, my major field of research has been computational fluid dynamics (CFD) for aeronautical applications, but my research has taken me into related areas in applied mathematics, numerical analysis, engineering and computational science, and more recently I have begun moving into computational finance.

At MIT my MSc thesis (2) was on the use of a discrete variant of WKB analysis in the numerical analysis of finite difference approximations of hyperbolic p.d.e.'s. My PhD thesis was on the development of an inverse design method for 2D airfoils and cascades (3,4). ISES/MISES, the resulting code developed jointly with Mark Drela, a fellow student, was licensed to most of the world's major aerospace companies and is still used today.

During the period 1985-92 when I was on the faculty in the MIT Dept. of Aeronautics and Astronautics, my main research focus was on the development of CFD methods for the computation of unsteady flows in turbomachinery, with research funding from Rolls-Royce plc. At the algorithmic level, my three main contributions were the `time-tilting' space-time transformation which I developed to overcome the problem of arbitrary pitch ratios in turbomachinery (6); the development of non-reflecting boundary conditions for the Euler equations to reduce the arbitrary reflections at truncated far-field boundaries (11,15); and the proof that a linearised version of the discretised Euler equations using `shock capturing' is able to correctly predict the unsteady impulse due to an oscillating shock (18). I also used the UNSFLO program which I developed for Rolls-Royce (14), to investigate, on my own and with others, a number of engineering aspects of the unsteady flows. The computation of unsteady shock propagation (10) and resultant unsteady heat transfer (13) in a transonic turbine were particularly challenging and the good agreement with experimental data was very satisfying. A second example involving comparison with experimental data and mathematical modelling was a spatial variation in time-averaged stagnation temperature, again due to stator/rotor interaction (16). A third investigation used second order asymptotic analysis in conjunction with CFD calculations to understand the time-averaged changes in engine efficiency due to unsteady effects (19).

In 1992, I joined the Numerical Analysis Group in the Oxford University Computing Laboratory. This move led to an increase in the breadth of my research interests, giving me the freedom to investigate a number of problems in numerical analysis arising from practical CFD computations. Two of these concerned the stability and accuracy of interface treatments in multidisciplinary applications (26,27); another two dealt with the accuracy of discrete approximations to flows with shocks (22) and the stability of a popular class of methods for approximating the Navier-Stokes equations (25,46). The last of these led to some more fundamental numerical analysis of the stability and convergence of numerical discretisations of partial differential equations (30). I have also used asymptotic analysis to understand and interpret the results of CFD calculations for the prediction of aircraft lift and drag (35,36).

As part of the move to Oxford, I founded the Rolls-Royce University Technology Centre in CFD. The research in this group has been centred on the development and analysis of CFD algorithms using unstructured grids. Paul Crumpton first developed an inviscid flow solver (31), and then developed a viscous solver with Pierre Moinier (32). In both cases, considerable convergence acceleration was achieved using multigrid, plus Jacobi preconditioning based on the DPhil research of Niles Pierce on structured grids (29). Another important aspect was the parallelisation of the unstructured grid solvers. This was accomplished through the development, primarily by Paul Crumpton, of a general purpose library called OPlus for the parallelisation of a large class of unstructured grid applications (21).

These elements formed the basis for a new suite of codes called HYDRA with three main elements: a nonlinear code for both steady and unsteady flow calculations, a linear harmonic unsteady perturbation code for flutter and forced response analysis, and an adjoint code for design optimisation (39,54) and forced response minimisation (60). The main algorithmic developments in this work included the preconditioned multigrid for hybrid grids (48), the techniques used to stabilise the iterative solution of the linear equations (52,53,57), and various aspects of the formulation and solution of the discrete adjoint equations (43,50). Mihai Duta, Pierre Moinier, Jens Muller and Niles Pierce all contributed to different aspects of HYDRA's initial development. Further development has since taken place within Rolls-Royce and other University Technology Centres, and HYDRA is now the main CFD code used within Rolls-Royce.

As well as pursuing the use of adjoint equations for design optimisation, I have also worked with Niles Pierce on error analysis using adjoint solutions. In particular, we developed a technique of adjoint error correction which corrects for the leading order discretisation errors in the evaluation of integral functionals, thereby doubling the order of accuracy for the functional output. (37,42,44,56). I have also investigated exact analytic solutions (40), and issues concerning the approximation of adjoint solutions when there is a discontinuity in the underlying nonlinear solution (51).

My work with Rolls-Royce included a brief excursion into aeroacoustics, developing a particularly efficient technique for non-axisymmetric engine nacelles (58,62,65) and a technique for preconditioning the iterative solution of Helmholtz and similar acoustic equations (66).

My most recent research has been in the area of computational finance, working with both PDE and Monte Carlo methods. On the PDE side, two papers (64,67) analysed the convergence properties of Crank-Nicolson and Rannacher time-marching. My first publication on Monte Carlo methods was joint work with Professor Paul Glasserman of Columbia University concerns on the use of adjoints for the efficient evaluation of financial sensitivities known as "Greeks" (61); Risk Magazine named us "Quants of the Year 2007" for this paper. My current recent is on multilevel Monte Carlo methods; papers are awaiting publication in Operations Research and a Springer-Verlag proceedings of the MCQMC06 conference.

Journal/book publications

M.B. Giles and M. Rose. `A numerical study of the steady scalar convective diffusion equation for small viscosity'. Journal of Computational Physics, 56(3):513-529, 1984.
M.B. Giles and W.T. Thompkins. `Propagation and stability of wavelike solutions of finite difference equations with variable coefficients'. Journal of Computational Physics, 58(3):349-360, 1985.
M.B. Giles and M. Drela. `A two-dimensional transonic aerodynamic design method'. AIAA Journal, 25(9):1199-1206, 1987.
M. Drela and M.B. Giles. `Viscous-inviscid analysis of transonic and low Reynolds number airfoils'. AIAA Journal, 25(10):1347-1355, 1987.
A.H. Epstein, J.B. Gertz, P.R. Owen and M.B. Giles. `Vortex shedding in high-speed compressor blade wakes'. AIAA Journal of Propulsion and Power, 4(3):236-244, 1988.
M.B. Giles. `Calculation of unsteady wake rotor interaction'. AIAA Journal, 4(4):356-362, 1988.
G.R. Guenette, A.H. Epstein, M.B. Giles, R. Haimes and R.J.G. Norton. `Fully scaled transonic turbine rotor heat transfer measurements'. Journal of Turbomachinery, 111:1-7, 1989.
B. Krouthen and M.B. Giles. `Numerical investigation of hot streaks in turbines'. AIAA Journal of Propulsion and Power, 6(6):769-776, 1990.
J.F. Dannenhoffer and M.B. Giles. `Convergence acceleration through the use of time inclining'. AIAA Journal, 28(8):1457-1463, 1990.
M.B. Giles. `Stator/rotor interaction in a transonic turbine'. AIAA Journal of Propulsion and Power, 6(5):621-627, 1990.
M.B. Giles. `Non-reflecting boundary conditions for Euler equation calculations'. AIAA Journal, 28(12):2050-2058, 1990.
M.B. Giles and R. Haimes. `Advanced interactive visualization for CFD'. Computing Systems in Engineering, 1(1):51-62, 1990.
R.S. Abhari, G.R. Guenette, A.H. Epstein and M.B. Giles. `Comparison of time-resolved turbine rotor blade heat transfer measurements and numerical calculations'. Journal of Turbomachinery, 114:818-826, 1992.
M.B. Giles and R. Haimes. `Validation of a numerical method for unsteady flow calculations'. Journal of Turbomachinery, 115:110-117, 1993.
A. Saxer and M.B. Giles. `Quasi-3D nonreflecting boundary conditions for Euler equation calculations'. AIAA Journal of Propulsion and Power, 9(2):263-271, 1993.
A.H. Epstein, M.B. Giles, T. Shang and A.K. Sehra. `Blade row interaction effects on compressor measurements'. AIAA Journal of Propulsion and Power, 9(4):569-578, 1993.
A.P. Saxer and M.B. Giles. `Predictions of three-dimensional steady and unsteady inviscid transonic stator/rotor interaction with inlet radial temperature nonuniformity'. Journal of Turbomachinery, 116:347-357, 1994.
D.R. Lindquist and M.B. Giles. `Validity of linearized unsteady Euler equations with shock capturing'. AIAA Journal, 32(1):46, 1994.
G. Fritsch and M.B. Giles. `An asymptotic analysis of mixing loss'. Journal of Turbomachinery, 117:367-374, 1995.
K.F.C. Yiu and M.B. Giles. `Simultaneous viscous-inviscid coupling via transpiration'. Journal of Computational Physics, 120:157-170, 1995.
P.I. Crumpton and M.B. Giles. `Multigrid aircraft computations using the OPlus parallel library'. in Parallel Computational Fluid Dynamics: Implementations and Results Using Parallel Computers, 339-346. A. Ecer, J. Periaux, N. Satofuka, and S. Taylor, editors, North-Holland, 1996.
M.B. Giles. `Analysis of the accuracy of shock-capturing in the steady quasi-1D Euler equations'. Computational Fluid Dynamics Journal, 5(2):247-258, 1996.
R.S. Abhari and M.B. Giles. `A Navier Stokes analysis of airfoils in oscillating transonic cascades for the prediction of aerodynamic damping'. Journal of Turbomachinery, 119:77-84, 1997.
D.A. Burgess and M.B. Giles `Renumbering unstructured grids to improve the performance of codes on hierarchical memory machines', Advances in Engineering Software, 28(3):189-201, 1997.
M.B. Giles. `Stability analysis of a Galerkin/Runge-Kutta Navier-Stokes discretisation on unstructured tetrahedral grids'. Journal of Computational Physics, 132:201-214, 1997.
M.B. Giles. `Stability and accuracy of numerical boundary conditions in aeroelastic analysis'. International Journal for Numerical Methods in Fluids, 24:739-757, 1997.
M.B. Giles. `Stability analysis of numerical interface boundary conditions in fluid-structure thermal analysis'. International Journal for Numerical Methods in Fluids, 25:421-436, 1997.
M.B. Giles. `Progress in applied numerical analysis for Computational Fluid Dynamics'. In Barriers and Challenges in CFD, Kluwer, 1997.
N.A. Pierce and M.B. Giles. `Preconditioned multigrid methods for compressible flow calculations on stretched meshes'. Journal of Computational Physics, 136:425-445, 1997.
M.B. Giles. `On the stability and convergence of discretisations of initial value p.d.e.s'. IMA Journal of Numerical Analysis, 17:563-576, 1997.
P.I. Crumpton and M.B. Giles. `Implicit time-accurate solutions on unstructured dynamic grids'. International Journal for Numerical Methods in Fluids, 25:1285-1300, 1997.
P.I. Crumpton, P. Moinier and M.B. Giles. `An unstructured algorithm for high Reynolds number flows on highly stretched grids', in Numerical Methods in Laminar and Turbulent Flow , 561-572. C. Taylor and J.T. Cross editors, Pineridge Press, 1997.
M.B. Giles. `On adjoint equations for error analysis and optimal grid adaptation', in Frontiers of Computational Fluid Dynamics 1998, 155-170. D.A. Caughey and M.M. Hafez editors, World Scientific, 1998.
K. Isomura and M.B. Giles. `A numerical study of flutter in a transonic fan'. Journal of Turbomachinery, 120(3):500-507, 1998.
M.B. Giles and R.M. Cummings. `Wake integration for three-dimensional flowfield computations: theoretical development', Journal of Aircraft , 36(2):357-365, 1999.
D.L. Hunt, R.M. Cummings and M.B. Giles `Wake integration for three-dimensional flowfield computations: applications', Journal of Aircraft , 36(2):366-373, 1999.
N.A. Pierce and M.B. Giles. `Adjoint recovery of superconvergent functionals from PDE approximations'. SIAM Review, 42(2):247-264, 2000.
D.L. Darmofal, P. Moinier and M.B. Giles. `Eigenmode analysis of boundary conditions for the one-dimensional preconditioned Euler equations'. Journal of Computational Physics, 160(1):369-384, 2000.
M.B. Giles and N.A. Pierce. `An introduction to the adjoint approach to design'. Flow, Turbulence and Combustion, 65(3-4):393-415, 2000.
M.B. Giles and N.A. Pierce. `Analytic adjoint solutions for the quasi-one-dimensional Euler equations'. Journal of Fluid Mechanics, 426:327-345, 2001.
M.S. Campobasso and M.B. Giles. `Analysis of the effect of mistuning on turbomachinery aeroelasticity' in Unsteady Aerodynamics, Aeroacoustics and Aeroelasticity in Turbomachines. P. Ferrand and S. Aubert editors, Presses Universitaire de Grenoble, 2001.
M.B. Giles and N.A. Pierce. `Superconvergent lift estimates through adjoint error analysis', in Innovative Methods for Numerical Solutions of Partial Differential Equations. M.M. Hafez and J.J. Chattot editors, World Scientific, 2001.
M.B. Giles `On the iterative solution of adjoint equations', in Automatic Differentiation: From Simulation to Optimization, pages 145-152. G. Corliss, C. Faure, A. Griewank, L. Hascoet, U. Naumann, editors, Springer-Verlag, 2001.
M.B. Giles. `Defect and adjoint error correction', in Computational Fluid Dynamics 2000. N. Satofuka, editor, Springer-Verlag, 2001.
M.B. Giles and N.A. Pierce. `Adjoint error correction for integral outputs', in Error Estimation and Adaptive Discretization Methods in Computational Fluid Dynamics, pages 47-96, editors T. Barth and H. Deconinck, volume 25 in Lecture Notes in Computational Science and Engineering. Springer-Verlag, 2002.
P. Moinier and M.B. Giles. `Stability analysis of preconditioned approximations of the Euler equations on unstructured meshes'. Journal of Computational Physics, 178:498-519, 2002.
M.B. Giles and E. Suli. `Adjoint methods for PDEs: a posteriori error analysis and postprocessing by duality'. Acta Numerica 2002, pages 145-236, Cambridge University Press, 2002.
P. Moinier, J.-D. Muller and M.B. Giles. `Edge-based multigrid and preconditioning for hybrid grids'. AIAA Journal, 40(10):1954-1960, 2002.
M.C. Duta, M.B. Giles and M.S. Campobasso. `The harmonic adjoint approach to unsteady turbomachinery design'. International Journal for Numerical Methods in Fluids, 40(3-4):323-332, 2002.
M.B. Giles, M.C. Duta, J.-D. Muller and N.A. Pierce. `Algorithm developments for discrete adjoint methods'. AIAA Journal, 41(2), 2003.
M.B. Giles. `Discrete adjoint approximations with shocks'. Hyperbolic Problems: Theory, Numerics, Applications, editors T. Hou and E. Tadmor, Springer-Verlag 2003.
M.S. Campobasso and M.B. Giles. `Stabilization of a linearized Navier-Stokes solver for turbomachinery aeroelasticity' in Computational Fluid Dynamics 2002. Springer-Verlag, 2003.
M.S. Campobasso and M.B. Giles. `Effect of flow instabilities on the linear analysis of turbomachinery aeroelasticity', AIAA Journal of Propulsion and Power, 19(2), 2003.
M.S. Campobasso, M.C. Duta and M.B. Giles. `Adjoint calculation of sensitivities of turbomachinery objective functions', AIAA Journal of Propulsion and Power, 19(4), 2003.
M.B. Giles, N.A. Pierce and E. Suli . `Progress in adjoint error correction for integral functionals', Computing and Visualisation in Science, 6(2-3), 2004.
N.A. Pierce and M.B. Giles. `Adjoint and Defect Error Bounding and Correction for Functional Estimates' Journal of Computational Physics, 200:769-794, 2004.
M.S. Campobasso and M.B. Giles. `Stabilization of a linear flow solver for turbomachinery aeroelasticity by means of the recursive projection method', AIAA Journal, 42(9) 1765-1774, 2004.
M.C. Duta, A. Laird and M.B. Giles. `Aeroacoustic analysis using a hybrid finite element method', Journal of Power and Energy, Proceedings of the IMechE Part A, 219:413-420, 2005.
P. Moinier and M.B. Giles. `Eigenmode analysis for turbomachinery applications', AIAA Journal of Propulsion and Power, 21(6): 973-978, 2005.
M.C. Duta, M.S. Campobasso, M.B. Giles and L.B. Lapworth. `Adjoint harmonic sensitivities for forced response minimisation', ASME Journal of Turbomachinery, 128:183-189, 2006.
M.B. Giles and P. Glasserman. `Smoking adjoints: fast Monte Carlo Greeks', RISK, January 2006.
M.C. Duta, M.B. Giles and A. Laird. `A hybrid FE/spectral analysis of turbofan aeroacoustics', in Computational Fluid Dynamics 2004. Springer-Verlag, 2006.
M.S. Campobasso and M.B. Giles. `Stabilizing linear harmonic flow solvers for turbomachinery aeroelasticity with complex iterative algorithms', AIAA Journal, 44(5):1048-1059, 2006. (PDF file: 700kb).
M.B. Giles and R. Carter. `Convergence analysis of Crank-Nicolson and Rannacher time-marching', Journal of Computational Finance, 9(4):89-112, 2006.
M.C. Duta and M.B. Giles. `A three-dimensional hybrid finite element/spectral analysis of noise radiation from turbofan inlets', Journal of Sound and Vibration, 296:623-642, 2006. (PDF file: 640kb).
A.L. Laird and M.B. Giles. `Preconditioning harmonic unsteady potential flow calculations', AIAA Journal, 44(11):2654-2662. 2006.
R. Carter and M.B. Giles. `Sharp error estimates for discretisations of the 1D convection/diffusion equation with Dirac initial data', IMA Journal of Numerical Analysis, 27(2):406-425, 2007