Edit Profile (opens in new tab) Giles, Michael B. Co-Author Distance Author ID: giles.michael-b Published as: Giles, Michael B.; Giles, M. B.; Giles, Mike; Giles, Michael; Giles, Mike B.; B. Giles, Michael; Giles, M. more...less Homepage: http://people.maths.ox.ac.uk/~gilesm/ External Links: MGP · ORCID · ResearchGate · dblp Documents Indexed: 91 Publications since 1984, including 9 Additional arXiv Preprints 1 Contribution as Editor Co-Authors: 70 Co-Authors with 72 Joint Publications 1,621 Co-Co-Authors all top 5 Co-Authors 20 single-authored 8 Pierce, Niles A. 5 Fang, Wei 5 Ritter, Klaus 5 Szpruch, Lukasz 3 Croci, Matteo 3 Haji-Ali, Abdul-Lateef 3 Hefter, Mario 3 Mayer, Lukas 3 Nagapetyan, Tigran 3 Scheichl, Robert 3 Sheridan-Methven, Oliver 2 Campobasso, M. Sergio 2 Drela, Mark 2 Farrell, Patrick E. 2 Goda, Takashi 2 Kuo, Frances Y. 2 Lester, Christopher G. 2 Moinier, Pierre 2 Nguyen, Ngoc Cuong 2 Sloan, Ian Hugh 2 Süli, Endre E. 2 Teckentrup, Aretha L. 2 Thompkins, W. T. jun. 2 Ulbrich, Stefan 2 Vidal-Codina, F. 2 Vollmer, Sebastian J. 2 Waterhouse, Benjamin J. 2 Xia, Yuan 2 Zygalakis, Konstantinos C. 1 Appleyard, Jeremy 1 Baines, Michael J. 1 Baker, Ruth Elizabeth 1 Bernal, Francisco 1 Burgos, Sylvestre 1 Carter, Rebecca 1 Cliffe, K. Andrew 1 Crumpton, P. I. 1 Darmofal, David L. 1 Debrabant, Kristian 1 Duta, M. C. 1 Farmer, Christopher L. 1 He, Zhijian 1 Higham, Desmond J. 1 Hironaka, Tomohiko 1 Jammy, Satya P. 1 Jentzen, Arnulf 1 Katsiolides, Grigoris 1 László, Endre 1 Lindquist, Dana R. 1 Majka, Mateusz B. 1 Mao, Xuerong 1 Mudalige, Gihan R. 1 Müller, Eike Hermann 1 Rabbitt, Michael 1 Reguly, István Z. 1 Reisinger, Christoph 1 Rognes, Marie Elisabeth 1 Rose, Milton E. 1 Rößler, Andreas 1 Sandham, Neil D. 1 Schmitz Abe, Klaus 1 Shardlow, Tony 1 Thom, Howard 1 Thomson, David J. 1 Ullmann, Elisabeth 1 Welti, Timo 1 Whittle, James 1 Xie, Fei 1 Yates, Christian A. 1 Yiu, Ka Fai Cedric all top 5 Serials 10 Journal of Computational Physics 8 SIAM/ASA Journal on Uncertainty Quantification 5 International Journal for Numerical Methods in Fluids 3 IMA Journal of Numerical Analysis 2 AIAA Journal 2 ACM Transactions on Mathematical Software 2 SIAM Journal on Numerical Analysis 2 The Annals of Applied Probability 2 Finance and Stochastics 2 Computing and Visualization in Science 2 Acta Numerica 2 Statistics and Computing 1 Journal of Fluid Mechanics 1 Journal of Mathematical Analysis and Applications 1 Bulletin of Mathematical Biology 1 Numerische Mathematik 1 Operations Research 1 Journal of Complexity 1 SIAM Review 1 SIAM Journal on Scientific Computing 1 International Journal of Computational Fluid Dynamics 1 Flow, Turbulence and Combustion 1 The ANZIAM Journal 1 Foundations of Computational Mathematics 1 Discrete and Continuous Dynamical Systems. Series B 1 HERMIS-\(\mu\pi\). Hellenic European Research on Mathematics and Informatics Science 1 SIAM Journal on Financial Mathematics all top 5 Fields 73 Numerical analysis (65-XX) 36 Probability theory and stochastic processes (60-XX) 25 Fluid mechanics (76-XX) 20 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 14 Partial differential equations (35-XX) 6 Ordinary differential equations (34-XX) 3 Statistics (62-XX) 2 Approximations and expansions (41-XX) 2 Mechanics of deformable solids (74-XX) 1 General and overarching topics; collections (00-XX) 1 Difference and functional equations (39-XX) 1 Computer science (68-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Geophysics (86-XX) 1 Operations research, mathematical programming (90-XX) 1 Biology and other natural sciences (92-XX) 1 Mathematics education (97-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 76 Publications have been cited 2,318 times in 1,368 Documents Cited by ▼ Year ▼ Multilevel Monte Carlo path simulation. Zbl 1167.65316 Giles, Michael B. 499 2008 Multilevel Monte Carlo methods. Zbl 1316.65010 Giles, Michael B. 237 2015 Multilevel Monte Carlo methods and applications to elliptic PDEs with random coefficients. Zbl 1241.65012 Cliffe, K. A.; Giles, M. B.; Scheichl, R.; Teckentrup, A. L. 212 2011 Adjoint methods for PDEs: a posteriori error analysis and postprocessing by duality. Zbl 1105.65350 Giles, Michael B.; Süli, Endre 193 2002 An introduction to the adjoint approach to design. Zbl 0996.76023 Giles, Michael B.; Pierce, Niles A. 163 2000 Adjoint recovery of superconvergent functionals from PDE approximations. Zbl 0948.65119 Pierce, Niles A.; Giles, Michael B. 106 1998 Further analysis of multilevel Monte Carlo methods for elliptic PDEs with random coefficients. Zbl 1306.65009 Teckentrup, A. L.; Scheichl, R.; Giles, M. B.; Ullmann, E. 90 2013 Improved multilevel Monte Carlo convergence using the Milstein scheme. Zbl 1141.65321 Giles, Mike 81 2008 Antithetic multilevel Monte Carlo estimation for multi-dimensional SDEs without Lévy area simulation. Zbl 1373.65007 Giles, Michael B.; Szpruch, Lukasz 54 2014 Adjoint and defect error bounding and correction for functional estimates. Zbl 1058.65121 Pierce, Niles A.; Giles, Michael B. 42 2004 Analytic adjoint solutions for the quasi-one-dimensional Euler equations. Zbl 0967.76079 Giles, Michael B.; Pierce, Niles A. 37 2001 Multilevel quasi-Monte Carlo path simulation. Zbl 1181.91335 Giles, Michael B.; Waterhouse, Benjamin J. 35 2009 Preconditioned multigrid methods for compressible flow calculations on stretched meshes. Zbl 0893.76061 Pierce, Niles A.; Giles, Michael B. 31 1997 Stability analysis of numerical interface conditions in fluid-structure thermal analysis. Zbl 0891.76058 Giles, M. B. 29 1997 Viscous-inviscid analysis of transonic and low Reynolds number airfoils. Zbl 0635.76057 Drela, Mark; Giles, Michael B. 28 1987 Analyzing multi-level Monte Carlo for options with non-globally Lipschitz payoff. Zbl 1199.65008 Giles, Michael B.; Higham, Desmond J.; Mao, Xuerong 28 2009 Stochastic finite differences and multilevel Monte Carlo for a class of SPDEs in finance. Zbl 1257.35200 Giles, Michael B.; Reisinger, Christoph 25 2012 Multilevel Monte Carlo approximation of distribution functions and densities. Zbl 1322.65014 Giles, Michael B.; Nagapetyan, Tigran; Ritter, Klaus 23 2015 Convergence of linearized and adjoint approximations for discontinuous solutions of conservation laws. I: Linearized approximations and linearized output functionals. Zbl 1215.65146 Giles, Mike; Ulbrich, Stefan 20 2010 Adaptive Euler-Maruyama method for SDEs with nonglobally Lipschitz drift. Zbl 1464.60061 Fang, Wei; Giles, Michael B. 19 2020 Convergence of linearized and adjoint approximations for discontinuous solutions of conservation laws. II: Adjoint approximations and extensions. Zbl 1215.65147 Giles, Mike; Ulbrich, Stefan 18 2010 Adjoint error correction for integral outputs. Zbl 1128.76356 Giles, Michael B.; Pierce, Niles A. 17 2003 Progress in adjoint error correction for integral functionals. Zbl 1061.65091 Giles, Michael B.; Pierce, Niles; Süli, Endre 17 2004 Discrete adjoint approximations with shocks. Zbl 1134.76396 Giles, M. B. 15 2003 The harmonic adjoint approach to unsteady turbomachinery design. Zbl 1036.76056 Duta, M. C.; Giles, M. B.; Campobasso, M. S. 14 2002 Multilevel Monte Carlo methods. Zbl 1302.65004 Giles, Michael B. 14 2013 Multilevel nested simulation for efficient risk estimation. Zbl 1457.91416 Giles, Michael B.; Haji-Ali, Abdul-Lateef 14 2019 Collected matrix derivative results for forward and reverse mode algorithmic differentiation. Zbl 1154.65308 Giles, Mike B. 13 2008 Multilevel path simulation for jump-diffusion SDEs. Zbl 1270.91099 Xia, Yuan; Giles, Michael B. 13 2012 A model and variance reduction method for computing statistical outputs of stochastic elliptic partial differential equations. Zbl 1349.65635 Vidal-Codina, F.; Nguyen, N. C.; Giles, M. B.; Peraire, J. 13 2015 Efficient white noise sampling and coupling for multilevel Monte Carlo with nonnested meshes. Zbl 07003649 Croci, Matteo; Giles, Mike B.; Rognes, M. E.; Farrell, Patrick E. 13 2018 Decision-making under uncertainty: using MLMC for efficient estimation of EVPPI. Zbl 1430.62027 Giles, Michael B.; Goda, Takashi 11 2019 Multilevel Monte Carlo for exponential Lévy models. Zbl 1403.91371 Giles, Michael B.; Xia, Yuan 11 2017 Adaptive Euler-Maruyama method for SDEs with non-globally Lipschitz drift. Zbl 1412.65116 Fang, Wei; Giles, Michael B. 9 2018 Extending the multi-level method for the simulation of stochastic biological systems. Zbl 1352.92062 Lester, Christopher; Baker, Ruth E.; Giles, Michael B.; Yates, Christian A. 9 2016 Quasi-Monte Carlo for finance applications. Zbl 1360.91150 Giles, Mike B.; Kuo, Frances Y.; Sloan, Ian H.; Waterhouse, Benjamin J. 9 2008 Random bit quadrature and approximation of distributions on Hilbert spaces. Zbl 1432.60044 Giles, Michael B.; Hefter, Mario; Mayer, Lukas; Ritter, Klaus 8 2019 Multilevel Monte Carlo method for ergodic SDEs without contractivity. Zbl 1417.65022 Fang, Wei; Giles, Michael B. 8 2019 Implicit time-accurate solutions on unstructured dynamic grids. Zbl 0909.76059 Crumpton, P. I.; Giles, M. B. 8 1997 Propagation and stability of wavelike solutions of finite difference equations with variable coefficients. Zbl 0584.65062 Giles, M. B.; Thompkins, W. T. jun. 8 1985 Multilevel Monte Carlo methods for applications in finance. Zbl 1277.91193 Giles, Mike; Szpruch, Lukasz 7 2013 Stability analysis of a Galerkin/Runge-Kutta Navier-Stokes discretisation on unstructured tetrahedral grids. Zbl 0879.76067 Giles, M. B. 6 1997 Eigenmode analysis of boundary conditions for the one-dimensional preconditioned Euler equations. Zbl 0972.76065 Darmofal, David L.; Moinier, Pierre; Giles, Michael B. 6 2000 Algorithm 955: Approximation of the inverse Poisson cumulative distribution function. Zbl 1347.65019 Giles, Michael B. 6 2016 Antithetic multilevel Monte Carlo estimation for multidimensional SDEs. Zbl 1302.65026 Giles, Michael B.; Szpruch, Lukasz 6 2013 Non-nested adaptive timesteps in multilevel Monte Carlo computations. Zbl 1356.65017 Giles, Michael B.; Lester, Christopher; Whittle, James 6 2016 Vibrato Monte Carlo sensitivities. Zbl 1182.91197 Giles, Michael B. 6 2009 Sharp error estimates for discretizations of the 1D convection-diffusion equation with Dirac initial data. Zbl 1122.65080 Carter, Rebecca; Giles, Michael B. 5 2007 An introduction to multilevel Monte Carlo methods. Zbl 1523.65002 Giles, Michael B. 5 2018 Multilevel Monte Carlo estimation of the expected value of sample information. Zbl 1455.65007 Hironaka, Tomohiko; Giles, Michael B.; Goda, Takashi; Thom, Howard 5 2020 Multi-level Monte Carlo methods for the approximation of invariant measures of stochastic differential equations. Zbl 1505.62159 Giles, Michael B.; Majka, Mateusz B.; Szpruch, Lukasz; Vollmer, Sebastian J.; Zygalakis, Konstantinos C. 5 2020 Multilevel estimation of expected exit times and other functionals of stopped diffusions. Zbl 1405.60076 Giles, Michael B.; Bernal, Francisco 5 2018 Random bit multilevel algorithms for stochastic differential equations. Zbl 1480.65015 Giles, Michael B.; Hefter, Mario; Mayer, Lukas; Ritter, Klaus 5 2019 Analysis of multilevel Monte Carlo path simulation using the Milstein discretisation. Zbl 1420.60063 B. Giles, Michael; Debrabant, Kristian; Rössler, Andreas 5 2019 An adjoint equations for error analysis and optimal grid adaptation in CFD. Zbl 0989.76050 Giles, Michael B. 4 1998 Stability and accuracy of numerical boundary conditions in aeroelastic analysis. Zbl 0878.73076 Giles, M. B. 4 1997 On the stability and convergence of discretizations of initial value PDEs. Zbl 0896.65057 Giles, M. B. 4 1997 Stability analysis of preconditioned approximations of the Euler equations on unstructured meshes. Zbl 1139.76331 Moinier, P.; Giles, M. B. 4 2002 Monte Carlo evaluation of sensitivities in computational finance. Zbl 1214.91134 Giles, M. B. 3 2008 Manycore algorithms for batch scalar and block tridiagonal solvers. Zbl 1369.65047 László, Endre; Giles, Mike; Appleyard, Jeremy 3 2016 MLMC for nested expectations. Zbl 1405.65009 Giles, Michael B. 3 2018 Combining sparse grids, multilevel MC and QMC for elliptic PDEs with random coefficients. Zbl 1412.65210 Giles, Michael B.; Kuo, Frances Y.; Sloan, Ian H. 2 2018 Effects of round-to-nearest and stochastic rounding in the numerical solution of the heat equation in low precision. Zbl 07726036 Croci, M.; Giles, M. B. 2 2023 Multilevel Monte Carlo and improved timestepping methods in atmospheric dispersion modelling. Zbl 1380.65012 Katsiolides, Grigoris; Müller, Eike H.; Scheichl, Robert; Shardlow, Tony; Giles, Michael B.; Thomson, David J. 2 2018 An empirical interpolation and model-variance reduction method for computing statistical outputs of parametrized stochastic partial differential equations. Zbl 1386.65044 Vidal-Codina, F.; Nguyen, N. C.; Giles, M. B.; Peraire, J. 2 2016 A numerical study of the steady scalar convective diffusion equation for small viscosity. Zbl 0572.76087 Giles, Michael B.; Rose, Milton E. 2 1984 Computing Greeks using multilevel path simulation. Zbl 1270.91091 Burgos, Sylvestre; Giles, Michael B. 2 2012 Validity of linearized unsteady Euler equations with shock capturing. Zbl 0792.76036 Lindquist, Dana R.; Giles, Michael B. 1 1994 Superconvergent lift estimates through adjoint error analysis. Zbl 1036.76047 Giles, M. B.; Pierce, N. A. 1 2002 Stabilization of a linearized Navier-Stokes solver for turbomachinery aeroelasticity. Zbl 1140.76413 Campobasso, M. Sergio; Giles, Michael B. 1 2003 An adaptive random bit multilevel algorithm for SDEs. Zbl 1523.65005 Giles, Michael B.; Hefter, Mario; Mayer, Lukas; Ritter, Klaus 1 2020 Newton solution of coupled Euler and boundary-layer equations. Zbl 0604.76060 Drela, M.; Giles, M.; Thompkins, W. T. jun. 1 1986 Analysis of nested multilevel Monte Carlo using approximate normal random variables. Zbl 1482.65006 Giles, Michael; Sheridan-Methven, Oliver 1 2022 Block-structured compressible Navier-Stokes solution using the OPS high-level abstraction. Zbl 1497.65126 Jammy, Satya P.; Mudalige, Gihan R.; Reguly, Istvan Z.; Sandham, Neil D.; Giles, Mike 1 2016 Multilevel quasi Monte Carlo methods for elliptic PDEs with random field coefficients via fast white noise sampling. Zbl 07385001 Croci, Matteo; Giles, Michael; Farrell, Patrick E. 1 2021 Importance sampling for pathwise sensitivity of stochastic chaotic systems. Zbl 1481.60106 Fang, Wei; Giles, Mike B. 1 2021 Effects of round-to-nearest and stochastic rounding in the numerical solution of the heat equation in low precision. Zbl 07726036 Croci, M.; Giles, M. B. 2 2023 Analysis of nested multilevel Monte Carlo using approximate normal random variables. Zbl 1482.65006 Giles, Michael; Sheridan-Methven, Oliver 1 2022 Multilevel quasi Monte Carlo methods for elliptic PDEs with random field coefficients via fast white noise sampling. Zbl 07385001 Croci, Matteo; Giles, Michael; Farrell, Patrick E. 1 2021 Importance sampling for pathwise sensitivity of stochastic chaotic systems. Zbl 1481.60106 Fang, Wei; Giles, Mike B. 1 2021 Adaptive Euler-Maruyama method for SDEs with nonglobally Lipschitz drift. Zbl 1464.60061 Fang, Wei; Giles, Michael B. 19 2020 Multilevel Monte Carlo estimation of the expected value of sample information. Zbl 1455.65007 Hironaka, Tomohiko; Giles, Michael B.; Goda, Takashi; Thom, Howard 5 2020 Multi-level Monte Carlo methods for the approximation of invariant measures of stochastic differential equations. Zbl 1505.62159 Giles, Michael B.; Majka, Mateusz B.; Szpruch, Lukasz; Vollmer, Sebastian J.; Zygalakis, Konstantinos C. 5 2020 An adaptive random bit multilevel algorithm for SDEs. Zbl 1523.65005 Giles, Michael B.; Hefter, Mario; Mayer, Lukas; Ritter, Klaus 1 2020 Multilevel nested simulation for efficient risk estimation. Zbl 1457.91416 Giles, Michael B.; Haji-Ali, Abdul-Lateef 14 2019 Decision-making under uncertainty: using MLMC for efficient estimation of EVPPI. Zbl 1430.62027 Giles, Michael B.; Goda, Takashi 11 2019 Random bit quadrature and approximation of distributions on Hilbert spaces. Zbl 1432.60044 Giles, Michael B.; Hefter, Mario; Mayer, Lukas; Ritter, Klaus 8 2019 Multilevel Monte Carlo method for ergodic SDEs without contractivity. Zbl 1417.65022 Fang, Wei; Giles, Michael B. 8 2019 Random bit multilevel algorithms for stochastic differential equations. Zbl 1480.65015 Giles, Michael B.; Hefter, Mario; Mayer, Lukas; Ritter, Klaus 5 2019 Analysis of multilevel Monte Carlo path simulation using the Milstein discretisation. Zbl 1420.60063 B. Giles, Michael; Debrabant, Kristian; Rössler, Andreas 5 2019 Efficient white noise sampling and coupling for multilevel Monte Carlo with nonnested meshes. Zbl 07003649 Croci, Matteo; Giles, Mike B.; Rognes, M. E.; Farrell, Patrick E. 13 2018 Adaptive Euler-Maruyama method for SDEs with non-globally Lipschitz drift. Zbl 1412.65116 Fang, Wei; Giles, Michael B. 9 2018 An introduction to multilevel Monte Carlo methods. Zbl 1523.65002 Giles, Michael B. 5 2018 Multilevel estimation of expected exit times and other functionals of stopped diffusions. Zbl 1405.60076 Giles, Michael B.; Bernal, Francisco 5 2018 MLMC for nested expectations. Zbl 1405.65009 Giles, Michael B. 3 2018 Combining sparse grids, multilevel MC and QMC for elliptic PDEs with random coefficients. Zbl 1412.65210 Giles, Michael B.; Kuo, Frances Y.; Sloan, Ian H. 2 2018 Multilevel Monte Carlo and improved timestepping methods in atmospheric dispersion modelling. Zbl 1380.65012 Katsiolides, Grigoris; Müller, Eike H.; Scheichl, Robert; Shardlow, Tony; Giles, Michael B.; Thomson, David J. 2 2018 Multilevel Monte Carlo for exponential Lévy models. Zbl 1403.91371 Giles, Michael B.; Xia, Yuan 11 2017 Extending the multi-level method for the simulation of stochastic biological systems. Zbl 1352.92062 Lester, Christopher; Baker, Ruth E.; Giles, Michael B.; Yates, Christian A. 9 2016 Algorithm 955: Approximation of the inverse Poisson cumulative distribution function. Zbl 1347.65019 Giles, Michael B. 6 2016 Non-nested adaptive timesteps in multilevel Monte Carlo computations. Zbl 1356.65017 Giles, Michael B.; Lester, Christopher; Whittle, James 6 2016 Manycore algorithms for batch scalar and block tridiagonal solvers. Zbl 1369.65047 László, Endre; Giles, Mike; Appleyard, Jeremy 3 2016 An empirical interpolation and model-variance reduction method for computing statistical outputs of parametrized stochastic partial differential equations. Zbl 1386.65044 Vidal-Codina, F.; Nguyen, N. C.; Giles, M. B.; Peraire, J. 2 2016 Block-structured compressible Navier-Stokes solution using the OPS high-level abstraction. Zbl 1497.65126 Jammy, Satya P.; Mudalige, Gihan R.; Reguly, Istvan Z.; Sandham, Neil D.; Giles, Mike 1 2016 Multilevel Monte Carlo methods. Zbl 1316.65010 Giles, Michael B. 237 2015 Multilevel Monte Carlo approximation of distribution functions and densities. Zbl 1322.65014 Giles, Michael B.; Nagapetyan, Tigran; Ritter, Klaus 23 2015 A model and variance reduction method for computing statistical outputs of stochastic elliptic partial differential equations. Zbl 1349.65635 Vidal-Codina, F.; Nguyen, N. C.; Giles, M. B.; Peraire, J. 13 2015 Antithetic multilevel Monte Carlo estimation for multi-dimensional SDEs without Lévy area simulation. Zbl 1373.65007 Giles, Michael B.; Szpruch, Lukasz 54 2014 Further analysis of multilevel Monte Carlo methods for elliptic PDEs with random coefficients. Zbl 1306.65009 Teckentrup, A. L.; Scheichl, R.; Giles, M. B.; Ullmann, E. 90 2013 Multilevel Monte Carlo methods. Zbl 1302.65004 Giles, Michael B. 14 2013 Multilevel Monte Carlo methods for applications in finance. Zbl 1277.91193 Giles, Mike; Szpruch, Lukasz 7 2013 Antithetic multilevel Monte Carlo estimation for multidimensional SDEs. Zbl 1302.65026 Giles, Michael B.; Szpruch, Lukasz 6 2013 Stochastic finite differences and multilevel Monte Carlo for a class of SPDEs in finance. Zbl 1257.35200 Giles, Michael B.; Reisinger, Christoph 25 2012 Multilevel path simulation for jump-diffusion SDEs. Zbl 1270.91099 Xia, Yuan; Giles, Michael B. 13 2012 Computing Greeks using multilevel path simulation. Zbl 1270.91091 Burgos, Sylvestre; Giles, Michael B. 2 2012 Multilevel Monte Carlo methods and applications to elliptic PDEs with random coefficients. Zbl 1241.65012 Cliffe, K. A.; Giles, M. B.; Scheichl, R.; Teckentrup, A. L. 212 2011 Convergence of linearized and adjoint approximations for discontinuous solutions of conservation laws. I: Linearized approximations and linearized output functionals. Zbl 1215.65146 Giles, Mike; Ulbrich, Stefan 20 2010 Convergence of linearized and adjoint approximations for discontinuous solutions of conservation laws. II: Adjoint approximations and extensions. Zbl 1215.65147 Giles, Mike; Ulbrich, Stefan 18 2010 Multilevel quasi-Monte Carlo path simulation. Zbl 1181.91335 Giles, Michael B.; Waterhouse, Benjamin J. 35 2009 Analyzing multi-level Monte Carlo for options with non-globally Lipschitz payoff. Zbl 1199.65008 Giles, Michael B.; Higham, Desmond J.; Mao, Xuerong 28 2009 Vibrato Monte Carlo sensitivities. Zbl 1182.91197 Giles, Michael B. 6 2009 Multilevel Monte Carlo path simulation. Zbl 1167.65316 Giles, Michael B. 499 2008 Improved multilevel Monte Carlo convergence using the Milstein scheme. Zbl 1141.65321 Giles, Mike 81 2008 Collected matrix derivative results for forward and reverse mode algorithmic differentiation. Zbl 1154.65308 Giles, Mike B. 13 2008 Quasi-Monte Carlo for finance applications. Zbl 1360.91150 Giles, Mike B.; Kuo, Frances Y.; Sloan, Ian H.; Waterhouse, Benjamin J. 9 2008 Monte Carlo evaluation of sensitivities in computational finance. Zbl 1214.91134 Giles, M. B. 3 2008 Sharp error estimates for discretizations of the 1D convection-diffusion equation with Dirac initial data. Zbl 1122.65080 Carter, Rebecca; Giles, Michael B. 5 2007 Adjoint and defect error bounding and correction for functional estimates. Zbl 1058.65121 Pierce, Niles A.; Giles, Michael B. 42 2004 Progress in adjoint error correction for integral functionals. Zbl 1061.65091 Giles, Michael B.; Pierce, Niles; Süli, Endre 17 2004 Adjoint error correction for integral outputs. Zbl 1128.76356 Giles, Michael B.; Pierce, Niles A. 17 2003 Discrete adjoint approximations with shocks. Zbl 1134.76396 Giles, M. B. 15 2003 Stabilization of a linearized Navier-Stokes solver for turbomachinery aeroelasticity. Zbl 1140.76413 Campobasso, M. Sergio; Giles, Michael B. 1 2003 Adjoint methods for PDEs: a posteriori error analysis and postprocessing by duality. Zbl 1105.65350 Giles, Michael B.; Süli, Endre 193 2002 The harmonic adjoint approach to unsteady turbomachinery design. Zbl 1036.76056 Duta, M. C.; Giles, M. B.; Campobasso, M. S. 14 2002 Stability analysis of preconditioned approximations of the Euler equations on unstructured meshes. Zbl 1139.76331 Moinier, P.; Giles, M. B. 4 2002 Superconvergent lift estimates through adjoint error analysis. Zbl 1036.76047 Giles, M. B.; Pierce, N. A. 1 2002 Analytic adjoint solutions for the quasi-one-dimensional Euler equations. Zbl 0967.76079 Giles, Michael B.; Pierce, Niles A. 37 2001 An introduction to the adjoint approach to design. Zbl 0996.76023 Giles, Michael B.; Pierce, Niles A. 163 2000 Eigenmode analysis of boundary conditions for the one-dimensional preconditioned Euler equations. Zbl 0972.76065 Darmofal, David L.; Moinier, Pierre; Giles, Michael B. 6 2000 Adjoint recovery of superconvergent functionals from PDE approximations. Zbl 0948.65119 Pierce, Niles A.; Giles, Michael B. 106 1998 An adjoint equations for error analysis and optimal grid adaptation in CFD. Zbl 0989.76050 Giles, Michael B. 4 1998 Preconditioned multigrid methods for compressible flow calculations on stretched meshes. Zbl 0893.76061 Pierce, Niles A.; Giles, Michael B. 31 1997 Stability analysis of numerical interface conditions in fluid-structure thermal analysis. Zbl 0891.76058 Giles, M. B. 29 1997 Implicit time-accurate solutions on unstructured dynamic grids. Zbl 0909.76059 Crumpton, P. I.; Giles, M. B. 8 1997 Stability analysis of a Galerkin/Runge-Kutta Navier-Stokes discretisation on unstructured tetrahedral grids. Zbl 0879.76067 Giles, M. B. 6 1997 Stability and accuracy of numerical boundary conditions in aeroelastic analysis. Zbl 0878.73076 Giles, M. B. 4 1997 On the stability and convergence of discretizations of initial value PDEs. Zbl 0896.65057 Giles, M. B. 4 1997 Validity of linearized unsteady Euler equations with shock capturing. Zbl 0792.76036 Lindquist, Dana R.; Giles, Michael B. 1 1994 Viscous-inviscid analysis of transonic and low Reynolds number airfoils. Zbl 0635.76057 Drela, Mark; Giles, Michael B. 28 1987 Newton solution of coupled Euler and boundary-layer equations. Zbl 0604.76060 Drela, M.; Giles, M.; Thompkins, W. T. jun. 1 1986 Propagation and stability of wavelike solutions of finite difference equations with variable coefficients. Zbl 0584.65062 Giles, M. B.; Thompkins, W. T. jun. 8 1985 A numerical study of the steady scalar convective diffusion equation for small viscosity. Zbl 0572.76087 Giles, Michael B.; Rose, Milton E. 2 1984 all cited Publications top 5 cited Publications all top 5 Cited by 2,217 Authors 34 Tempone, Raúl F. 32 Schwab, Christoph 30 Giles, Michael B. 28 Jasra, Ajay 22 Nobile, Fabio 18 Scheichl, Robert 17 Tavener, Simon J. 16 Jentzen, Arnulf 15 Estep, Donald J. 14 Law, Kody J. H. 13 Darmofal, David L. 12 Giannakoglou, Kyriakos C. 12 Mishra, Siddhartha 12 Peherstorfer, Benjamin 12 Reisinger, Christoph 11 Chaudhry, Jehanzeb Hameed 11 Hutzenthaler, Martin 11 Szpruch, Lukasz 11 Ullmann, Elisabeth 11 Willcox, Karen E. 10 Barth, Andrea 10 Fidkowski, Krzysztof J. 10 Kuo, Frances Y. 9 Baker, Ruth Elizabeth 9 Haji-Ali, Abdul-Lateef 9 Vandewalle, Stefan G. 8 Abdulle, Assyr 8 Dereich, Steffen 8 Dick, Josef 8 Goda, Takashi 8 Gunzburger, Max D. 8 Jourdain, Benjamin 8 Kebaier, Ahmed 8 Navon, Ionel Michael 8 Praetorius, Dirk 8 Wang, Qiqi 7 Bayer, Christian 7 Dolejší, Vít 7 Harbrecht, Helmut 7 Herrmann, Lukas 7 Kruse, Thomas 7 Lang, Annika 7 Nordström, Jan 7 Pagès, Gilles 7 Papadimitriou, Dimitrios I. 7 Ritter, Klaus 7 Teckentrup, Aretha L. 7 Van Brummelen, Harald 7 Zuazua, Enrique 6 Alekseev, Aleksey K. 6 Bernal, Francisco 6 Bordas, Stéphane Pierre Alain 6 Geraci, Gianluca 6 Ginting, Victor 6 Gobet, Emmanuel 6 Lozano, Carlos J. 6 Mao, Xuerong 6 Marzouk, Youssef M. 6 Müller-Gronbach, Thomas 6 Multerer, Michael D. 6 Nuyens, Dirk 6 Ollivier-Gooch, Carl F. 6 Oosterlee, Cornelis Willebrordus 6 Patera, Anthony T. 6 Rozza, Gianluigi 6 Sloan, Ian Hugh 6 Šukys, Jonas 6 van der Zee, Kristoffer George 6 Vassilevski, Panayot Spirov 6 Villa, Umberto E. 6 Wohlmuth, Barbara I. 6 Zhong, Hongzhi 6 Zhou, Yan 5 Acebrón, Juan A. 5 Alaya, Mohamed Ben 5 Alfonsi, Aurélien 5 Babaee, Hessam 5 Belomestny, Denis 5 Bespalov, Alexei 5 Dang, Duy Minh 5 Doostan, Alireza 5 Fairbanks, Hillary R. 5 Gantner, Robert Nicholas 5 Gnewuch, Michael 5 Heitzinger, Clemens 5 Higham, Desmond J. 5 Hoffman, Johan 5 Luo, Xianbing 5 May, Georg 5 Motamed, Mohammad 5 Narayan, Akil C. 5 Neuenkirch, Andreas 5 Nguyen, Ngoc Cuong 5 Oden, John Tinsley 5 Pain, Christopher C. 5 Pareschi, Lorenzo 5 Perotto, Simona 5 Pironneau, Olivier 5 Roskovec, Filip 5 Samaey, Giovanni ...and 2,117 more Authors all top 5 Cited in 193 Serials 182 Journal of Computational Physics 96 Computer Methods in Applied Mechanics and Engineering 70 SIAM Journal on Scientific Computing 69 Computers and Fluids 66 SIAM/ASA Journal on Uncertainty Quantification 39 Journal of Computational and Applied Mathematics 31 Journal of Scientific Computing 28 Computers & Mathematics with Applications 28 SIAM Journal on Numerical Analysis 23 Numerische Mathematik 21 Applied Numerical Mathematics 19 BIT 19 Statistics and Computing 18 Mathematics of Computation 17 The Annals of Applied Probability 16 International Journal for Numerical Methods in Engineering 16 International Journal of Computational Fluid Dynamics 15 Stochastic and Partial Differential Equations. Analysis and Computations 13 Journal of Fluid Mechanics 13 Computational Mechanics 13 Applied Mathematical Modelling 12 Journal of Complexity 12 Monte Carlo Methods and Applications 11 Stochastic Processes and their Applications 11 Multiscale Modeling & Simulation 11 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 10 International Journal for Numerical Methods in Fluids 10 Journal of Mathematical Analysis and Applications 10 Numerical Algorithms 10 Computational Geosciences 9 Applied Mathematics and Computation 9 Mathematics and Computers in Simulation 9 Foundations of Computational Mathematics 8 International Journal of Computer Mathematics 8 Finance and Stochastics 7 Numerical Methods for Partial Differential Equations 7 Advances in Computational Mathematics 7 Communications in Computational Physics 7 SIAM Journal on Financial Mathematics 7 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings and Surveys 6 Advances in Applied Probability 6 Bulletin of Mathematical Biology 6 Stochastic Analysis and Applications 6 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 6 European Journal of Operational Research 6 Computing and Visualization in Science 6 International Journal of Theoretical and Applied Finance 6 Methodology and Computing in Applied Probability 6 Acta Numerica 5 Computer Physics Communications 5 Inverse Problems 5 SIAM Review 5 Computational Optimization and Applications 5 Combustion Theory and Modelling 5 Quantitative Finance 5 Discrete and Continuous Dynamical Systems. Series B 4 Journal of Approximation Theory 4 Journal of Optimization Theory and Applications 4 SIAM Journal on Control and Optimization 4 Computational and Applied Mathematics 4 Optimization Methods & Software 4 Optimization and Engineering 4 Computational Methods in Applied Mathematics 4 Stochastics 4 Journal of Computational and Graphical Statistics 3 International Journal of Control 3 Mathematical Methods in the Applied Sciences 3 Insurance Mathematics & Economics 3 Operations Research Letters 3 Linear Algebra and its Applications 3 Applied Mathematical Finance 3 Electronic Journal of Probability 3 Bernoulli 3 Mathematical Problems in Engineering 3 Mathematical Finance 3 European Journal of Mechanics. B. Fluids 3 Communications in Nonlinear Science and Numerical Simulation 3 Archives of Computational Methods in Engineering 3 GAMM-Mitteilungen 3 Advances in Applied Mathematics and Mechanics 3 GEM - International Journal on Geomathematics 2 Journal of Engineering Mathematics 2 Journal of Mathematical Biology 2 Mathematical Biosciences 2 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki 2 Theoretical and Computational Fluid Dynamics 2 ACM Transactions on Mathematical Software 2 Calcolo 2 Journal of Applied Probability 2 Mathematics of Operations Research 2 Memoirs of the American Mathematical Society 2 Operations Research 2 RAIRO. Modélisation Mathématique et Analyse Numérique 2 Journal of Theoretical Probability 2 SIAM Journal on Matrix Analysis and Applications 2 Annals of Operations Research 2 Computational Mathematics and Mathematical Physics 2 SIAM Journal on Optimization 2 Journal of Computational Neuroscience 2 Engineering Analysis with Boundary Elements ...and 93 more Serials all top 5 Cited in 45 Fields 1,022 Numerical analysis (65-XX) 410 Probability theory and stochastic processes (60-XX) 371 Fluid mechanics (76-XX) 332 Partial differential equations (35-XX) 168 Statistics (62-XX) 112 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 86 Mechanics of deformable solids (74-XX) 76 Calculus of variations and optimal control; optimization (49-XX) 65 Computer science (68-XX) 47 Ordinary differential equations (34-XX) 41 Operations research, mathematical programming (90-XX) 37 Classical thermodynamics, heat transfer (80-XX) 37 Biology and other natural sciences (92-XX) 35 Systems theory; control (93-XX) 30 Geophysics (86-XX) 27 Statistical mechanics, structure of matter (82-XX) 25 Approximations and expansions (41-XX) 18 Dynamical systems and ergodic theory (37-XX) 16 Linear and multilinear algebra; matrix theory (15-XX) 14 Optics, electromagnetic theory (78-XX) 9 Information and communication theory, circuits (94-XX) 8 Functional analysis (46-XX) 8 Operator theory (47-XX) 7 Measure and integration (28-XX) 5 Number theory (11-XX) 5 Real functions (26-XX) 5 Global analysis, analysis on manifolds (58-XX) 4 Harmonic analysis on Euclidean spaces (42-XX) 4 Mechanics of particles and systems (70-XX) 4 Quantum theory (81-XX) 3 Integral equations (45-XX) 2 General and overarching topics; collections (00-XX) 2 Potential theory (31-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Special functions (33-XX) 2 Difference and functional equations (39-XX) 2 Differential geometry (53-XX) 2 Manifolds and cell complexes (57-XX) 2 Mathematics education (97-XX) 1 History and biography (01-XX) 1 Combinatorics (05-XX) 1 Field theory and polynomials (12-XX) 1 Topological groups, Lie groups (22-XX) 1 Integral transforms, operational calculus (44-XX) 1 Astronomy and astrophysics (85-XX) Citations by Year