Fang, Wei; Giles, Michael B. Adaptive Euler-Maruyama method for SDEs with nonglobally Lipschitz drift. (English) Zbl 1464.60061 Ann. Appl. Probab. 30, No. 2, 526-560 (2020). MSC: 60H10 60H35 65C30 PDF BibTeX XML Cite \textit{W. Fang} and \textit{M. B. Giles}, Ann. Appl. Probab. 30, No. 2, 526--560 (2020; Zbl 1464.60061) Full Text: DOI arXiv Euclid OpenURL
Fang, Wei; Giles, Michael B. Multilevel Monte Carlo method for ergodic SDEs without contractivity. (English) Zbl 1417.65022 J. Math. Anal. Appl. 476, No. 1, 149-176 (2019). MSC: 65C30 65C05 60H10 60H35 60J60 PDF BibTeX XML Cite \textit{W. Fang} and \textit{M. B. Giles}, J. Math. Anal. Appl. 476, No. 1, 149--176 (2019; Zbl 1417.65022) Full Text: DOI arXiv OpenURL
Fang, Wei; Giles, Michael B. Adaptive Euler-Maruyama method for SDEs with non-globally Lipschitz drift. (English) Zbl 1412.65116 Owen, Art B. (ed.) et al., Monte Carlo and quasi-Monte Carlo methods, MCQMC 2016. Proceedings of the 12th international conference on ‘Monte Carlo and quasi-Monte Carlo methods in scientific computing’, Stanford, CA, August 14–19, 2016. Cham: Springer. Springer Proc. Math. Stat. 241, 217-234 (2018). MSC: 65M12 65C20 60H35 60J65 82C31 PDF BibTeX XML Cite \textit{W. Fang} and \textit{M. B. Giles}, Springer Proc. Math. Stat. 241, 217--234 (2018; Zbl 1412.65116) Full Text: DOI OpenURL
Giles, Michael B.; Higham, Desmond J.; Mao, Xuerong Analyzing multi-level Monte Carlo for options with non-globally Lipschitz payoff. (English) Zbl 1199.65008 Finance Stoch. 13, No. 3, 403-413 (2009). Reviewer: Yuliya Mishura (Kyïv) MSC: 65C30 65C05 60H10 60H35 91G60 65L20 65L70 PDF BibTeX XML Cite \textit{M. B. Giles} et al., Finance Stoch. 13, No. 3, 403--413 (2009; Zbl 1199.65008) Full Text: DOI OpenURL
Giles, Michael B.; Pierce, Niles; Süli, Endre Progress in adjoint error correction for integral functionals. (English) Zbl 1061.65091 Comput. Vis. Sci. 6, No. 2-3, 113-121 (2004). MSC: 65M25 65N30 65N15 35J05 35Q53 65M15 PDF BibTeX XML Cite \textit{M. B. Giles} et al., Comput. Vis. Sci. 6, No. 2--3, 113--121 (2004; Zbl 1061.65091) Full Text: DOI OpenURL
Giles, M. B.; Pierce, N. A. Superconvergent lift estimates through adjoint error analysis. (English) Zbl 1036.76047 Hafez, M. M. (ed.) et al., Innovative methods for numerical solutions of partial differential equations. Proceedings of the symposium on progress in numerical solutions of partial differential equations, Arcachon, France, July 11–13, 1998. In honor of Phil Roe on the occasion of his 60th birthday. Singapore: World Scientific (ISBN 981-02-4810-5/hbk). 198-211 (2002). MSC: 76M25 76N15 65N15 PDF BibTeX XML Cite \textit{M. B. Giles} and \textit{N. A. Pierce}, in: Innovative methods for numerical solutions of partial differential equations. Proceedings of the symposium on progress in numerical solutions of partial differential equations, Arcachon, France, July 11--13, 1998. In honor of Phil Roe on the occasion of his 60th birthday. Singapore: World Scientific. 198--211 (2002; Zbl 1036.76047) OpenURL
Giles, Michael B.; Pierce, Niles A. Analytic adjoint solutions for the quasi-one-dimensional Euler equations. (English) Zbl 0967.76079 J. Fluid Mech. 426, 327-345 (2001). MSC: 76N15 76G25 76L05 76H05 PDF BibTeX XML Cite \textit{M. B. Giles} and \textit{N. A. Pierce}, J. Fluid Mech. 426, 327--345 (2001; Zbl 0967.76079) Full Text: DOI OpenURL
Darmofal, David L.; Moinier, Pierre; Giles, Michael B. Eigenmode analysis of boundary conditions for the one-dimensional preconditioned Euler equations. (English) Zbl 0972.76065 J. Comput. Phys. 160, No. 1, 369-384 (2000). MSC: 76M12 76M20 76G25 PDF BibTeX XML Cite \textit{D. L. Darmofal} et al., J. Comput. Phys. 160, No. 1, 369--384 (2000; Zbl 0972.76065) Full Text: DOI Link OpenURL
Giles, Michael B. An adjoint equations for error analysis and optimal grid adaptation in CFD. (English) Zbl 0989.76050 Caughey, D. A. (ed.) et al., Frontiers of computational fluid dynamics 1998. Papers from the symposium on thirty years of CFD and transonic flow held in honour of Earll Murman in Everett, WA, USA, June 24-26, 1997. Singapore: World Scientific Publishing. 155-169 (1998). MSC: 76M12 76M10 65N15 65N50 PDF BibTeX XML Cite \textit{M. B. Giles}, in: Frontiers of computational fluid dynamics 1998. Papers from the symposium on thirty years of CFD and transonic flow held in honour of Earll Murman in Everett, WA, USA, June 24--26, 1997. Singapore: World Scientific Publishing. 155--169 (1998; Zbl 0989.76050) OpenURL
Pierce, Niles A.; Giles, Michael B. Adjoint recovery of superconvergent functionals from PDE approximations. (English) Zbl 0948.65119 SIAM Rev. 42, No. 2, 247-264 (2000). Reviewer: S.K.Rangarajan (Bangalore) MSC: 65N30 65N12 65N15 35J05 35J65 PDF BibTeX XML Cite \textit{N. A. Pierce} and \textit{M. B. Giles}, SIAM Rev. 42, No. 2, 247--264 (1998; Zbl 0948.65119) Full Text: DOI OpenURL
Giles, M. B. Progress in applied numerical analysis for computational fluid dynamics. (English) Zbl 0939.76061 Venkatakrishnan, V. (ed.) et al., Barriers and challenges in computational fluid dynamics. Proceedings of the ICASE/ LaRC workshop, Hampton, VA, USA, August 5-7, 1996. Dordrecht: Kluwer Academic Publishers. ICASE/LaRC Interdisciplinary Series in Science and Engineering. 6, 1-25 (1998). Reviewer: A.Meister (Hamburg) MSC: 76M20 65M12 76-02 PDF BibTeX XML Cite \textit{M. B. Giles}, in: Barriers and challenges in computational fluid dynamics. Proceedings of the ICASE/ LaRC workshop, Hampton, VA, USA, August 5--7, 1996. Dordrecht: Kluwer Academic Publishers. 1--25 (1998; Zbl 0939.76061) OpenURL
Crumpton, P. I.; Giles, M. B. Implicit time-accurate solutions on unstructured dynamic grids. (English) Zbl 0909.76059 Int. J. Numer. Methods Fluids 25, No. 11, 1285-1300 (1997). MSC: 76M20 76N10 65M55 PDF BibTeX XML Cite \textit{P. I. Crumpton} and \textit{M. B. Giles}, Int. J. Numer. Methods Fluids 25, No. 11, 1285--1300 (1997; Zbl 0909.76059) Full Text: DOI OpenURL
Pierce, Niles A.; Giles, Michael B. Preconditioned multigrid methods for compressible flow calculations on stretched meshes. (English) Zbl 0893.76061 J. Comput. Phys. 136, No. 2, 425-445 (1997). Reviewer: E.Krause (Aachen) MSC: 76M20 76N10 PDF BibTeX XML Cite \textit{N. A. Pierce} and \textit{M. B. Giles}, J. Comput. Phys. 136, No. 2, 425--445 (1997; Zbl 0893.76061) Full Text: DOI Link OpenURL
Giles, Michael Non-reflecting boundary conditions for unsteady airfoil calculations. (English) Zbl 0777.76007 Hyperbolic problems. Theory, numerical methods and applications. Vol. I, Proc. Conf., Uppsala/Sweden 1990, 462-476 (1991). Reviewer: T.Petrila (Cluj-Napoca) MSC: 76B10 65N99 PDF BibTeX XML Cite \textit{M. Giles}, in: Third international conference on hyperbolic problems. Theory, numerical methods and applications. Proceedings of the conference dedicated to Professor Heinz-Otto Kreiss on his 60th birthday, held in Uppsala, Sweden, June 11-15, 1990. Vol. I. Lund: Studentlitteratur; Bromley: Chartwell-Bratt Ltd.. 462--476 (1991; Zbl 0777.76007) OpenURL
Drela, Mark; Giles, Michael B. Viscous-inviscid analysis of transonic and low Reynolds number airfoils. (English) Zbl 0635.76057 AIAA J. 25, 1347-1355 (1987). MSC: 76H05 76M99 PDF BibTeX XML Cite \textit{M. Drela} and \textit{M. B. Giles}, AIAA J. 25, 1347--1355 (1987; Zbl 0635.76057) Full Text: DOI Link OpenURL
Drela, M.; Giles, M.; Thompkins, W. T. jun. Newton solution of coupled Euler and boundary-layer equations. (English) Zbl 0604.76060 Numerical and physical aspects of aerodynamic flows III, Proc. 3rd Symp., Long Beach/Calif. 1985, 143-154 (1986). MSC: 76N10 76N15 76M99 PDF BibTeX XML OpenURL