Spectral/hp element methods

Spectral/hp element methods

 

Open Software and Numerical Analysis: Our applied research effort is built upon the development and application of high-order methods for computational fluid dynamics and transient physics. We have developed three-dimensional algorithms using hybrid and unstructured discretisations and developing efficient implementation for both high and low order polynomial approximations. These tools are available through open software and offer a range of solution techniques using Continuous and Discontinuous Galerkin method on highly parallel platforms. Current efforts are focused on providing greater efficiency and flexibility through adaptive polynomial orders and time stepping.

 

Research and application highlights include:

  • First unstructured triangular and tetrahedral spectral/hp methods for fluid mechanics.
  • Open software library Nektar++ (www.nektar.info)
  • Platform for Research Into Simulation Methods (www.prism.ac.uk).

 

Recent publications:

  • E. Ferrer, D. Moxey, R. Willden, and S. Sherwin, “Stability of projection methods for incompressible flows using high order pressure-velocity pairs of same degree: continuous and discontinuous galerkin formulations,” Communications in computational physics, vol. 16, pp. 817-840, 2014. doi:10.4208/cicp.290114.170414a
    [BibTeX] [Download PDF]
    @article{ferrer2014stabilityformulations,
    author = "Ferrer, E and Moxey, D and Willden, RHJ and Sherwin, SJ",
    journal = "COMMUNICATIONS IN COMPUTATIONAL PHYSICS",
    month = "Sep",
    pages = "817--840",
    publisher = "GLOBAL SCIENCE PRESS",
    title = "Stability of Projection Methods for Incompressible Flows Using High Order Pressure-Velocity Pairs of Same Degree: Continuous and Discontinuous Galerkin Formulations",
    url = "http://www2.imperial.ac.uk/ssherw/spectralhp/papers/CICP_FeMoShWi_2014.pdf",
    volume = "16",
    year = "2014",
    doi = "10.4208/cicp.290114.170414a",
    issn = "1815-2406",
    issue = "3",
    keyword = "Science \\& Technology",
    keyword = "Physical Sciences",
    keyword = "Physics, Mathematical",
    keyword = "Physics",
    keyword = "PHYSICS, MATHEMATICAL",
    keyword = "Incompressible Navier-Stokes equations",
    keyword = "projection methods",
    keyword = "velocity-correction",
    keyword = "continuous Galerkin",
    keyword = "discontinuous Galerkin",
    keyword = "inf-sup LBB condition",
    keyword = "NAVIER-STOKES EQUATIONS",
    keyword = "FINITE-ELEMENT METHODS",
    language = "English",
    day = "1",
    publicationstatus = "published",
    }

  • J. King, S. Yakovlev, Z. Fu, R. Kirby, and S. Sherwin, “Exploiting batch processing on streaming architectures to solve 2d elliptic finite element problems: a hybridized discontinuous galerkin (hdg) case study,” Journal of scientific computing, vol. 60, pp. 457-482, 2014. doi:10.1007/s10915-013-9805-x
    [BibTeX] [Download PDF]
    @article{king2014exploitingstudy,
    author = "King, J and Yakovlev, S and Fu, Z and Kirby, RM and Sherwin, SJ",
    journal = "JOURNAL OF SCIENTIFIC COMPUTING",
    month = "Aug",
    pages = "457--482",
    publisher = "SPRINGER/PLENUM PUBLISHERS",
    title = "Exploiting Batch Processing on Streaming Architectures to Solve 2D Elliptic Finite Element Problems: A Hybridized Discontinuous Galerkin (HDG) Case Study",
    url = "http://www2.imperial.ac.uk/ssherw/spectralhp/papers/JSC_KiYaFuKiSh_2013.pdf",
    volume = "60",
    year = "2014",
    doi = "10.1007/s10915-013-9805-x",
    issn = "0885-7474",
    issue = "2",
    keyword = "Science \\& Technology",
    keyword = "Physical Sciences",
    keyword = "Mathematics, Applied",
    keyword = "Mathematics",
    keyword = "MATHEMATICS, APPLIED",
    keyword = "High-order finite elements",
    keyword = "Spectral/hp elements",
    keyword = "Discontinuous Galerkin method",
    keyword = "Hybridization",
    keyword = "Streaming processors",
    keyword = "Graphical processing units (GPUs)",
    language = "English",
    day = "1",
    publicationstatus = "published",
    }

  • D. De Grazia, G. Mengaldo, D. Moxey, P. Vincent, and S. Sherwin, “Connections between the discontinuous galerkin method and high-order flux reconstruction schemes,” International journal for numerical methods in fluids, vol. 75, pp. 860-877, 2014. doi:10.1002/fld.3915
    [BibTeX] [Download PDF]
    @article{degrazia2014connectionsschemes,
    author = "De Grazia, D and Mengaldo, G and Moxey, D and Vincent, PE and Sherwin, SJ",
    journal = "INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS",
    month = "Aug",
    pages = "860--877",
    publisher = "WILEY-BLACKWELL",
    title = "Connections between the discontinuous Galerkin method and high-order flux reconstruction schemes",
    url = "http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2\\&SrcApp=PARTNER_APP\\&SrcAuth=LinksAMR\\&KeyUT=000339423000003\\&DestLinkType=FullRecord\\&DestApp=ALL_WOS\\&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202",
    url = "http://wwwf.imperial.ac.uk/ssherw/spectralhp/papers/IJNMF_DeMeViMoSh_14.pdf",
    volume = "75",
    year = "2014",
    doi = "10.1002/fld.3915",
    issn = "0271-2091",
    issue = "12",
    keyword = "Science \\& Technology",
    keyword = "Technology",
    keyword = "Physical Sciences",
    keyword = "Computer Science, Interdisciplinary Applications",
    keyword = "Mathematics, Interdisciplinary Applications",
    keyword = "Mechanics",
    keyword = "Physics, Fluids \\& Plasmas",
    keyword = "Computer Science",
    keyword = "Mathematics",
    keyword = "Physics",
    keyword = "COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS",
    keyword = "MATHEMATICS, INTERDISCIPLINARY APPLICATIONS",
    keyword = "MECHANICS",
    keyword = "PHYSICS, FLUIDS \\& PLASMAS",
    keyword = "flux reconstruction",
    keyword = "spectral/hp element methods",
    keyword = "discontinuous Galerkin",
    keyword = "tensor-product grids",
    keyword = "collocation",
    keyword = "SPECTRAL DIFFERENCE METHOD",
    language = "English",
    day = "30",
    publicationstatus = "published",
    }

  • A. Bolis, C. Cantwell, R. Kirby, and S. Sherwin, “From h to p efficiently: optimal implementation strategies for explicit time-dependent problems using the spectral/hp element method,” International journal for numerical methods in fluids, vol. 75, pp. 591-607, 2014. doi:10.1002/fld.3909
    [BibTeX] [Download PDF]
    @article{bolis2014frommethod,
    author = "Bolis, A and Cantwell, CD and Kirby, RM and Sherwin, SJ",
    journal = "INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS",
    month = "Jul",
    pages = "591--607",
    publisher = "WILEY-BLACKWELL",
    title = "From h to p efficiently: optimal implementation strategies for explicit time-dependent problems using the spectral/hp element method",
    url = "http://www2.imperial.ac.uk/ssherw/spectralhp/papers/IJNMF-BoCaKiSh-14.pdf",
    volume = "75",
    year = "2014",
    doi = "10.1002/fld.3909",
    issn = "0271-2091",
    issue = "8",
    keyword = "spectral",
    keyword = "hp element method",
    keyword = "hyperbolic problems",
    keyword = "discontinuous Galerkin",
    keyword = "explicit time-integration methods",
    keyword = "DISCONTINUOUS GALERKIN METHOD",
    keyword = "ELASTIC-WAVE PROPAGATION",
    keyword = "GENERAL LINEAR METHODS",
    keyword = "DISPERSION",
    keyword = "EQUATION",
    keyword = "APPROXIMATIONS",
    keyword = "STABILITY",
    language = "English",
    day = "20",
    publicationstatus = "published",
    }

  • G. Markall, A. Slemmer, D. Ham, P. Kelly, C. Cantwell, and S. Sherwin, “Finite element assembly strategies on multi- and many-core architectures,” International journal for numerical methods in fluids, 2012. doi:10.1002/fld.3648
    [BibTeX] [Download PDF]
    @article{markall2012finitearchitectures,
    author = "Markall, GR and Slemmer, A and Ham, DA and Kelly, PHJ and Cantwell, CD and Sherwin, SJ",
    journal = "International Journal for Numerical Methods in Fluids",
    title = "Finite element assembly strategies on multi- and many-core architectures",
    url = "http://www2.imperial.ac.uk/ssherw/spectralhp/papers/IJNMF_MaSlHaKeCaSh_11.pdf",
    year = "2012",
    doi = "10.1002/fld.3648",
    publicationstatus = "published",
    }

  • R. Kirby, S. Sherwin, and B. Cockburn, “To cg or to hdg: a comparative study,” Journal of scientific computing, vol. 51, pp. 183-212, 2012. doi:10.1007/s10915-011-9501-7
    [BibTeX] [Download PDF]
    @article{kirby2012tostudy,
    author = "Kirby, RM and Sherwin, SJ and Cockburn, B",
    journal = "JOURNAL OF SCIENTIFIC COMPUTING",
    month = "Apr",
    pages = "183--212",
    publisher = "SPRINGER/PLENUM PUBLISHERS",
    title = "To CG or to HDG: A Comparative Study",
    url = "http://www2.imperial.ac.uk/ssherw/spectralhp/papers/JSC_KiShCo_11.pdf",
    volume = "51",
    year = "2012",
    doi = "10.1007/s10915-011-9501-7",
    issn = "0885-7474",
    issue = "1",
    keyword = "Science \\& Technology",
    keyword = "Physical Sciences",
    keyword = "Mathematics, Applied",
    keyword = "Mathematics",
    keyword = "MATHEMATICS, APPLIED",
    keyword = "High-order finite elements",
    keyword = "Spectral/hp elements",
    keyword = "Discontinuous Galerkin method",
    keyword = "Hybridization",
    keyword = "Domain decomposition",
    keyword = "2ND-ORDER ELLIPTIC PROBLEMS",
    keyword = "DISCONTINUOUS GALERKIN METHOD",
    keyword = "FINITE-ELEMENT APPROXIMATIONS",
    keyword = "NAVIER-STOKES EQUATIONS",
    keyword = "ERROR ANALYSIS",
    keyword = "MIXED METHODS",
    keyword = "FLOW",
    keyword = "HYBRIDIZATION",
    keyword = "INSTABILITY",
    keyword = "TRANSITION",
    language = "English",
    day = "1",
    publicationstatus = "published",
    }

  • C. Cantwell, S. Sherwin, R. Kirby, and P. Kelly, “From h to p efficiently: selecting the optimal spectral/hp discretisation in three dimensions,” Mathematical modelling of natural phenomena, vol. 6, pp. 84-96, 2011. doi:10.1051/mmnp/20116304
    [BibTeX] [Download PDF]
    @article{cantwell2011fromdimensions,
    author = "Cantwell, CD and Sherwin, SJ and Kirby, RM and Kelly, PHJ",
    journal = "MATHEMATICAL MODELLING OF NATURAL PHENOMENA",
    month = "Jan",
    pages = "84--96",
    publisher = "EDP SCIENCES S A",
    title = "From h to p Efficiently: Selecting the Optimal Spectral/hp Discretisation in Three Dimensions",
    url = "http://www2.imperial.ac.uk/ssherw/spectralhp/papers/MMNP_CaShKiKe_10.pdf",
    volume = "6",
    year = "2011",
    doi = "10.1051/mmnp/20116304",
    issn = "0973-5348",
    issue = "3",
    keyword = "Science \\& Technology",
    keyword = "Life Sciences \\& Biomedicine",
    keyword = "Physical Sciences",
    keyword = "Mathematical \\& Computational Biology",
    keyword = "Mathematics, Interdisciplinary Applications",
    keyword = "Multidisciplinary Sciences",
    keyword = "Mathematics",
    keyword = "Science \\& Technology - Other Topics",
    keyword = "MATHEMATICAL \\& COMPUTATIONAL BIOLOGY",
    keyword = "MATHEMATICS, INTERDISCIPLINARY APPLICATIONS",
    keyword = "MULTIDISCIPLINARY SCIENCES",
    keyword = "spectral/hp element",
    keyword = "optimisation",
    keyword = "code performance",
    keyword = "FINITE-ELEMENTS",
    keyword = "EQUATIONS",
    keyword = "FLOW",
    language = "English",
    day = "1",
    publicationstatus = "published",
    }

  • P. Vos, C. Eskilsson, A. Bolis, S. Chun, R. Kirby, and S. Sherwin, “A generic framework for time-stepping partial differential equations (pdes): general linear methods, object-oriented implementation and application to fluid problems,” International journal of computational fluid dynamics, vol. 25, iss. PII 938278170, pp. 107-125, 2011. doi:10.1080/10618562.2011.575368
    [BibTeX] [Download PDF]
    @article{vos2011aproblems,
    author = "Vos, PEJ and Eskilsson, C and Bolis, A and Chun, S and Kirby, RM and Sherwin, SJ",
    journal = "INTERNATIONAL JOURNAL OF COMPUTATIONAL FLUID DYNAMICS",
    month = "Jan",
    number = "PII 938278170",
    pages = "107--125",
    publisher = "TAYLOR \\& FRANCIS LTD",
    title = "A generic framework for time-stepping partial differential equations (PDEs): general linear methods, object-oriented implementation and application to fluid problems",
    url = "http://www2.imperial.ac.uk/ssherw/spectralhp/papers/IJCFD_VoChBoEsKiSh_10.pdf",
    volume = "25",
    year = "2011",
    doi = "10.1080/10618562.2011.575368",
    issn = "1061-8562",
    issue = "3",
    keyword = "Science \\& Technology",
    keyword = "Technology",
    keyword = "Physical Sciences",
    keyword = "Mechanics",
    keyword = "Physics, Fluids \\& Plasmas",
    keyword = "Physics",
    keyword = "MECHANICS",
    keyword = "PHYSICS, FLUIDS \\& PLASMAS",
    keyword = "time-stepping methods",
    keyword = "Method of Lines",
    keyword = "IMEX-schemes",
    keyword = "object-oriented implementation",
    keyword = "time-dependent boundary conditions",
    keyword = "fluid problems",
    keyword = "RUNGE-KUTTA METHODS",
    keyword = "DIMSIMS",
    language = "English",
    day = "1",
    publicationstatus = "published",
    }

  • P. Vos, S. Sherwin, and R. Kirby, “From h to p efficiently: implementing finite and spectral/hp element methods to achieve optimal performance for low- and high-order discretisations,” Journal of computational physics, vol. 229, pp. 5161-5181, 2010. doi:10.1016/j.jcp.2010.03.031
    [BibTeX] [Download PDF]
    @article{vos2010fromdiscretisations,
    author = "Vos, PEJ and Sherwin, SJ and Kirby, RM",
    journal = "JOURNAL OF COMPUTATIONAL PHYSICS",
    month = "Jul",
    pages = "5161--5181",
    publisher = "ACADEMIC PRESS INC ELSEVIER SCIENCE",
    title = "From h to p efficiently: Implementing finite and spectral/hp element methods to achieve optimal performance for low- and high-order discretisations",
    url = "http://www2.imperial.ac.uk/ssherw/spectralhp/papers/JCP-VoShKi-09.pdf",
    volume = "229",
    year = "2010",
    doi = "10.1016/j.jcp.2010.03.031",
    issn = "0021-9991",
    issue = "13",
    keyword = "Science \\& Technology",
    keyword = "Technology",
    keyword = "Physical Sciences",
    keyword = "Computer Science, Interdisciplinary Applications",
    keyword = "Physics, Mathematical",
    keyword = "Computer Science",
    keyword = "Physics",
    keyword = "COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS",
    keyword = "PHYSICS, MATHEMATICAL",
    keyword = "Spectral/hp element method",
    keyword = "Implementation",
    keyword = "Elliptic problems",
    keyword = "DOMAIN DECOMPOSITION SCHEMES",
    keyword = "NAVIER-STOKES EQUATIONS",
    keyword = "STABLE PENALTY METHOD",
    language = "English",
    day = "1",
    publicationstatus = "published",
    }

  • G. Karniadakis and S. Sherwin, Spectral/hp element methods for computational fluid dynamics, 2 ed., Oxford University Press, 2005.
    [BibTeX]
    @book{karniadakisg.2005spectral/hpdynamics,
    author = "Karniadakis,G. and Sherwin,S.",
    edition = "2",
    pages = "1--650",
    publisher = "Oxford University Press",
    school = "Oxford",
    title = "Spectral/hp element methods for computational fluid dynamics",
    year = "2005",
    confidential = "False",
    isbn = "0-1985-2869-8",
    isbn = "9780198528692",
    }

For full publication list see here