{"id":229,"date":"2012-09-23T23:38:05","date_gmt":"2012-09-24T03:38:05","guid":{"rendered":"https:\/\/www.bu.edu\/pasi-tsunami\/?page_id=229"},"modified":"2012-10-24T19:57:51","modified_gmt":"2012-10-24T23:57:51","slug":"discontinuous-galerkin","status":"publish","type":"page","link":"https:\/\/www.bu.edu\/pasi-tsunami\/program\/discontinuous-galerkin\/","title":{"rendered":"Discontinuous Galerkin models"},"content":{"rendered":"

of shallow-water phenomena<\/h2>\n

by Dr Timothy Warburton<\/a><\/h3>\n
Department of Computational and Applied Mathematics, Rice University<\/address>\n

Syllabus<\/h3>\n

(1) Background machinery for Discontinuous Galerkin methods<\/p>\n

    \n
  • Orthogonal polynomials<\/li>\n
  • Langrange polynomials and interpolation<\/li>\n
  • Differentiation matrices<\/li>\n
  • Projection operators<\/li>\n
  • Lift matrices<\/li>\n
  • Cubature: multi-dimensional quadrature rules and dealiasing<\/li>\n<\/ul>\n

    (2) Discretization of Discontinuous Galerkin methods for the shallow water equations<\/p>\n

      \n
    • Discretization of the Shallow Water equations using DG methods on triangular elements, with emphasis on unstructured\/adaptive grids<\/li>\n
    • Wetting-drying algorithms for run-up simulations<\/li>\n<\/ul>\n

      (3) Advanced Time-Integration for the Shallow Water Equations<\/p>\n

        \n
      • Method of lines<\/li>\n
      • High-order explicit methods<\/li>\n
      • Implicit-explicit methods (including multi-step single-stage and single-step multi-stage methods)<\/li>\n
      • Fully-implicit methods<\/li>\n
      • Multi-rate methods<\/li>\n<\/ul>\n

        (4) CUDA & OpenCL kernels for DG shallow water and tsunami simulations<\/p>\n

          \n
        • CUDA & OpenCL kernels for time-stepping and for computing the volume and flux integrals in DG methods<\/li>\n
        • Setting up the initial grid of any region of the world oceans<\/li>\n
        • Bathymetry<\/li>\n
        • Initial conditions<\/li>\n
        • Role of data assimilation\/observability of such events<\/li>\n
        • Loo.py based kernel generation<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"

          of shallow-water phenomena by Dr Timothy Warburton Department of Computational and Applied Mathematics, Rice University Syllabus (1) Background machinery for Discontinuous Galerkin methods Orthogonal polynomials Langrange polynomials and interpolation Differentiation matrices Projection operators Lift matrices Cubature: multi-dimensional quadrature rules and dealiasing (2) Discretization of Discontinuous Galerkin methods for the shallow water equations Discretization of the […]<\/p>\n","protected":false},"author":6513,"featured_media":0,"parent":188,"menu_order":9,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"_links":{"self":[{"href":"https:\/\/www.bu.edu\/pasi-tsunami\/wp-json\/wp\/v2\/pages\/229"}],"collection":[{"href":"https:\/\/www.bu.edu\/pasi-tsunami\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.bu.edu\/pasi-tsunami\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.bu.edu\/pasi-tsunami\/wp-json\/wp\/v2\/users\/6513"}],"replies":[{"embeddable":true,"href":"https:\/\/www.bu.edu\/pasi-tsunami\/wp-json\/wp\/v2\/comments?post=229"}],"version-history":[{"count":7,"href":"https:\/\/www.bu.edu\/pasi-tsunami\/wp-json\/wp\/v2\/pages\/229\/revisions"}],"predecessor-version":[{"id":522,"href":"https:\/\/www.bu.edu\/pasi-tsunami\/wp-json\/wp\/v2\/pages\/229\/revisions\/522"}],"up":[{"embeddable":true,"href":"https:\/\/www.bu.edu\/pasi-tsunami\/wp-json\/wp\/v2\/pages\/188"}],"wp:attachment":[{"href":"https:\/\/www.bu.edu\/pasi-tsunami\/wp-json\/wp\/v2\/media?parent=229"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}