A parallel local timestepping Runge-Kutta discontinuous Galerkin method with applications to coastal ocean modeling

[1]  J. Garratt.  Review of Drag Coefficients over Oceans and Continents , 1977 .

[2]  G. Holland.  An Analytic Model of the Wind and Pressure Profiles in Hurricanes , 1980 .

[3]  S. Osher,et al.  Numerical approximations to nonlinear conservation laws with locally varying time and space grids , 1983 .

[4]  Chi-Wang Shu.  TVB uniformly high-order schemes for conservation laws , 1987 .

[5]  G. R. Shubin,et al.  An unsplit, higher order Godunov method for scalar conservation laws in multiple dimensions , 1988 .

[6]  S. Osher,et al.  Efficient implementation of essentially non-oscillatory shock-capturing schemes,II , 1989 .

[7]  Clint N. Dawson,et al.  High resolution upwind‐mixed finite element methods for advection‐diffusion equations with variable time‐stepping , 1995 .

[8]  R. LeVeque,et al.  Adaptive Mesh Refinement Using Wave-Propagation Algorithms for Hyperbolic Systems , 1998 .

[9]  Vipin Kumar,et al.  A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs , 1998, SIAM J. Sci. Comput..

[10]  Clint Dawson,et al.  High Resolution Schemes for Conservation Laws with Locally Varying Time Steps , 2000, SIAM J. Sci. Comput..

[11]  R. Luettich,et al.  Eastcoast 2001, A Tidal Constituent Database for Western North Atlantic, Gulf of Mexico, and Caribbean Sea , 2002 .

[12]  Robert C. Kirby,et al.  On the convergence of high resolution methods with multiple time scales for hyperbolic conservation laws , 2003, Math. Comput..

[13]  Jean-François Remacle,et al.  An Adaptive Discontinuous Galerkin Technique with an Orthogonal Basis Applied to Compressible Flow Problems , 2003, SIAM Rev..

[14]  Ethan J. Kubatko,et al.  hp Discontinuous Galerkin methods for advection dominated problems in shallow water flow , 2006 .

[15]  Emil M. Constantinescu,et al.  Multirate Timestepping Methods for Hyperbolic Conservation Laws , 2007, J. Sci. Comput..

[16]  E. Montseny,et al.  Dissipative terms and local time-stepping improvements in a spatial high order Discontinuous Galerkin scheme for the time-domain Maxwell's equations , 2008, J. Comput. Phys..

[17]  Harley S. Winer,et al.  A real time storm surge forecasting system using ADCIRC , 2008 .

[18]  Brett F. Sanders,et al.  Integration of a shallow water model with a local time step , 2008 .

[19]  J. Feyen,et al.  A Basin to Channel-Scale Unstructured Grid Hurricane Storm Surge Model Applied to Southern Louisiana , 2008 .

[20]  Ethan J. Kubatko,et al.  A wetting and drying treatment for the Runge-Kutta discontinuous Galerkin solution to the shallow water equations , 2009 .

[21]  Emil M. Constantinescu,et al.  Multirate Explicit Adams Methods for Time Integration of Conservation Laws , 2009, J. Sci. Comput..

[22]  Julien Diaz,et al.  Energy Conserving Explicit Local Time Stepping for Second-Order Wave Equations , 2007, SIAM J. Sci. Comput..

[23]  Clint Dawson,et al.  A Performance Comparison of Continuous and Discontinuous Finite Element Shallow Water Models , 2009, J. Sci. Comput..

[24]  Ethan J. Kubatko,et al.  Dynamic p-adaptive Runge–Kutta discontinuous Galerkin methods for the shallow water equations , 2009 .

[25]  Xiaoliang Wan,et al.  Comput. Methods Appl. Mech. Engrg. , 2010 .

[26]  Markus Clemens,et al.  GPU Accelerated Adams–Bashforth Multirate Discontinuous Galerkin FEM Simulation of High-Frequency Electromagnetic Fields , 2010, IEEE Transactions on Magnetics.

[27]  Li Liu,et al.  Nonuniform time-step Runge-Kutta discontinuous Galerkin method for Computational Aeroacoustics , 2010, J. Comput. Phys..

[28]  Seizo Tanaka,et al.  A performance comparison of nodal discontinuous Galerkin methods on triangles and quadrilaterals , 2010 .

[29]  J. C. Dietrich,et al.  Origin of the Hurricane Ike forerunner surge , 2011 .

[30]  Clint Dawson,et al.  Adaptive hierarchic transformations for dynamically p-enriched slope-limiting over discontinuous Galerkin systems of generalized equations , 2010, J. Comput. Phys..

[31]  Randall J. LeVeque,et al.  The GeoClaw software for depth-averaged flows with adaptive refinement , 2010, 1008.0455.

[32]  Clint Dawson,et al.  Discontinuous Galerkin Methods for Modeling Hurricane Storm Surge , 2011 .

[33]  C. Dawson,et al.  Local time-stepping in Runge–Kutta discontinuous Galerkin finite element methods applied to the shallow-water equations , 2012 .

[34]  Adrian Sandu,et al.  Extrapolated Multirate Methods for Differential Equations with Multiple Time Scales , 2013, J. Sci. Comput..