126 6.2.1 Linear-SDIRK methods with s stages of order (s + 1), p.127 ,
139 6.4.1 Computation of the right hand side (RHS), p.139 ,
144 6.5.1 Convergence curves and numerical results in 1-D, p.145 ,
199 8.5.1 Convergence curves and numerical results on a 2D regular mesh ,
A fully asynchronous multi-frontal solver using distributed dynamic scheduling, SIAM Journal on Matrix Analysis and Applications, vol.23, pp.15-41, 2001. ,
Real valued iterative methods for solving complex linear systems, Tech. rep, 1999. ,
High-order Padé and singly diagonally Runge-Kutta schemes for linear ODEs, application to wave propagation problems, Numerical Methods for Partial Differential Equations, vol.220, pp.1-39, 2017. ,
Higher-order discontinuous Galerkin method for pyramidal elements using orthogonal bases, Numerical Methods for Partial Differential Equations, p.44, 2012. ,
Low-dissipation and lowdispersion fourth-order Runge-Kutta algorithm, Computers & Fluids, vol.35, pp.1459-1463, 2006. ,
Explicit Runge-Kutta schemes and finite elements with symmetric stabilization for first-order linear PDE systems, SIAM Journal on Numerical Analysis, vol.48, issue.1, pp.2019-2042, 2010. ,
URL : https://hal.archives-ouvertes.fr/hal-00380659
Numerical Methods for Ordinary Differential Equations Second Edition, pp.78-161, 2008. ,
DOI : 10.1002/0470868279
Fourth-order energy-preserving locally implicit time discretization for linear wave equations, International Journal for Numerical Methods in Engineering, vol.106, issue.8, pp.596-622, 2016. ,
Fast and efficient algorithms in Computational electromagnetics, p.49, 2001. ,
High-order triangular and tetrahedral finite elements with mass lumping for solving the wave equation, Journal of Engineering Mathematics, vol.35, pp.405-426, 1999. ,
An implicit hybridized discontinuous Galerkin method for the 3D time-domain Maxwell's equations, Applied Mathematics and Computation, vol.319, issue.29, pp.395-408, 2017. ,
Unified hybridization of discontinuous Galerkin, mixed and continuous Galerkin methods for second order elliptic problems, SIAM Journal on Numerical Analysis, vol.47, pp.1319-1365, 2009. ,
Mixed finite elements with mass-lumping for the transient wave equation, Journal of Computational Acoustics, vol.8, issue.29, pp.171-188, 2000. ,
Finite element and discontinuous Galerkin methods for transient wave equations, p.33, 2005. ,
Application of the perfectly matched absorbing layer model to the linear elastodynamic problem in anisotropic heterogeneous media, Geophysics, vol.66, pp.294-307, 2001. ,
Locally implicit time integration strategies in a discontinuous Galerkin method for Maxwell's equations, Tech. rep, 2012. ,
Locally implicit discontinuous Galerkin time domain method for electromagnetic wave propagation in dispersive media applied to numerical dosimetry in biological tissues, SIAM Journal on Scientific Computing, vol.38, pp.2611-2633, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01133694
Energy conserving explicit local time stepping for second-order wave equations, SIAM Journal on Scientific Computing, vol.31, 1985. ,
Optimized high-order explicit Runge- Kutta-Nyström schemes, Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2016, p.159, 2016. ,
On the parallel solution of parabolic equations, p.105, 1989. ,
Higher order time stepping for second order hyperbolic problems and optimal CFL conditions, Computational Methods in Applied Sciences, vol.16, pp.67-93, 2008. ,
A diagonal-mass matrix triangularspectral-element method based on cubature points, Journal of Engineering Mathematics, vol.56, pp.307-322, 2006. ,
Error analysis for a hybridizable discontinuous Galerkin method for the Helmholtz equation, Journal of Scientific Computing, vol.49, pp.291-310, 2011. ,
Explicit local time-stepping methods for Maxwell's equations, Journal of Computational and Applied Mathematics, vol.234, issue.1, pp.3283-3302, 2010. ,
Solving ordinary differential equations I nonstiff problem, p.5, 2008. ,
Solving ordinary differential equations II stiff and differential-algebraic problem, pp.69-76, 2010. ,
Nodal discontinuous Galerkin methods algorithms, analysis, and applications, 2008. ,
Phase-lag analysis of implicit Runge-Kutta methods, SIAM Journal on Numerical Analysis, vol.26, pp.214-229, 1989. ,
Low-dissipation and low-dispersion Runge-Kutta schemes for computational acoustics, Journal of Computational Physics, vol.124, issue.89, pp.177-191, 1996. ,
Optimized higher order time discretization of second order hyperbolic problems: Construction and numerical study, Journal of Computational and Applied Mathematics, vol.234, issue.5, pp.1953-1961, 2010. ,
Application of implicit-explicit high order Runge-Kutta methods to discontinuous-Galerkin schemes, Journal of Computational Physics, vol.225, issue.8, pp.1753-1781, 2007. ,
Optimal stability polynomials for numerical integration of initial value problems, Communications in Applied Mathematics And Computational Science, vol.7, issue.163, pp.247-271, 2012. ,
Rk-Opt Software for the design of Runge-Kutta methods version 0.2. Tech. rep, pp.2013-166 ,
Comparison of implicit and explicit hybridizable discontinuous Galerkin methods for the acoustics wave equation, International Journal for Numerical Methods in Engineering, vol.106, issue.29, pp.712-739, 2016. ,
A hybridizable discontinuous Galerkin method for time-harmonic Maxwell's equations, p.58, 2011. ,
Optimal Runge-Kutta methods for first order pseudospectral operators, Journal of Computational Physics, vol.90, pp.404-419, 1999. ,
Runge-Kutta-based explicit local time-stepping methods for wave propagation, A747?A775, 2015. ,
Nineteen dubious ways to compute the exponential of a matrix, twenty five years later BIBLIOGRAPHY [57] MONK, P. Finite element methods for Maxwell's equations, SIAM Review, vol.45, issue.50, pp.3-49, 2003. ,
A low-dispersion and lowdissipation implicit Runge-Kutta scheme, Journal of Computational Physics, vol.233, issue.90, pp.315-323, 2013. ,
High-order implicit hybridizable discontinuous Galerkin methods for acoustics and elastodynamics, Journal of Computational Physics, vol.230, issue.5, pp.3695-3718, 2011. ,
Hybridizable discontinuous Galerkin methods for partial differential equations in continuum mechanics, Journal of Computational Physics, vol.231, pp.5955-5988, 2012. ,
Performance of an implicit time integration scheme in the analysis of wave propagations, Computer and Structures, vol.123, issue.1, pp.93-105, 2013. ,
Optimized explicit Runge-Kutta schemes for the spectral difference method applied to wave propagation problems, SIAM Journal on Scientific Computing, vol.35, issue.5, pp.957-986, 2013. ,
Mathematical aspects of discontinuous Galerkin methods, 2012. ,
On the zeros and poles of Padé approximants to e z . iii, Numerische Mathematik, vol.30, pp.241-266, 1978. ,
Higher-order finite element methods, p.30, 2003. ,
Locally implicit time integration for linear Maxwell's equations, 0191. ,
Dispersion-relation-preserving finite difference schemes for computational acoustics, Computational Physics, vol.107, issue.76, pp.262-281, 1993. ,
Taming the CFL number for discontinuous Galerkin methods on structured meshes, SIAM Journal on Scientific Computing, vol.46, issue.1 6, pp.3151-3180, 2008. ,