Journal of Computational Physics
A spectral multidomain method for the solution of hyperbolic systems
Applied Numerical Mathematics - Special issue in honor of Milt Rose's sixtieth birthday
Computation of hyperbolic equations on complicated domains with patched and overset Chebyshev grids
SIAM Journal on Scientific and Statistical Computing
Domain decomposition methods for systems of conservation laws: spectral collocation approximations
SIAM Journal on Scientific and Statistical Computing
Multidomain spectral solution of the Euler Gas-dynamics equations
Journal of Computational Physics
Spectral methods on triangles and other domains
Journal of Scientific Computing
Monomial cubature rules since “Stroud”: a compilation
Journal of Computational and Applied Mathematics
Parallel, adaptive finite element methods for conservation laws
Proceedings of the third ARO workshop on Adaptive methods for partial differential equations
A spectral element-FCT method for the compressible Euler equations
Journal of Computational Physics
Tetrahedral hp finite elements: algorithms and flow simulations
Journal of Computational Physics
Spectral methods on arbitrary grids
Journal of Computational Physics
Spectral simulations of electromagnetic wave scattering
Journal of Computational Physics
Multilevel k-way partitioning scheme for irregular graphs
Journal of Parallel and Distributed Computing
On the construction and analysis of absorbing layers in CEM
Applied Numerical Mathematics - Special issue on absorbing boundary conditions
Spectral/hp methods for viscous compressible flows on unstructured 2D meshes
Journal of Computational Physics
SIAM Journal on Scientific Computing
A discontinuous Galerkin method for the viscous MHD equations
Journal of Computational Physics
Monomial cubature rules since “Stroud”: a compilation—part 2
Journal of Computational and Applied Mathematics - Numerical evaluation of integrals
Spectral collocation time-domain modeling of diffractive optical elements
Journal of Computational Physics
Proceedings of the fourth international conference on Spectral and high order methods (ICOSAHOM 1998)
Multidomain pseudospectral computation of Maxwell's equations in 3-D general curvilinear coordinates
Proceedings of the fourth international conference on Spectral and high order methods (ICOSAHOM 1998)
Stable Spectral Methods on Tetrahedral Elements
SIAM Journal on Scientific Computing
MPI: The Complete Reference
Finite Element Method for Elliptic Problems
Finite Element Method for Elliptic Problems
Nodal high-order methods on unstructured grids
Journal of Computational Physics
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Nodal high-order methods on unstructured grids
Journal of Computational Physics
Simulating Near-Field Effects in High-Density Optical-Disk Data Storage
Computing in Science and Engineering
A sequence of absorbing boundary conditions for Maxwell's equations
Journal of Computational Physics
DSC time-domain solution of Maxwell's equations
Journal of Computational Physics
Locally divergence-free discontinuous Galerkin methods for the Maxwell equations
Journal of Computational Physics
Dispersive and dissipative behaviour of high order discontinuous Galerkin finite element methods
Journal of Computational Physics
High-order FDTD methods via derivative matching for Maxwell's equations with material interfaces
Journal of Computational Physics
Algorithm 839: FIAT, a new paradigm for computing finite element basis functions
ACM Transactions on Mathematical Software (TOMS)
A Discontinuous Galerkin Method for Linear Symmetric Hyperbolic Systems in Inhomogeneous Media
Journal of Scientific Computing
High-order RKDG Methods for Computational Electromagnetics
Journal of Scientific Computing
A fast, higher-order solver for scattering by penetrable bodies in three dimensions
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
High-order RKDG methods for computational electromagnetics
Journal of Scientific Computing
A discontinuous Galerkin method for linear symmetric hyperbolic systems in inhomogeneous media
Journal of Scientific Computing
Journal of Scientific Computing
Spectral Element Methods on Unstructured Meshes: Comparisons and Recent Advances
Journal of Scientific Computing
High-order nodal discontinuous Galerkin particle-in-cell method on unstructured grids
Journal of Computational Physics
High-order discontinuous Galerkin methods using an hp-multigrid approach
Journal of Computational Physics
Spectral difference method for unstructured grids I: basic formulation
Journal of Computational Physics
Journal of Computational Physics
Idempotent filtering in spectral and spectral element methods
Journal of Computational Physics
A high-order discontinuous Galerkin method for the unsteady incompressible Navier-Stokes equations
Journal of Computational Physics
Grid stabilization of high-order one-sided differencing I: First-order hyperbolic systems
Journal of Computational Physics
Applied Numerical Mathematics
Interior penalty discontinuous Galerkin method for Maxwell's equations: Energy norm error estimates
Journal of Computational and Applied Mathematics
Application of the symplectic finite-difference time-domain scheme to electromagnetic simulation
Journal of Computational Physics
Application of implicit-explicit high order Runge-Kutta methods to discontinuous-Galerkin schemes
Journal of Computational Physics
Journal of Scientific Computing
The finite-volume time-domain algorithm using least square method in solving Maxwell's equations
Journal of Computational Physics
Flux limiting embedded boundary technique for electromagnetic FDTD
Journal of Computational Physics
Solution of the time-harmonic Maxwell equations using discontinuous Galerkin methods
Journal of Computational and Applied Mathematics
An integration scheme for electromagnetic scattering using plane wave edge elements
Advances in Engineering Software
Journal of Computational Physics
Improved Performance for Nodal Spectral Element Operators
International Journal of High Performance Computing Applications
Polymorphic nodal elements and their application in discontinuous Galerkin methods
Journal of Computational Physics
Optimal Error Estimates for the Fully Discrete Interior Penalty DG Method for the Wave Equation
Journal of Scientific Computing
Nodal discontinuous Galerkin methods on graphics processors
Journal of Computational Physics
Journal of Computational and Applied Mathematics
Singularity-free evaluation of collapsed-coordinate orthogonal polynomials
ACM Transactions on Mathematical Software (TOMS)
Interior Penalty Discontinuous Galerkin Method for Maxwell's Equations in Cold Plasma
Journal of Scientific Computing
Locally implicit discontinuous Galerkin method for time domain electromagnetics
Journal of Computational Physics
A high-order non-conforming discontinuous Galerkin method for time-domain electromagnetics
Journal of Computational and Applied Mathematics
Journal of Computational Physics
Journal of Computational and Applied Mathematics
Radiation boundary conditions for time-dependent waves based on complete plane wave expansions
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Explicit local time-stepping methods for Maxwell's equations
Journal of Computational and Applied Mathematics
Revisiting and Extending Interface Penalties for Multi-domain Summation-by-Parts Operators
Journal of Scientific Computing
Pseudospectral Modeling of Nano-Optics in Ag Sphere Arrays
Journal of Scientific Computing
Journal of Computational Physics
Error analysis of a discontinuous Galerkin method for Maxwell equations in dispersive media
Journal of Computational Physics
Spectral element methods on unstructured meshes: which interpolation points?
Numerical Algorithms
Adaptive sparse grid algorithms with applications to electromagnetic scattering under uncertainty
Applied Numerical Mathematics
Applied Numerical Mathematics
High-order implicit hybridizable discontinuous Galerkin methods for acoustics and elastodynamics
Journal of Computational Physics
A New Class of High-Order Energy Stable Flux Reconstruction Schemes
Journal of Scientific Computing
Solving Maxwell's equations in singular domains with a Nitsche type method
Journal of Computational Physics
Interior penalty DG methods for Maxwell's equations in dispersive media
Journal of Computational Physics
Hybridizable discontinuous Galerkin methods for the time-harmonic Maxwell's equations
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational and Applied Mathematics
Efficient low-storage Runge-Kutta schemes with optimized stability regions
Journal of Computational Physics
An error minimized pseudospectral penalty direct Poisson solver
Journal of Computational Physics
Source identification in time domain electromagnetics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational and Applied Mathematics
International Journal of Numerical Modelling: Electronic Networks, Devices and Fields
A p-adaptive LCP formulation for the compressible Navier-Stokes equations
Journal of Computational Physics
Time-integration methods for finite element discretisations of the second-order Maxwell equation
Computers & Mathematics with Applications
Journal of Computational Physics
Dispersion and Dissipation Errors of Two Fully Discrete Discontinuous Galerkin Methods
Journal of Scientific Computing
Journal of Scientific Computing
Journal of Computational Physics
Journal of Scientific Computing
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.67 |
We present a convergent high-order accurate scheme for the solution of linear conservation laws in geometrically complex domains. As our main example we include a detailed development and analysis of a scheme for the time-domain solution of Maxwell's equations in a three-dimensional domain. The fully unstructured spatial discretization is made possible by the use of a high-order nodal basis, employing multivariate Lagrange polynomials defined on the triangles and tetrahedra, while the equations themselves are satisfied in a discontinuous Galerkin form with the boundary conditions being enforced weakly through a penalty term. Accuracy, stability, and convergence of the semidiscrete approximation to Maxwell's equations is established rigorously and bounds on the growth of the global divergence error are provided. Concerns related to efficient implementations are discussed in detail. This sets the stage for the presentation of examples, verifying the theoretical results, and illustrating the versatility, flexibility, and robustness when solving two- and three-dimensional benchmark problems in computational electromagnetics. Pure scattering as well as penetration is discussed and high parallel performance of the scheme is demonstrated.