23 citations · 73 across the 31 of their papers we have counts for
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An Energy-Based Discontinuous Galerkin Method with Tame CFL Numbers for the Wave Equation
Daniel Appelö, Lu Zhang, Thomas Hagstrom +1
We extend and analyze the energy-based discontinuous Galerkin method for second order wave equations on staggered and structured meshes. By combining spatial staggering with local…
Energy-based discontinuous Galerkin difference methods for second-order wave equations
Lu Zhang, Daniel Appelö, Thomas Hagstrom
We combine the newly-constructed Galerkin difference basis with the energy-based discontinuous Galerkin method for wave equations in second order form. The approximation properties…
A Hermite Method with a Discontinuity Sensor for Hamilton-Jacobi Equations
Allen Alvarez Loya, Daniel Appelö
We present a Hermite interpolation based partial differential equation solver for Hamilton-Jacobi equations. Many Hamilton-Jacobi equations have a nonlinear dependency on the gradi…
Fourier Continuation Discontinuous Galerkin Methods for Linear Hyperbolic Problems
Daniel Appelo, Kiera van der Sande, Nathan Albin
Fourier continuation is an approach used to create periodic extensions of non-periodic functions in order to obtain highly-accurate Fourier expansions. These methods have been used…
EM-WaveHoltz: A flexible frequency-domain method built from time-domain solvers
Zhichao Peng, Daniel Appelö
A novel approach to computing time-harmonic solutions of Maxwell's equations by time-domain simulations is presented. The method, EM-WaveHoltz, results in a positive definite syste…
An energy-based summation-by-parts finite difference method for the wave equation in second order form
Siyang Wang, Daniel Appelö, Gunilla Kreiss
We develop a new finite difference method for the wave equation in second order form. The finite difference operators satisfy a summation-by-parts (SBP) property. With boundary con…
Accuracy of spectral element method for wave, parabolic and Schrödinger equations
Hao Li, Daniel Appelö, Xiangxiong Zhang
The spectral element method constructed by the () continuous finite element method with -point Gauss-Lobatto quadrature on rectangular meshes is a popular hig…