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Extensions and Analysis of an Iterative Solution of the Helmholtz Equation via the Wave Equation
Fortino Garcia, Daniel Appelö, Olof Runborg
In this paper we extend analysis of the WaveHoltz iteration -- a time-domain iterative method for the solution of the Helmholtz equation. We expand the previous analysis of energy…
Universal AMG Accelerated Embedded Boundary Method Without Small Cell Stiffness
Zhichao Peng, Daniel Appelö, Shuang Liu
We develop a universally applicable embedded boundary finite difference method, which results in a symmetric positive definite linear system and does not suffer from small cell sti…
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…
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…
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…
An energy-based discontinuous Galerkin method for semilinear wave equations
Daniel Appelo, Thomas Hagstrom, Qi Wang +1
We generalize the energy-based discontinuous Galerkin method proposed in [SIAM J. Num. Anal., 53(6):2705-2726, 2015.] to second-order semilinear wave equations. A stability and con…