8 citations · 20 across the 13 of their papers we have counts for
14 papers
An energy-based discontinuous Galerkin method for wave equations on complex geometric domains
Yangxin Fu, Yan Jiang, Siyang Wang +1
This paper develops a high-order cut energy-based discontinuous Galerkin (CutEDG) method for second-order acoustic wave equations on complex domains and across stationary material…
A Fully Discrete Energy-Based Discontinuous Galerkin Method for Variable-Order Time-Fractional Wave Equations
Lu Zhang
Variable-order time-fractional wave equations provide a flexible model for wave phenomena with evolving memory effects and anomalous temporal dynamics. Their numerical approximatio…
Discontinuous Galerkin methods for a first-order semi-linear hyperbolic continuum model of a topological resonator dimer array
Qiang Du, Huaiyu Li, Michael Weinstein +1
We present discontinuous Galerkin (DG) methods for solving a first-order semi-linear hyperbolic system, which was originally proposed as a continuum model for a one-dimensional dim…
A highly accurate perfectly-matched-layer boundary integral equation solver for acoustic layered-medium problems
Wangtao Lu, Liwei Xu, Tao Yin +1
Based on the perfectly matched layer (PML) technique, this paper develops a high-accuracy boundary integral equation (BIE) solver for acoustic scattering problems in locally defect…
On the hyper-singular boundary integral equation methods for dynamic poroelasticity: three dimensional case
Lu Zhang, Liwei Xu, Tao Yin
In our previous work [SIAM J. Sci. Comput. 43(3) (2021) B784-B810], an accurate hyper-singular boundary integral equation method for dynamic poroelasticity in two dimensions has be…
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…
A discontinuous Galerkin method for nonlinear biharmonic Schrödinger equations
Lu Zhang
This paper proposes and analyzes a fully discrete scheme that discretizes space with an ultra-weak local discontinuous Galerkin scheme and time with the Crank--Nicolson method for…
A local energy-based discontinuous Galerkin method for fourth order semilinear wave equations
Lu Zhang
This paper generalizes the earlier work on the energy-based discontinuous Galerkin method for second-order wave equations to fourth-order semilinear wave equations. We first rewrit…
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 high order finite difference method for the elastic wave equation in bounded domains with nonconforming interfaces
Lu Zhang, Siyang Wang
We develop a stable finite difference method for the elastic wave equation in bounded media, where the material properties can be discontinuous at curved interfaces. The governing…
An accurate hyper-singular boundary integral equation method for dynamic poroelasticity in two dimensions
Lu Zhang, Liwei Xu, Tao Yin
This paper is concerned with the boundary integral equation method for solving the exterior Neumann boundary value problem of dynamic poroelasticity in two dimensions. The main con…
Elastic wave propagation in curvilinear coordinates with mesh refinement interfaces by a fourth order finite difference method
Lu Zhang, Siyang Wang, N. Anders Petersson
We develop a fourth order accurate finite difference method for the three dimensional elastic wave equation in isotropic media with the piecewise smooth material property. In our m…
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…
An energy-based discontinuous Galerkin method for the wave equation with advection
Lu Zhang, Thomas Hagstrom, Daniel Appelo
An energy-based discontinuous Galerkin method for the advective wave equation is proposed and analyzed. Energy-conserving or energy-dissipating methods follow from simple, mesh-ind…