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math.NA2026
A Robust Helmholtz-Decomposition-Based Real Compressed Layer Method for Time-Harmonic Elastic Wave Scattering
Li-Lian Wang, Lu Zhang
Time-harmonic elastic wave scattering involves both compressional (P-) and shear (S-) waves, which propagate with different wavenumbers and polarization characteristics. The naive…
math.NA2025
A discontinuous Galerkin method for one-dimensional nonlocal wave problems
Qiang Du, Kui Ren, Lu Zhang +1
This paper presents a fully discrete numerical scheme for one-dimensional nonlocal wave equations and provides a rigorous theoretical analysis. To facilitate the spatial discretiza…
math.NA2023
An energy-based discontinuous Galerkin method for the nonlinear Schrödinger equation with wave operator
Kui Ren, Lu Zhang, Yin Zhou
This work develops an energy-based discontinuous Galerkin (EDG) method for the nonlinear Schrödinger equation with the wave operator. The focus of the study is on the energy-conser…