4 papers
Symplectic Hamiltonian Direct Discontinuous Galerkin Method for Wave Propagation
Haomiao Li, Yumiao Li, Jiaxin Wang +2
This paper presents a symplectic Hamiltonian direct discontinuous Galerkin (DDG) method for approximating wave propagation problems, including the linear and semilinear wave equati…
Quantum circuits for the advection-diffusion equation with boundary conditions based on LCHS
Leyu Chen, Tiegang Liu, Liang Xu +1
This paper proposes a systematic and explicit quantum circuit framework for solving advection-diffusion equations with boundary conditions, based on the Linear Combination of Hamil…
CLINN: Conservation Law Informed Neural Network for Approximating Discontinuous Solutions
Weiheng Zeng, Kun Wang, Ruoxi Lu +1
Physics-informed Neural Network (PINN) faces significant challenges when approximating solutions to conservation laws, particularly in ensuring conservation and accurately resolvin…
Investigation of discontinuous Galerkin methods in adjoint gradient-based aerodynamic shape optimization
Yiwei Feng, Lili Lv, Tiegang Liu +2
This work develops a robust and efficient framework of the adjoint gradient-based aerodynamic shape optimization (ASO) using high-order discontinuous Galerkin methods (DGMs) as the…