5 papers
Quantum Frozen--Oseen homotopy analysis method with LCHS for solving nonlinear partial differential equations
Jinhao Yuan, Leyu Chen, Tiegang Liu +1
Nonlinear partial differential equations (PDEs) underpin computational fluid dynamics, yet resolving nonlinear transport on fine grids remains computationally demanding. Quantum li…
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 +2
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…