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…
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…
A machine learning enhanced discontinuous Galerkin method for simulating transonic airfoil flow-fields
Yiwei Feng, Lili Lv, Weixiong Yuan +2
Accurate and rapid prediction of flow-fields is crucial for aerodynamic design. This work proposes a discontinuous Galerkin method (DGM) whose performance enhances with increasing…
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…