Speaker: Dr. Meng Chen（陈朦博士）

Time: 10:00-11:00, 4 January 2025 (Sunday) (Beijing time)

Venue: CC126 (华信书院)

Abstract

We introduce a fast, constrained meshfree solver designed specifically to inherit energy conservation (EC) in second-order time-dependent Hamiltonian wave equations. For discretization, we adopt the Kansa method, also known as the kernel-based collocation method, combined with time-stepping. This approach ensures that the critical structural feature of energy conservation is maintained over time by embedding a quadratic constraint into the definition of the numerical solution. To address the computational challenges posed by the nonlinearity in the Hamiltonian wave equations and the EC constraint, we propose a fast iterative solver based on the Newton method with successive linearization. This novel solver significantly accelerates the computation, making the method highly effective for practical applications. Numerical comparisons with the traditional secant methods highlight the competitive performance of our scheme. These results demonstrate that our method not only conserves the energy but also offers a promising new direction for solving Hamiltonian wave equations more efficiently. While we focus on the Kansa method and corresponding convergence theories in this study, the proposed solver is based solely on linear algebra techniques and has the potential to be applied to EC constrained optimization problems arising from other PDE discretization methods.

About the Speaker

陈朦博士，毕业于香港浸会大学，现为南昌大学副教授、硕士生导师，江西省高校中青年学科（专业）带头人。主要研究无网格数值方法在偏微分方程上的求解与应用。主持国家自然科学基金委员会（NSFC）青年基金项目1项（2020年获批）、NSFC地区基金1项（2023年获批）、江西省自然科学基金委员会青年基金项目1项，并参与NSFC面上基金项目2项（2017年、2023年获批）；获美国国家专利1项；在 SIAM J. Numer. Anal., J. Comput. Phys., J. Sci. Comput.等期刊发表学术论文十余篇。