报告题目：Solving PDEs on surfaces of pipe geometries using new coordinate transformations and high-order methods

报告时间：2025-09-19   16:00-17:00

报  告 人 ：焦裕建  教授  （上海师范大学）

报告地点：雷军科技楼六楼报告厅（644）

Abstract:We propose new curvilinear coordinate systems for pipes and their variants, which transform partial differential equations (PDEs) on pipe surfaces or solids into computational domains with fixed ranges. These coordinates are non-orthogonal in two directions, leading to Laplace–Beltrami operators with mixed derivatives. To address the variable coefficients arising from coordinate transformations and complex geometries, we develop efficient fourth-order compact finite difference schemes, rigorously prove their convergence, and validate their performance with extensive numerical experiments. We further consider twisted tube surfaces, derive the corresponding Laplace–Beltrami operators, and apply a Fourier–Legendre mixed spectral-Galerkin method to the Allen–Cahn equation. Theoretical analysis and simulations confirm the stability, accuracy, and efficiency of the proposed approaches.