Byungjoon Lee | Searcharxiv

arXiv2025

The Closest Point Method for Surface PDEs with General Boundary Conditions

We generalize the closest point method (CPM) to solve surface partial differential equations with general boundary conditions. The proposed extrapolation method provides a unified framework for treating a broad class of inhomogeneous Neumann and Robin boundary conditions within the framework of CPM. The accuracy and robustness of the method are demonstrated through numerical convergence studies of an elliptic problem, Steklov eigenvalue problems, and a nonlinear reaction-diffusion system.

math.NA↗

arXiv2025

The Closest Point Heat Method for Solving Eikonal Equations on Implicit Surfaces

We introduce the Closest Point Heat Method (CPHM), a novel approach for solving the surface Eikonal equation on general smooth surfaces. Building on the strengths of the classical heat method, such as simplicity of implementation and computational efficiency, CPHM integrates closest point techniques to reduce dependence on surface meshes. This embedding framework naturally extends the heat method to implicit surfaces while preserving both its efficiency and intrinsic geometric properties. Numerical experiments on benchmark geometries confirm the accuracy and convergence of the proposed method and demonstrate its effectiveness on complex shapes.

math.NA↗