3 papers
math.AP2025
On a calculation method of the thickness via partial differential equations
Atsushi Nakayasu, Takayuki Yamada
This paper presents a mathematical analysis of an elliptic partial differential equation (PDE) designed to compute the geometric thickness of a given shape. The PDE-based formulati…
math.AP2025
PDE methods for extracting normal vector fields and distance functions of shapes
Takahiro Hasebe, Jun Masamune, Hiroshi Teramoto +1
Partial differential equations can be used for extracting geometric features of shapes. This article summarizes recent methods to extract the normal vector field from an elliptic e…
math.AP2024
Mathematical analysis of a partial differential equation system on the thickness
Atsushi Nakayasu, Takayuki Yamada
This study focuses on linear partial differential equation (PDE) systems that arise in topology optimization where the thickness of a structure is constrained. The thickness derive…