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Numerical analysis for the Plateau problem by the method of fundamental solutions
Koya Sakakibara, Yuuki Shimizu
Towards identifying the number of minimal surfaces sharing the same boundary from the geometry of the boundary, we propose a numerical scheme with high speed and high accuracy. Our…
Structure-preserving numerical methods for constrained gradient flows of planar closed curves with explicit tangential velocities
Tomoya Kemmochi, Yuto Miyatake, Koya Sakakibara
In this paper, we consider numerical approximation of constrained gradient flows of planar closed curves, including the Willmore and the Helfrich flows. These equations have energy…
A simple numerical method for Hele-Shaw type problems by the method of fundamental solutions
Koya Sakakibara, Yusaku Shimoji, Shigetoshi Yazaki
Hele-Shaw flows with time-dependent gaps create fingering patterns, and magnetic fluids in Hele-Shaw cells create intriguing patterns.We propose a simple numerical method for Hele-…
A fully discrete curve-shortening polygonal evolution law for moving boundary problems
Koya Sakakibara, Yuto Miyatake
We consider the numerical integration of moving boundary problems with the curve-shortening property, such as the mean curvature flow and Hele-Shaw flow. We propose a fully discret…
Bidirectional numerical conformal mapping based on the dipole simulation method
Koya Sakakibara
Many authors have studied the numerical computation of conformal mappings (numerical conformal mapping), and there are nowadays several efficient numerical schemes. Among them, Ama…