6 papers
On a singular limit of the Kobayashi--Warren--Carter energy
Yoshikazu Giga, Jun Okamoto, Koya Sakakibara +1
By introducing a new topology, a representation formula of the Gamma limit of the Kobayashi-Warren-Carter energy is given in a multi-dimensional domain. A key step is to study the…
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-…
Asymptotic behavior of fronts and pulses of the bidomain model
Hiroshi Matano, Yoichiro Mori, Mitsunori Nara +1
The bidomain model is the standard model for cardiac electrophysiology. In this paper, we investigate the instability and asymptotic behavior of planar fronts and planar pulses of…
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…
A new numerical scheme for constrained total variation flows and its convergence
Yoshikazu Giga, Koya Sakakibara, Kazutoshi Taguchi +1
In this paper, we propose a new numerical scheme for a spatially discrete model of constrained total variation flows, which are total variation flows whose values are constrained i…