4 papers
Mathematical and numerical study of symmetry and positivity of the tensor-valued spring constant defined from P1-FEM for two- and three-dimensional linear elasticity
Oussama Ounissi, Masato Kimura, Hirofumi Notsu
In this study, we consider a spring-block system that approximates a -dimensional linear elastic body, where or . We derive a matrix as the spring constan…
Universal approximation property of ODENet and ResNet with a single activation function
Masato Kimura, Kazunori Matsui, Yosuke Mizuno
We study a universal approximation property of ODENet and ResNet. The ODENet is a map from an initial value to the final value of an ODE system in a finite interval. It is consider…
On the well-posedness of a Hele-Shaw-like system resulting from an inverse geometry problem formulated through a shape optimization setting
Julius Fergy Tiongson Rabago, Masato Kimura
The purpose of this study is twofold. First, we revisit a shape optimization reformulation of a prototypical shape inverse problem and briefly propose a simple yet efficient numeri…
Second order numerical scheme for motion of polygonal curves with constant area speed
M. Benes, M. Kimura, S. Yazaki
We study polygonal analogues of several moving boundary problems and their time discretization which preserves the constant area speed property. We establish various polygonal anal…