Structure preserving methods based on finite difference methods with unstructured Voronoi meshes

基于非结构化 Voronoi 网格有限差分法的结构保持方法

• 批准号: 23656070
• 负责人: FURIHATA Daisuke
• 金额: $ 2.33万
• 依托单位: Osaka University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Challenging Exploratory Research
• 财政年份: 2011
• 资助国家: 日本
• 起止时间: 2011 至 2013
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-23656070/
• 关键词: 数値解析; 偏微分方程式; 非構造メッシュ; 構造保存数値解法; 離散変分導関数法; ボロノイ格子; 構造保存解法; Voronoi 格子; 局所保存則; 大域保存則

We have evaluated some mathematical features of finite difference operators with various error orders based on some Voronoi meshes in bounded domains and have studied error evaluations of them on nonsymmetric meshes. We also applied our methods to concrete partial differential equations, such as the Cahn-Hilliard equation, and obtained results that confirm our estimations. To decrease computation cost for those compromised numerical schemes, moreover, we have developed fast schemes based on predictor-corrector method with relaxed discrete variational derivative method and this attempt was a quite success.We have also attended and given talks on some international conferences in this three years, for example, we gave a invited talk at the SciCADE 2011.

本文在有界区域上的某些Voronoi网格上讨论了具有不同误差阶的有限差分算子的数学性质，并在非对称网格上研究了它们的误差估计。我们还将我们的方法应用于具体的偏微分方程，如Cahn-Hilliard方程，并得到了证实我们的估计的结果。为了减少这些折衷格式的计算量，我们还开发了基于预估-校正方法和松弛离散变分导数方法的快速格式，并取得了很大的成功。

项目成果

Predictor corrector algorithm with the discrete variational derivative method

采用离散变分导数法的预测校正算法

• 发表时间: 2013
• 作者: 木村俊之，高橋大輔;Tetsuya Ishiwata;D.Takahashi;Daisuke Furihata;中谷友洋，高橋大輔;Daisuke Furihata
• 通讯作者: Daisuke Furihata

Conservative finite difference schemes for the modified Camassa-Holm equation

• DOI: 10.14495/jsiaml.3.37
• 发表时间: 2011
• 期刊: JSIAM Lett.
• 作者: Y. Miyatake;Takayasu Matsuo;Daisuke Furihata

Weakly nonlinear structure preserving schemes for strongly nonlinear partial differential equations

强非线性偏微分方程的弱非线性结构保持方案

• 发表时间: 2012
• 作者: Daisuke Furihata;Takayasu Matsuo
• 通讯作者: Takayasu Matsuo

An iteration method for the numerical solution of the discrete variational derivative schemes

离散变分导数格式数值求解的迭代方法

• 发表时间: 2014
• 作者: Mariko Akutsu;Yasuhiro Oikawa;Yoshio Yamasaki;Daisuke Furihata
• 通讯作者: Daisuke Furihata

A new technique to design numerical schemes with weak nonlinearity based on discrete variational derivative method

基于离散变分导数法的弱非线性数值格式设计新技术

• 发表时间: 2012
• 作者: 小坂勇人;矢田部浩平;及川靖広;山崎芳男;Daisuke Furihata
• 通讯作者: Daisuke Furihata