Development of self-adaptive moving mesh methods for numerical computations of phenomena with large deformation based on the theory of integrable systems
| Project/Area Number |
15K04909
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Research Field |
Basic analysis
|
|---|
| Research Institution | Waseda University |
|---|
Principal Investigator |
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
太田 泰広 神戸大学, 理学研究科, 教授 (10213745)
高橋 大輔 早稲田大学, 理工学術院, 教授 (50188025)
|
|---|
| Project Period (FY) |
2015-04-01 – 2018-03-31
|
| Project Status |
Completed (Fiscal Year 2017)
|
| Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2017: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2015: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
|
|---|
| Keywords | 自己適合移動格子スキーム / 非線形波動 / 可積分離散化 / 構造保存型差分スキーム / 離散微分幾何学 / 可積分系 / パフィアン / 構造保存型離散化 |
|---|
| Outline of Final Research Achievements |
We developed the theory of integrable discretization of nonlinear wave equations and self-adaptive moving mesh schemes. We constructed discrete analogues of coupled short pulse equation, coupled Yajima-Oikawa system, reduced Ostrovsky equation, modified short pulse equation, Degasperis-Procesi equation based on the theory of integrable systems. We also studied accuracy of numerical computations of our self-adaptive moving mesh scheme of the modified short pulse equation which has cusped soliton solutions. We also studied numerical schemes of a mathematical model of one-dimensional soil water infiltration using self-adaptive moving mesh schemes and we verified its numerical accuracy. We also investigated the relationship between self-adaptive moving mesh schemes and discrete differential geometry.
|
Report
(4 results)
Research Products
(25 results)
