Mathematical Sciences: Numerical Methods for Nonlinear Variational Problems

数学科学：非线性变分问题的数值方法

• 批准号: 8902018
• 负责人: Alexander Eydeland
• 金额: $ 5.2万
• 依托单位: University of Massachusetts Amherst
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-07-01 至 1991-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8902018&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Numerical; Methods; Nonlinear

This research is concerned with the development and implementation of general and efficient numerical algorithms for solving a wide range of nonlinear variational problems as well as nonlinear eigenvalue problems. Two complementary principles are utilized for creating new computational solvers. They are the method of transformation of the objective functional and the use of matching numerical techniques for solving the resulting problem. Methods developed will be used in a number of applications which include solving two and three dimensional free boundary problems in magnetohydrodynamics, finding new solutions for problems in the theory of solitary waves in fluids, and developing new numerical techniques for evolution problems with a large number of conservation laws.

这项研究致力于开发和实现通用和高效的数值算法来解决广泛的非线性变分问题和非线性特征值问题。利用两个互补的原则来创建新的计算求解器。它们是目标泛函的变换方法和使用匹配的数值技术来解决由此产生的问题。所开发的方法将被用于许多应用，包括解决磁流体力学中的二维和三维自由边界问题，为流体中的孤立波理论问题寻找新的解，以及为具有大量守恒律的演化问题开发新的数值技术。