任意阶次功能适配能量减少方法用于梯度系统
Arbitrary-order functionally fitted energy-diminishing methods for gradient systems
AI总结：
本文提出任意阶次功能适配能量减少方法，用于保持梯度系统的能量单调递减特性，证明其无条件能量减少性和对非常陡梯度系统的阻尼能力，并通过数值测试验证其有效性。
摘要：
众所周知，欧几里得空间或黎曼流形上的梯度系统的能量沿解单调递减。本文推导并分析了功能适配的能量减少方法，以保持梯度系统的这一关键特性。证明了新方法无条件能量减少，并能对非常陡的梯度系统实现阻尼。还展示了这些方法可以达到任意高阶，并讨论了其实现方式。报告了一个数值测试，以说明新方法与文献中三种现有数值方法的效率比较。
英文摘要：
It is well known that for gradient systems in Euclidean space or on a Riemannian manifold, the energy decreases monotonically along solutions. In this letter we derive and analyse functionally fitted energy-diminishing methods to preserve this key property of gradient systems. It is proved that the novel methods are unconditionally energy-diminishing and can achieve damping for very stiff gradient systems. We also show that the methods can be of arbitrarily high order and discuss their implementations. A numerical test is reported to illustrate the efficiency of the new methods in comparison with three existing numerical methods in the literature.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
