Variational methods for the numerical solution of nonlinear elliptic problems
Variational methods for the numerical solution of nonlinear elliptic problems
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DOI：
10.1137/1.9781611973785
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发表时间：
2015-11
期刊：
影响因子：
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通讯作者：
R. Glowinski
中科院分区：
文献类型：
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作者：
R. Glowinski
非线性椭圆型问题数值解的变分方法解决了已被证明有效地解决各种非线性椭圆型问题的计算方法。这些方法可以应用于科学和工程中的许多问题，但本书侧重于它们在连续介质力学和物理问题上的应用。这本书在这个主题上与其他书不同，提供了算符分裂方法的能力和多功能性的例子；详细介绍了乘子的交替方向方法及其对解决科学和工程中的非线性(可能不光滑)问题的适用性；并展示了非线性最小二乘方法，与算符分裂和共轭梯度算法相结合，为解决高度非线性问题提供了有效的工具。读者：本书提供了一些有用的见解，适合应用和计算数学领域的高级研究生、教师和研究人员，以及研究工程师、数学物理学家和系统工程师。
Variational Methods for the Numerical Solution of Nonlinear Elliptic Problems addresses computational methods that have proven efficient for the solution of a large variety of nonlinear elliptic problems. These methods can be applied to many problems in science and engineering, but this book focuses on their application to problems in continuum mechanics and physics. This book differs from others on the topic by presenting examples of the power and versatility of operator-splitting methods; providing a detailed introduction to alternating direction methods of multipliers and their applicability to the solution of nonlinear (possibly nonsmooth) problems from science and engineering; and showing that nonlinear least-squares methods, combined with operator-splitting and conjugate gradient algorithms, provide efficient tools for the solution of highly nonlinear problems. Audience: The book provides useful insights suitable for advanced graduate students, faculty, and researchers in applied and computational mathematics as well as research engineers, mathematical physicists, and systems engineers.