Mathematical Foundation of the Boundary Integro-Differential Equation Method
暫譯: 邊界積分微分方程方法的數學基礎

Han, Houde, Yin, Dongsheng

Mathematical Foundation of the Boundary Integro-Differential Equation Method
  • 出版商: Springer
  • 出版日期: 2026-01-14
  • 售價: $7,230
  • 貴賓價: 9.8 折 $7,085
  • 語言: 英文
  • 頁數: 305
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 9819510872
  • ISBN-13: 9789819510870
  • 相關分類: 工程數學 Engineering-mathematics

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商品描述

The book focuses on the mathematical foundations of boundary integro-differential equation method, with a primary focus on reducing the hypersingular integrals in traditional boundary integral equations into boundary integro-differential equations with weak singularities. It briefly introduces the theory of distributions, while the boundary integral equations method is grounded in the fundamental solutions of linear partial differential equations, hence a relatively detailed exposition of the fundamental solutions of differential equations is also provided. In the subsequent chapters, the authors sequentially discuss the boundary integro-differential equation methods and theories for Laplace equation, Helmholtz equation, Navier equations, Stokes equations, among others. Furthermore, the book addresses the boundary integro-differential equation method for certain nonlinear problems, such as thermal radiation, variational inequalities, and Steklov eigenvalue problems. Lastly, it explores the symmetric coupling issues between finite element and boundary element methods.

商品描述(中文翻譯)

本書專注於邊界積分微分方程方法的數學基礎，主要著重於將傳統邊界積分方程中的超奇異積分轉化為具有弱奇異性的邊界積分微分方程。書中簡要介紹了分佈理論，而邊界積分方程方法則基於線性偏微分方程的基本解，因此也提供了相對詳細的偏微分方程基本解的闡述。在隨後的章節中，作者依次討論了拉普拉斯方程、亥姆霍茲方程、納維方程、斯托克斯方程等的邊界積分微分方程方法和理論。此外，本書還探討了某些非線性問題的邊界積分微分方程方法，例如熱輻射、變分不等式和斯特克洛夫特徵值問題。最後，書中探討了有限元素法與邊界元素法之間的對稱耦合問題。

作者簡介

Han Houde is a professor at Tsinghua University who has devoted himself to the teaching and scientific research of computational mathematics. He has achieved significant breakthroughs in the study of numerical solutions of partial differential equations, demonstrating a series of creative research results. In particular, he has made important contributions to the numerical solutions of partial differential equations on unbounded domains and the coupling method of the finite element method and boundary element method. Additionally, he has contributed to the numerical solutions of boundary integral-differential equations and variational inequalities problems, as well as the numerical solutions of singular perturbation problems, ill-posed problems, and infinite element methods.


Yin Dongsheng is an associate professor at Tsinghua University whose research interest is mainly focused on high frequency waves, partial differential equations on unbounded domains, and fractional differential equations.

作者簡介(中文翻譯)

韓厚德是清華大學的教授，專注於計算數學的教學與科學研究。他在偏微分方程數值解的研究中取得了顯著的突破，展現了一系列創新的研究成果。特別是，他對於無界域上偏微分方程的數值解以及有限元素法與邊界元素法的耦合方法做出了重要貢獻。此外，他還對邊界積分-微分方程和變分不等式問題的數值解、奇異擾動問題、病態問題以及無限元素法的數值解做出了貢獻。

尹東生是清華大學的副教授，他的研究興趣主要集中在高頻波、無界域上的偏微分方程以及分數微分方程。

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