A First Course in Boundary Element Methods

Crouch, Steven L., Mogilevskaya, Sofia G.

A First Course in Boundary Element Methods
  • 出版商: Springer
  • 出版日期: 2024-07-23
  • 售價: $7,130
  • 貴賓價: 9.5 折 $6,774
  • 語言: 英文
  • 頁數: 477
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 3031633407
  • ISBN-13: 9783031633409

    • 海外代購書籍(需單獨結帳)

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商品描述

This textbook delves into the theory and practical application of boundary integral equation techniques, focusing on their numerical solution for boundary value problems within potential theory and linear elasticity. Drawing parallels between single and double layer potentials in potential theory and their counterparts in elasticity, the book introduces various numerical procedures, namely boundary element methods, where unknown quantities reside on the boundaries of the region of interest. Through the approximation of boundary value problems into systems of algebraic equations, solvable by standard numerical methods, the text elucidates both indirect and direct approaches. While indirect methods involve single or double layer potentials separately, yielding physically ambiguous results, direct methods combine potentials using Green's or Somigliana's formulas, providing physically meaningful solutions. Tailored for beginning graduate students, this self-contained textbook offers detailed analytical and numerical derivations for isotropic and anisotropic materials, prioritizing simplicity in presentation while progressively advancing towards more intricate mathematical concepts, particularly focusing on two-dimensional problems within potential theory and linear elasticity.

商品描述(中文翻譯)

這本教科書深入探討邊界積分方程技術的理論和實際應用，專注於在位勢理論和線性彈性中對邊界值問題的數值解。通過將位勢理論中的單層和雙層位勢與彈性中的對應物進行類比，本書介紹了各種數值方法，即邊界元方法，其中未知量存在於感興趣區域的邊界上。通過將邊界值問題的近似轉化為代數方程組，可以通過標準數值方法求解，本書闡明了間接和直接方法。間接方法分別涉及單層或雙層位勢，產生物理上模糊的結果，而直接方法使用格林或索米利亞納公式結合位勢，提供物理上有意義的解。這本自成一體的教科書針對初級研究生，提供了對各向同性和非各向同性材料的詳細分析和數值推導，優先考慮簡潔的呈現方式，並逐步深入探討更複雜的數學概念，特別關注位勢理論和線性彈性中的二維問題。

作者簡介

Steven L. Crouch, Professor Emeritus in the Department of Civil, Environmental, and Geo-Engineering at the University of Minnesota, is a distinguished member of the National Academy of Engineering. Serving as Dean of the College of Science and Engineering from 2005 to 2019, Crouch has made significant contributions to academia and research. His expertise lies in boundary element methods, particularly in the field of geoengineering and composite materials. His research interests focus on the development of boundary integral methods for modeling elastic and viscoelastic materials with inhomogeneities and voids, as well as for transient heat conduction and thermoelasticity in nonhomogeneous materials. His work stands at the forefront of advancing understanding and application in these critical areas of study.

Sofia Mogilevskaya, a distinguished research professor at the University of Minnesota's Department of Civil, Environmental, and Geo-Engineering, earned her Ph.D. from the Scotchinsky Research Institute of Mining, Russian Academy of Sciences, Moscow, in 1987. With expertise in applied mathematics and computational mechanics, she focuses on geomaterials and composite materials. Her work involves developing numerical algorithms for simulating fracture propagation and studying material behavior at both microscopic and macroscopic levels. Her research finds applications in mining, hydraulic fracturing, and material design. Beyond research, she is a dedicated educator, guiding graduate students and fostering their growth.

作者簡介(中文翻譯)

史蒂芬·L·克勞奇（Steven L. Crouch）是明尼蘇達大學土木、環境和地質工程系的名譽教授，也是美國國家工程院的傑出成員。克勞奇曾擔任科學與工程學院院長，任期從2005年到2019年，對學術和研究做出了重要貢獻。他的專業領域是邊界元方法，尤其在地質工程和複合材料領域。他的研究興趣集中在發展邊界積分方法，用於模擬具有非均質性和空洞的彈性和粘彈性材料，以及非均質材料中的瞬態熱傳導和熱彈性。他的工作在這些重要研究領域中處於前沿地位，推動了對這些領域的理解和應用。

索菲亞·莫吉列夫斯卡婭（Sofia Mogilevskaya）是明尼蘇達大學土木、環境和地質工程系的傑出研究教授，於1987年在俄羅斯科學院莫斯科斯基研究所獲得博士學位。她擁有應用數學和計算力學的專業知識，專注於地質材料和複合材料。她的工作涉及開發數值算法，用於模擬斷裂擴展並研究材料在微觀和宏觀層面上的行為。她的研究在礦業、水力壓裂和材料設計等領域有應用。除了研究工作，她還是一位教育家，指導研究生並促進他們的成長。

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