An Introduction to Element-Based Galerkin Methods on Tensor-Product Bases: Analysis, Algorithms, and Applications
暫譯: 基於張量積基的元素型Galerkin方法導論：分析、演算法與應用

Giraldo, Francis X.

An Introduction to Element-Based Galerkin Methods on Tensor-Product Bases: Analysis, Algorithms, and Applications
  • 出版商: Springer
  • 出版日期: 2020-10-31
  • 售價: $4,130
  • 貴賓價: 9.5 折 $3,924
  • 語言: 英文
  • 頁數: 559
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 3030550680
  • ISBN-13: 9783030550684
  • 相關分類: Algorithms-data-structures

    • 海外代購書籍(需單獨結帳)

商品描述

This book introduces the reader to solving partial differential equations (PDEs) numerically using element-based Galerkin methods. Although it draws on a solid theoretical foundation (e.g. the theory of interpolation, numerical integration, and function spaces), the book's main focus is on how to build the method, what the resulting matrices look like, and how to write algorithms for coding Galerkin methods. In addition, the spotlight is on tensor-product bases, which means that only line elements (in one dimension), quadrilateral elements (in two dimensions), and cubes (in three dimensions) are considered. The types of Galerkin methods covered are: continuous Galerkin methods (i.e., finite/spectral elements), discontinuous Galerkin methods, and hybridized discontinuous Galerkin methods using both nodal and modal basis functions. In addition, examples are included (which can also serve as student projects) for solving hyperbolic and elliptic partial differential equations, including both scalar PDEs and systems of equations.


商品描述(中文翻譯)

本書介紹讀者如何使用基於元素的 Galerkin 方法數值解決偏微分方程 (PDEs)。雖然本書基於堅實的理論基礎（例如插值理論、數值積分和函數空間），但主要重點在於如何構建該方法、所產生的矩陣樣貌以及如何編寫 Galerkin 方法的演算法。此外，本書特別關注張量積基底，這意味著僅考慮一維的線元素、二維的四邊形元素和三維的立方體。所涵蓋的 Galerkin 方法類型包括：連續 Galerkin 方法（即有限/譜元素）、不連續 Galerkin 方法，以及使用節點和模態基函數的混合不連續 Galerkin 方法。此外，本書還包含解決雙曲型和橢圓型偏微分方程的範例（這些範例也可以作為學生專案），包括標量 PDE 和方程組。

作者簡介

Francis (Frank) Giraldo is a Distinguished Professor of Applied Mathematics at the Naval Postgraduate School and a founding member of the Scientific Computing group. He and his team built the NUMA model using the element-based Galerkin (EBG) methods described in this text; NUMA is a Navier-Stokes solver used for atmospheric, ocean, and fluid dynamics simulations. Frank Giraldo (and colleagues) hosted the 2012 Gene Golub SIAM Summer School on Simulation and Supercomputing in the Geosciences where EBG methods was one of the topics of the summer course. In addition, Frank has served on the National Earth Systems Prediction Capability working groups for over 10 years, and has served on the Department of Energy's INCITE panels for over 5 years (including chairing the committee a number of times).

作者簡介(中文翻譯)

Francis (Frank) Giraldo 是海軍研究生院的應用數學特聘教授，也是科學計算小組的創始成員。他和他的團隊使用本書中描述的基於元素的 Galerkin (EBG) 方法建立了 NUMA 模型；NUMA 是一個用於大氣、海洋和流體動力學模擬的 Navier-Stokes 解算器。Frank Giraldo（及其同事）主辦了 2012 年的 Gene Golub SIAM 夏季學校，主題為地球科學中的模擬與超級計算，其中 EBG 方法是夏季課程的主題之一。此外，Frank 在國家地球系統預測能力工作小組中服務超過 10 年，並在能源部的 INCITE 委員會中服務超過 5 年（包括多次擔任委員會主席）。

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