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A first course in boundary element methods

Record Type:	Language materials, printed : Monograph/item
Title/Author:	A first course in boundary element methods/ by Steven L. Crouch, Sofia G. Mogilevskaya.
Author:	Crouch, Steven L.
other author:	Mogilevskaya, Sofia G.
Published:	Cham :Springer Nature Switzerland : : 2024.,
Description:	xiv, 477 p. :ill., digital ; : 24 cm.;
Contained By:	Springer Nature eBook
Subject:	Boundary element methods. -
Online resource:	https://doi.org/10.1007/978-3-031-63341-6
ISBN:	9783031633416

A first course in boundary element methods
Crouch, Steven L.

A first course in boundary element methods[electronic resource] /by Steven L. Crouch, Sofia G. Mogilevskaya. - Cham :Springer Nature Switzerland :2024. - xiv, 477 p. :ill., digital ;24 cm. - Mathematical engineering,2192-4740. - Mathematical engineering..

1. An Illustration of the Boundary Element Approach -- 2. Potential Theory -- 3. The Direct Boundary Integral Method for Laplace's Equation -- 4. Elasticity -- 5. The Stress Discontinuity Method.

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.

ISBN: 9783031633416

Standard No.: 10.1007/978-3-031-63341-6doiSubjects--Topical Terms:

558051
Boundary element methods.

LC Class. No.: TA347.B69

Dewey Class. No.: 620.00151535

A first course in boundary element methods
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505 0 $a 1. An Illustration of the Boundary Element Approach -- 2. Potential Theory -- 3. The Direct Boundary Integral Method for Laplace's Equation -- 4. Elasticity -- 5. The Stress Discontinuity Method.
520 $a 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.
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