Boundary Element MethodsSpringer Science & Business Media, 01.11.2010 - 561 Seiten This work presents a thorough treatment of boundary element methods (BEM) for solving strongly elliptic boundary integral equations obtained from boundary reduction of elliptic boundary value problems in $\mathbb{R}^3$. The book is self-contained, the prerequisites on elliptic partial differential and integral equations being presented in Chapters 2 and 3. The main focus is on the development, analysis, and implementation of Galerkin boundary element methods, which is one of the most flexible and robust numerical discretization methods for integral equations. For the efficient realization of the Galerkin BEM, it is essential to replace time-consuming steps in the numerical solution process with fast algorithms. In Chapters 5-9 these methods are developed, analyzed, and formulated in an algorithmic way. |
Inhalt
1 | |
Elliptic Differential Equations
| 20 |
Elliptic Boundary Integral Equations
| 101 |
Boundary Element Methods
| 183 |
Generating the Matrix Coefficients
| 288 |
Solution of Linear Systems of Equations
| 353 |
Cluster Methods
| 403 |
pParametric Surface Approximation
| 467 |
A Posteriori Error Estimation
| 517 |
545 | |
555 | |
559 | |
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Häufige Begriffe und Wortgruppen
affine algorithm analytic apply approximation associated assume Assumption Banach space basis boundary integral equations boundary integral operators boundary value problems bounded called cluster coefficients combination compact complexity computed consider consists constant continuous convergence coordinates Corollary defined Definition denotes depends derivative determined differential discretization domain elliptic error estimate estimate example exists expansion extended Find formulation Galerkin given gives global holds implies inequality interpolation introduce iteration kernel function layer potential Lemma linear mapping matrix means method norm Note obtain panels parameter points polynomial positive problem Proof properties Proposition prove quadrature reference regular Remark representation requires respect right-hand side satisfies Sect sesquilinear form smooth Sobolev solution sufficiently surface surface mesh term Theorem tion transformation triangle variational vector yields