Green's Kernels and Meso-Scale Approximations in Perforated Domains

There are a wide range of applications in physics and structural mechanics involving domains with singular perturbations of the boundary. Examples include perforated domains and bodies with defects of different types. The accurate direct numerical treatment of such problems remains a challenge. Asym...

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Bibliographic Details
Main Authors: Maz'ya, Vladimir, Movchan, Alexander (Author), Nieves, Michael (Author)
Format: eBook
Published: Cham Springer International Publishing 2013, 2013
Edition:1st ed. 2013
Series:Lecture Notes in Mathematics
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
Table of Contents:
  • Part I: Green’s functions in singularly perturbed domains: Uniform asymptotic formulae for Green’s functions for the Laplacian in domains with small perforations
  • Mixed and Neumann boundary conditions for domains with small holes and inclusions. Uniform asymptotics of Green’s kernels
  • Green’s function for the Dirichlet boundary value problem in a domain with several inclusions
  • Numerical simulations based on the asymptotic approximations
  • Other examples of asymptotic approximations of Green’s functions in singularly perturbed domains
  • Part II: Green’s tensors for vector elasticity in bodies with small defects: Green’s tensor for the Dirichlet boundary value problem in a domain with a single inclusion
  • Green’s tensor in bodies with multiple rigid inclusions
  • Green’s tensor for the mixed boundary value problem in a domain with a small hole
  • Part III Meso-scale approximations. Asymptotic treatment of perforated domains without homogenization: Meso-scale approximations for solutions of Dirichlet problems
  • Mixed boundary value problems in multiply-perforated domains