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

• Main Authors: Maz'ya, Vladimir. (Author), Movchan, Alexander. (Author), Nieves, Michael. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: Heidelberg : Springer International Publishing : Imprint: Springer, 2013.
• Series: Lecture Notes in Mathematics, 2077
• Subjects: Mathematics.; Differential equations, partial.; Partial Differential Equations.; Approximations and Expansions.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-3-319-00357-3

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...

Table of Contents:

• Part I: Greens functions in singularly perturbed domains: Uniform asymptotic formulae for Greens functions for the Laplacian in domains with small perforations
• Mixed and Neumann boundary conditions for domains with small holes and inclusions. Uniform asymptotics of Greens kernels
• Greens 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 Greens functions in singularly perturbed domains
• Part II: Greens tensors for vector elasticity in bodies with small defects: Greens tensor for the Dirichlet boundary value problem in a domain with a single inclusion
• Greens tensor in bodies with multiple rigid inclusions
• Greens 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.