Title    name
NIMS Workshop and Minicourse :Mathematical Analysis, Numerics and Application in fluid and gas dynamics'
  Speaker Bongsoo Jang
  Date 2009-02-03
  Place KAIST
  File  의 1 번째 Real Media 동영상입니다.   
Abstract : Many branches of science and engineering have adopted multi-sacle materials which consist of alternating volume of compounds with different materials. Composite material is the simple example. Since composite materials have unique qualities of highly strength and stiffness, they have been used to a lot of fields in our life. In the mathematical point of view, it is very challenging to analyze phenomena arising in multi-scale materials because of different scales(microscopic, macroscopic). Conventional computational methods such as FEM and FDM, require a very fine mesh size which is smaller than a microscopic scale size to obtain a meaningful approximate solution. However, it causes to solve a huge algebraic system so that it yields some issues such as memory and CPU time and so on. To overcome the diffculty coming from multi-scale media, analytic treatment leads to homogenization theory which captures the macroscopic behavior of multi-scale structure media by introducing an artificial material property(conductivity, elastic modulus). The homogenization theory is concerned with the analysis of PDEs with highly oscillating coefficients. In this work, we focus on several properties for the effective conductivity and introduce several ways to approximate the effective conductivity. Moreover, we consider the sensitivity of the shape of fiber inclusion in obtaining effective conductivities and discuss numerical results for the various shape of fiber inclusion in homogenized problem.