Parallel finite difference methods for multiscale material problems

Research output: Contribution to journalConference articlepeer-review


In this paper we discuss a parallel computer implementation of a finite difference method (equivalent to spring-networks) for elliptic-type boundary value problems. The parallelization consists in dividing the material domain into a number of connected subdomains, each of which corresponds to a single processor, and connecting them. The method is illustrated on an example of a functionally graded composite having circular inclusions with graded interphases - a material with many length scales. Rigorous scale-dependent bounds on the effective conductivity of such a composite are calculated from boundary value problems under the essential and natural boundary conditions. It is found that the presence of a narrow graded interphase dramatically changes the effective conductivity from that of a composite with perfect interfaces.

Original languageEnglish (US)
Pages (from-to)71-79
Number of pages9
JournalAmerican Society of Mechanical Engineers, Applied Mechanics Division, AMD
StatePublished - Dec 1 1995
Externally publishedYes
EventProceedings of the 1995 ASME International Mechanical Engineering Congress and Exposition - San Francisco, CA, USA
Duration: Nov 12 1995Nov 17 1995

ASJC Scopus subject areas

  • Mechanical Engineering


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