Shape-Measure Method for Introducing the Nearly Optimal Domain

Abstract

We deal with introducing a new algorithm for solving the optimal shape problems in which they are defined with respect to a pair of geometrical elements. The problem is to find the optimal domain approximately for a given functional that is involved with the solution of a linear or nonlinear elliptic equation with a boundary condition over a domain. The Shape-Measure method, in Cartesian coordinates will be used to find the nearly optimal solution in two steps. By transferring the problem into a measure-theoretical form, first we will find the solution of the elliptic problem for a given domain by using the embedding method. Then the Shape-Measure method will be applied to find the best domain approximately. An example will be given.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Jul 01, 2001
Accession Number
ADP013709

Entities

People

  • A. Fakharzadeh
  • J. E. Rubio

Organizations

  • University of Leeds

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Boundaries
  • Cartesian Coordinates
  • Coefficients
  • Differential Equations
  • Equations
  • Geometry
  • Linear Systems
  • Mathematics
  • Partial Differential Equations
  • Sequences
  • Simplex Method
  • Technical Information Centers
  • Theorems
  • Topology
  • Vector Spaces

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Operations Research