Numerical algorithm for determining a coefficient in an elliptic equation Conference Paper uri icon

abstract

  • We consider the question of recovering coefficients such as q or k from the equation - ▽ (k▽uj) + q(x)uj = fj(x) in a domain Ω ⊃ Rn where uj(x) is subject to Dirichlet boundary conditions. The non-homogeneous source terms {fj(x)}j∞=1 form a basis for L2(Ω). We will prove that a unique determination is possible from data measurements consisting of the average flux leaving a fixed subset of the boundary of the region for each input source. The particular application we have in mind is the recovery of interior parameters in heat conduction problems given that we can only make measurements on the boundary, but are able to generate a sequence of internal heat sources. An algorithm that allows efficient numerical reconstruction of the coefficients from finite data will be given.

author list (cited authors)

  • Lowe, B. D., & Rundell, W.

publication date

  • December 1995