Laplace-transform analytic-element method for transient porous-media flow

Kristopher L. Kuhlman, Shlomo P. Neuman

Research output: Contribution to journalArticlepeer-review

19 Scopus citations


A unified theory of the Laplace-transform analytic-element method (LT-AEM) for solving transient porous-media flow problems is presented. LT-AEM applies the analytic-element method (AEM) to the modified Helmholtz equation, the Laplace-transformed diffusion equation. LT-AEM uses superposition and boundary collocation with Laplace-space convolution to compute flexible semi-analytic solutions from a small collection of fundamental elements. The elements discussed are derived using eigenfunction expansions of element shapes in their natural coordinates. A new formulation for a constant-strength line source is presented in terms of elliptical coordinates and complex-parameter Mathieu functions. Examples are given illustrating how leaky and damped-wave hydrologic problems can be solved with little modification using existing LT-AEM techniques.

Original languageEnglish (US)
Pages (from-to)113-130
Number of pages18
JournalJournal of Engineering Mathematics
Issue number2
StatePublished - 2009


  • Analytic element
  • Diffusion equation
  • Elliptical coordinates
  • Laplace transform
  • Mathieu functions
  • Modified Helmholtz equation
  • Transient line source

ASJC Scopus subject areas

  • General Mathematics
  • General Engineering


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