ADI, Elliptic

Don’t just review the notes to answer these questions, literally write the answers down on paper, as if you were taking a quiz.

  • What does the acronym ADI stand for?
  • Describe the essence of the ADI method. What makes it fast? Why do we alternate directions?
  • The ADI method was presented for elliptic problems. Can it also be used for parabolic problems?
  • If we have a 3x3 grid of unknowns, what is the size of the tridiagonal matrix solved with ADI 1, and with ADI 2?
  • Is ADI 1 more matrix-centric or more grid-centric? What about ADI 2?
    • Which do you prefer? (Obviously there is no right answer to this question.)
  • T/F: variations of the methods presented can lag the whole term (for the uncoupled direction), or just the neighbor points but not the center point?
  • What are the differences between the ADI methods presented for elliptic problems and the ADI method of Hoffman?
  • Review the provided ADI algorithm example in detail, so that you understand every line of code.
    • After doing that, a useful exercise would be to code it from scratch yourself.