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In article <C0pKup.vJ@news.udel.edu> mccalpin@perelandra.cms.udel.edu (John D. McCalpin) writes:

   In article <EIJKHOUT.93Jan11153758@cupid.cs.utk.edu> eijkhout@cupid.cs.utk.edu (Victor Eijkhout) writes:
   >In article <C0p5JD.M0L@news.udel.edu> mccalpin@perelandra.cms.udel.edu (John D. McCalpin) writes:
   >
   >  In article <1993Jan8.201645.14915@news.eng.convex.com> dodson@convex.COM (Dave Dodson) writes:
   >  >I'd like to point out that it is almost never required or desirable to
   >  >compute the inverse of a matrix.
   >
   >  The direct use of the inverse matrix is generally the fastest way to
   >  solve a dense system of equations with multiple, consecutive right-hand-sides
   >  (as in a time-dependent fluid dynamics problem).
   >
   >Where do dense systems come from in fluid dynamics? Usually
   >differential equations (partial or otherwise) give sparse
   >matrices, and then calculating the inverse is at least a major
   >waste of space.

   The matrices are dense for spectral integration or differentiation
   using any basis functions except trig functions.   The last time I
   checked, this was still the fastest way to solve separable Poisson-like
   equations using Chebyshev discretization, for example.

But only on domains that are a Cartesian product of intervals, right?
Or can you handle separable equations on arbitrarily shaped domains
(Chessapeake bay?) this way?

   Dense matrices alse arise in the capacitance matrix method for solving
   the elliptic PDE's that often arise in fluid dynamics problems.

Isn't that after eliminating most of a *sparse* matrix onto
some subset of the variables (corresponding to an interior line
in the domain) so that there is an outer problem that is sparse?

   John D. McCalpin
--
Victor Eijkhout ................................ `There are also a few bugs,
Department of Computer Science .......... though not as many as I've come to
University of Tennessee ............... expect in new [MS]Windows products.'
Knoxville TN 37919 ................................ (from a software review)