🚀 go-pugleaf

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.

Dense matrices alse arise in the capacitance matrix method for solving
the elliptic PDE's that often arise in fluid dynamics problems.
-- 
--
John D. McCalpin                        mccalpin@perelandra.cms.udel.edu
Assistant Professor                     mccalpin@brahms.udel.edu
College of Marine Studies, U. Del.      John.McCalpin@mvs.udel.edu