Chapters 2 and 3 (more minor comments)

[Constantine Khrulev]

I used revision 58a575b.

• tex/linearsystem.tex:152

  Thus if $Ax=b$ for some $x$ then row $i$ of $A$ is on the rank $m$ processor if and if entry $i$ of $b$ is on the rank $m$ processor.

  Should this be "if and only if"?

• tex/linearsystem.tex:558

  Our $A$ is allocated as dense so the exact LU factorization requires no fill-in.

  Define fill-in or provide a reference.

• tex/linearsystem.tex:691

  to time some bigger solves

  Consider saying "some bigger systems". "Solve" is rarely a noun.

• tex/linearsystem.tex:706

  We can try a direct solve

  Should probably say "a direct solver".

• tex/linearsystem.tex:758

  X11 windows are installed.

  Consider saying "if PETSc was built with the X Window System support" (see https://en.wikipedia.org/wiki/X_Window_System).

• tex/linearsystem.tex:794

  For any nontrivial preconditioner, even one based on diagonal blocks of a tridiagonal matrix as here, different sets of rows ``communicate'' at the preconditioning stage depending on the processor count.

  This sentence should probably be re-phrased. (I can't parse it.)

• tex/linearsystem.tex:798

  significant spectral effect.

  Hmm. There must be a better way to say this.

• tex/structured.tex:36

  $c\rho \partial u/\partial t = - \Div\bq + f$

  Add \, (c\rho\, \partial...) to get better spacing.

• tex/structured.tex:243

  i.e.~pass-by-reference

  I.e. via an output argument.

• tex/structured.tex:42

  in the next Chapter we apply a finite element approach

  Reference the chapter. (It's not the next one currently.)

• tex/structured.tex:547

  and we explicitly ask for the \pVec objects to be assembled by calling \texttt{VecAssemblyBegin/End()}

  There is no need to do this if you access Vecs using DMDAVecGetArray() and DMDAVecRestoreArray().

  When VecSetValues() is used, VecAssemblyBegin/End() is needed, though.