My background is mainly engineering and applied research and I have been a developer or some CFD software, but mostly at high level without worrying about linear solvers and the like. This has been changing lately, has we have been wishing to integrate PETSc without our own software instead of using our own in-house sparse libraries (for reason that I believe are evident. There is no way our small lab can develop a better library of linear solver than PETSc or Trillinos).
However, coming from an engineering background, I find I totally lack knowledge on iterative linear solvers (Krylov subspace, multigrid, etc.). Would there be a reference ( a book preferably, I am still oldschool) that would cover this type of material in a way that would be readable without undergraduate or graduate studies in math, but coming from a more engineering background?
On a relevant note, I have seen that there are many tutorials regarding PETSc on their homepage (http://www.mcs.anl.gov/petsc/documentation/tutorials/HandsOnExercise.html), but I fear I am struggling to find a starting point to learn this type of library or even install it on my local linux distribution correctly. What would be the best starting document for a)installation (and making sure its ok with MPI) and b) learning steps by steps?