I was looking for a classification of algorithms used in Computational Science and Engineering for Stillwater's trifecta. In all classification problems, selecting the right attributes is key. I was on the wrong path since I was trying to use a classification based on solver algorithm structure and that caused significant problems since it appears to cause a decoupling of the physical intuition of the original problems. So I started to look for others who have attempted to construct a structure for CSE: and I found it in a familiar place. Gilbert Strang just published a new book called "Computational Science and Engineering" where he brings together the intuitive with the numerical math.
I am a big Gilbert Strang fan since his Linear Algebra book was one of the few that made sense in college. I like his prose and I like the attention to detail in describing the associated truths surrounding a solution scheme. The publisher is Wellesley Cambridge Press (http://www.wellesleycambridge.com/) and the CSE book has its own website (http://www-math.mit.edu/cse/). For anybody trying to make sense of CSE this book should be on your shelf.
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