O/T: Patenting a computational scheme?

I have come up with a computational scheme for structural analysis
which I believe is novel. I have spoken to one of my professors about
it and they agree that some concepts in it are unique. However, they
have suggested that I research the literature more for similar schemes.

Can a *scheme* for computing something be granted Intellectual Property
protection?
E.g. hypothetically speaking, could the inventor of Finite Elements
have patented his work and gotten royalties for every subsequent code
that used his ideas? What about the inventors of CFD & SPH?

How are IP rights enforced? Without a decompiler, it is not possible to
know for certain if a compiled binary breaches someone's IP rights.

Is there a patent search database for computational schemes (I'm
assuming it is protectable!)? It would save time rather than trawling
through lots of disparate fields whilst juggling my research.

Thanks.

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