@Sichao25 you may want to wait until @abhiyan123 indicates if he will merge these changes back to #209 or not to do the review. Once he indicates his preference I'd like to move quickly to get this finalized.

There is still a lot of cleanup that could and maybe should be done to better decouple components. My strategy was to try to at least:

1. move all non-templated functions out of headers
2. factor out complex code that was repeated multiple times

The error handling bits of this are still a mess, but the PR is already big enough as is. We will have to take a pass at resolving the error handling mismatch when we fix the exceptions in the rest of the library. For the petsc errors, we can utilze the macro/exception type I previously implemented for MuMFiM.

It looks like using PkgConfig for the petsc configuration broke the CI build...In my personal builds I've had better luck with the PkgConfig based targets, but we'll need to double check if there is an easy way to fix the CI for this.

The issue with the PkgConfig based petsc installation here is that the Petsc target only seems to behave nicely when petsc is build in shared library mode.

@abhiyan123 all but the one test is running on GPU. We just need to debug that and we should be able to merge.