refactor: splitting up of NonlinearSolve #113

Job	Run time
test (1.10, ubuntu-latest, core)	48s
test (1.10, ubuntu-latest, adjoint)	47s
test (1.10, ubuntu-latest, alloc_check)	47s
test (1.10, macos-latest, core)	1s
test (1.10, macos-latest, adjoint)	1s
test (1.10, macos-latest, alloc_check)	1s
test (1.10, windows-latest, core)	38s
test (1.10, windows-latest, adjoint)	37s
test (1.10, windows-latest, alloc_check)	40s
test (1, ubuntu-latest, core)	39s
test (1, ubuntu-latest, adjoint)	40s
test (1, ubuntu-latest, alloc_check)	39s
test (1, macos-latest, core)	1s
test (1, macos-latest, adjoint)	1s
test (1, macos-latest, alloc_check)	1s
test (1, windows-latest, core)	36s
test (1, windows-latest, adjoint)	39s
test (1, windows-latest, alloc_check)	43s
	8m 19s

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