refactor: splitting up of NonlinearSolve #80

Job	Run time
test (min, ubuntu-latest, core)	14m 2s
test (min, ubuntu-latest, adjoint)	9m 51s
test (min, ubuntu-latest, alloc_check)	9m 11s
test (min, macos-latest, core)	8m 8s
test (min, macos-latest, adjoint)	5m 54s
test (min, macos-latest, alloc_check)	5m 45s
test (min, windows-latest, core)	16m 27s
test (min, windows-latest, adjoint)	12m 44s
test (min, windows-latest, alloc_check)	10m 29s
test (1, ubuntu-latest, core)	21m 26s
test (1, ubuntu-latest, adjoint)	12m 24s
test (1, ubuntu-latest, alloc_check)	12m 7s
test (1, macos-latest, core)	17m 33s
test (1, macos-latest, adjoint)	7m 53s
test (1, macos-latest, alloc_check)	7m 42s
test (1, windows-latest, core)	22m 41s
test (1, windows-latest, adjoint)	14m 20s
test (1, windows-latest, alloc_check)	13m 41s
	3h 42m 18s

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