refactor: splitting up of NonlinearSolve #127

Job	Run time
test (1.10, ubuntu-latest, core)	12m 30s
downgrade (1.10, core)	12m 44s
test (1.10, ubuntu-latest, adjoint)	8m 27s
downgrade (1.10, adjoint)	8m 20s
test (1.10, ubuntu-latest, alloc_check)	8m 32s
downgrade (1.10, alloc_check)	8m 24s
test (1.10, macos-latest, core)	12m 40s
test (1.10, macos-latest, adjoint)	5m 12s
test (1.10, macos-latest, alloc_check)	5m 52s
test (1.10, windows-latest, core)	14m 29s
test (1.10, windows-latest, adjoint)	11m 21s
test (1.10, windows-latest, alloc_check)	11m 16s
test (1, ubuntu-latest, core)	22m 10s
test (1, ubuntu-latest, adjoint)	16m 34s
test (1, ubuntu-latest, alloc_check)	14m 38s
test (1, macos-latest, core)	17m 31s
test (1, macos-latest, adjoint)	11m 34s
test (1, macos-latest, alloc_check)	10m 18s
test (1, windows-latest, core)	22m 41s
test (1, windows-latest, adjoint)	16m 53s
test (1, windows-latest, alloc_check)	17m 9s
	4h 29m 15s

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