refactor: splitting up of NonlinearSolve #122

Job	Run time
downgrade (1.10, core)	14m 22s
downgrade (1.10, adjoint)	8m 30s
downgrade (1.10, alloc_check)	8m 28s
test (1.10, ubuntu-latest, core)	14m 28s
test (1.10, ubuntu-latest, adjoint)	8m 30s
test (1.10, ubuntu-latest, alloc_check)	8m 40s
test (1.10, macos-latest, core)	18m 0s
test (1.10, macos-latest, adjoint)	5m 24s
test (1.10, macos-latest, alloc_check)	7m 25s
test (1.10, windows-latest, core)	15m 59s
test (1.10, windows-latest, adjoint)	10m 8s
test (1.10, windows-latest, alloc_check)	10m 9s
test (1, ubuntu-latest, core)	24m 29s
test (1, ubuntu-latest, adjoint)	15m 7s
test (1, ubuntu-latest, alloc_check)	15m 16s
test (1, macos-latest, core)	17m 31s
test (1, macos-latest, adjoint)	11m 34s
test (1, macos-latest, alloc_check)	9m 20s
test (1, windows-latest, core)	27m 0s
test (1, windows-latest, adjoint)	17m 3s
test (1, windows-latest, alloc_check)	16m 8s
	4h 43m 31s

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