refactor: splitting up of NonlinearSolve #121

Job	Run time
test (1.10, ubuntu-latest, core)	54s
test (1.10, ubuntu-latest, adjoint)	47s
test (1.10, ubuntu-latest, alloc_check)	55s
test (1.10, macos-latest, core)	44s
downgrade (1.10, core)	48s
test (1.10, macos-latest, adjoint)	47s
downgrade (1.10, adjoint)	49s
downgrade (1.10, alloc_check)	48s
test (1.10, macos-latest, alloc_check)	57s
test (1.10, windows-latest, core)	45s
test (1.10, windows-latest, adjoint)	48s
test (1.10, windows-latest, alloc_check)	46s
test (1, ubuntu-latest, core)	45s
test (1, ubuntu-latest, adjoint)	46s
test (1, ubuntu-latest, alloc_check)	46s
test (1, macos-latest, core)	1s
test (1, macos-latest, adjoint)	1s
test (1, macos-latest, alloc_check)	1s
test (1, windows-latest, core)	54s
test (1, windows-latest, adjoint)	53s
test (1, windows-latest, alloc_check)	51s
	14m 46s

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