What is the Mental Mechanics of Evolving Faith?
In how many aspects is the Ability of Faith purified?
The Ability of Faith is purified on these three occasions:
1: When one avoids Faithless persons,
2: When one cultivates, visits and respects Faithful persons,
3: When one study & reviews Suttas that inspire confidence.
Then the Faith Ability is purified by these three methods...

Using Faith as an Instrument, Enzyme & Elevator within the:
Way to Stream Entry contained in frequenting good men;
Way to Stream Entry contained in hearing the True Dhamma;
Way to Stream Entry contained in rational attention;
Way to Stream Entry contained in praxis according with Dhamma:
The Faith Ability is found within resolute determined devotion;
The Energy Ability is found within exerted enthusiastic effort;
The Awareness Ability is found within acute attentive presence;
The Concentration Ability is found within focused non-distraction;
The Understanding Ability is found within penetrating seeing.
Through the Faith Ability all the 5 Abilities are thus found among
the 4 factors of stream entry in these mutually enhancing ways.

Evaporating the opposing state: Sceptical Doubt in Enlightenment:
When one ends sceptical doubt, one is expanding the Faith Ability.
When one is enlarging the Faith Ability, one stops sceptical doubt.

Source:
The Canonical: Path of Discrimination: Patisambhidamagga. IV.
http://store.pariyatti.org/Path-of-Discrimination-2nd-Edition_p_2126.html

For fine further Faith (Saddhā)  please see:
https://What-Buddha-Said.net/drops/III/Going_Forth_Faith.htm
https://What-Buddha-Said.net/drops/III/Outstanding_Faith.htm
https://What-Buddha-Said.net/drops/III/Unwavering_Faith.htm
https://What-Buddha-Said.net/drops/III/Analysis_of_Faith.htm
https://What-Buddha-Said.net/drops/III/Power_of_Faith.htm
https://What-Buddha-Said.net/drops/III/Faith_Summary.htm
https://What-Buddha-Said.net/drops/III/Highest_Faith.htm
https://What-Buddha-Said.net/drops/III/Fruitful_Faith.htm
https://What-Buddha-Said.net/drops/III/Leaping_Faith.htm
https://What-Buddha-Said.net/drops/III/Mutual_Faith.htm
https://What-Buddha-Said.net/drops/III/Dual_Faith.htm
https://What-Buddha-Said.net/drops/III/Fine_Faith.htm
https://What-Buddha-Said.net/drops/III/Rich_Faith.htm
https://What-Buddha-Said.net/drops/III/Lay_Faith.htm