Process
If a general methodology is possible it is described here. In general first we make an appointment to discuss the problem where we can contribute to the solution. A first quick iteration/trade-off of the design/analysis is made and presented to the customer to check if the assumptions are correct and the solution is considered acceptable by the customer. Then this concept design/analysis is worked out in more detail and presented to the customer. But of course we can adjust to working within a team on location, concurrent engineering, etc. if needed.
Intake
We discuss the problem, hardware, requirements, work methodology, time, money, software, deliverables, deadlines and see if this fits in the agenda of both parties
Preliminary
A preliminary design based on the requirements, trade-off is made and/or analysed and the first iteration results are reported asap.
Check assumptions
The preliminary design/analysis is discussed with the client to assess the solution is acceptable to him and fits all constraints. For larger project this part will take more progress meetings
final
If the constraints are clear the design/analysis is detailed and reported in a format agreed with the client.