There is a way to avoid discussions that always end up in shouting to each other with no solutions found. Discuss problems in a public place. If you and your partner are prone to shouting at each other during arguments, try going to a public place to discuss problem topics.
Got to a library, a coffee shop, or the mall to talk through the issue. The knowledge that you may cause a scene if you yell at each other should help you to keep your voices down and have a more civil conversation.