How to apply to do a masters thesis in the US or Canada when departments don't post specific positions? I am enrolled in a Master's program (Computational Science and Engineering) in Germany and currently I am looking for a Master's Thesis abroad, preferably in the US or in Canada.
Unfortunately, I am not sure how to apply for a thesis and to be honest I am walking around in a vicious circle.

What I've done so far:
My first step was to visit the international office at our university. The lady there told me that I should have a look at some university/institute websites, look for specific research areas/topics of my interest and write application letters to the respective persons.

Additionally, I went to one of my professors who gave me a list of people that he has worked with in the past and which probably might have interesting topics available. However, after carefully working through the list and writing down what looked interesting to me he told me that there's a 99% chance that my application will be ignored or denied if I don't explicitly describe what work I want to do. So actually his attempt to help was not of much use to me.

My main concern is: How can I know what I want to do if I don't know what is being offered? Most departments do not explicitly offer positions, in particular I haven't found a single offer for a master thesis at US/Canada department sites.  

My area of interests involves fields such as the numerical treatment of partial differential equations (e.g. finite elements, solvers for hyperbolic problems...), numerical linear algebra, etc.
However, if there is no disclosure of potential necessities for a master student I don't see a chance to describe my interests more specific than that. On the other hand, I am afraid that my applications will be interpreted as "bulk letters" if I just write down everything that I would like to work with.

I also thought of reading through some publications/papers of the respective persons, which would be very time consuming. But regarding the fact that I can have at most a slight insight into the respective topics and that I don't even know if there is any need for further work at a master student's level I don't think it is reasonable to spend too much time with that without a gleam of any success.

I would appreciate if someone could help me with some hints on how to come across that. It would be even better if someone who faced the same situation and succeeded could share her/his approach.
Master's have a different meaning in North-America than in Germany. While the Master's thesis typically closes the university studies in Germany, it is considered 'graduate studies' in North America (the Bachelor is considered the 'university degree' and the majority of students join the workforce with it). Masters are either specializations or given to graduate students who wish or have to stop graduate school before completing a PhD. That is the reason why you didn't find any offers for 'Master's theses' on institution websites there.

You approach of asking a local faculty for contacts is probably your best shot, don't give up. Narrow down to a few options and write them an email, explaining your skills, interests and field of study. Ask if they can think of a possible project for you. In your inquiries explain the requirements for a foreign Master thesis host at your university. Stress out the fact that you are merely asking for the right to use the local facilities and a co-supervision of your work. In my case, a professor told me about a project he had in mind, and I expanded it in a short proposal that was accepted by the local faculty and my program. 

North-American professors have to worry about funding for their local Master students. You have to make clear that you want to be a visiting student and thus you will most likely be able to waive tuition fees (with some exceptions, like MIT). Along that line, explain that like Masters students in Germany, you will pay for your ramen noodles yourself and don't necessarily need a stipend if it can't be provided (on that note, Canada and the USA require that you prove you have sufficient means to support yourself while on their territory, so start a piggy bank).

With this in mind, there are few reasons for a group leader abroad not to consider your project, since you might contribute to their research while not costing anything. These few reasons include: too much supervision burden already.