In this talk I will present some background on the coupling interface conditions with multi-domain problems. These kind of models arise when multiple processes are model together and their interactions in terms of mathematical equations such as PDEs or ODEs or both in coupled. For understanding this procedure I will explain the model related to the calcium interaction in human cell signaling. These signaling of calcium concentration is between  two regions, namely ER and cytosol with a membrane in which the channels are placed. Exactly the same modelscan be apply in heat transfer between two regions, ocean and atmosphere coupling and fluid structure interactions (FSI) problems. In the numerical implementation there are some challenging issues occurs in this process, such as the maintainability of the mass/energy conservation of the overall scheme, stability issues. For better comparison we used three coupling Algorithms namely explicit, implicit monolithic and partitioned iterative coupling approaches. I will also give the comparison of the computational time of these coupling Algorithms. I will also give the detail of my ongoing projects, publications and some future goals.