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The book presents in a systematic way a methodology for the development of parallel multi-physics models and its employment in geophysical and biomedical applications. The methodology includes conservative methods of discretization of PDEs on general meshes, as well as data structures and algorithms for organization of parallel simulations on general meshes. The structures and algorithms form the core of the Integrated Numerical Modeling Object-oriented Supercomputing Technologies (INMOST) platform for the development of parallel models on general meshes. For applications, we consider geophysical and biomedical challenges. The geophysical applications address radioactive contaminant propagation with subsurface waters and reservoir simulation. The biomedical application deals with clot formation in blood flow.