The work toward achieving the Laboratory’s objectives is organized in a number of Research Components (RC). These include (1) mathematical analysis and development of new conceptual tools, and advanced discretizations and algorithms, applicable to a wide range of multiscale problems (RC1, RC2, RC3), implementation of the developed algorithms in an integrated software toolbox enabling fast solution of various multiscale problems (RC4), and application-specific research components (RC5, RC6, RC7). Mathematicians from several subdisciplines, along with PhD students, will be assigned to each project. Intensive interdisciplinary cooperation with other NEFU researchers is planned, along with extensive cooperation with partner researchers from beyond Russia in Australia, Germany, Hong Kong, UK, and USA and their institutions. Below, we list the seven research components of the laboratory. We will consider other components as needs arise.

RC1. Local multiscale model reduction concepts

RC2. Analysis and advanced discretizations

RC3. Decoupling techniques for multiphysics problems

RC4. Developing HP integrated software toolbox for adaptive multiscale model reduction

RC5. Flow and mechanics in fracture networks

R6. Li-ion battery

RC7. Heat and mass transfer problems in the permafrost.