MSU scientists have found a new method to solve complex problems without a supercomputer
Employees of the Department of Computational Mathematics and Cybernetics (CMC) of Moscow State University have proposed a new method for solving nonstationary mathematical problems and demonstrated the possibility of its effective application: https://argoprep.com/blog/k8/go-math-grade-1-vs-argoprep/. As a result, they managed to expand the class of problems that can be solved quickly without using supercomputers on standard workstations or laptops. The research was published in the journal Reports of the Russian Academy of Sciences.
In nature, there are a huge number of processes, for the qualitative description of which it is required to solve difficult multidimensional computational problems. These are spring oscillations, combustion of fuel in an engine, diffusion and transport of matter in the atmosphere, as well as the description of blood coagulation during platelet adhesion, the study of the dynamics of toxic particles in the air, etc. As a rule, they can be solved using supercomputers, but MSU scientists managed to find a new approach to their solution – without using supercomputers, on standard workstations or laptops.
“Since the growth of particles is possible from the smallest components, the mathematical description of their growth process requires numerically solving a huge number of equations, which is difficult to do even on supercomputers,” explained Alexander Smirnov, associate professor at the Department of Scientific Research Automation, Faculty of Mathematics and Cybernetics.
In theory, the new methodology of MSU scientists is suitable for solving very different problems, including https://argoprep.com/blog/k8/go-math-grade-2-vs-argoprep/ but it was decided to demonstrate its effectiveness on the specific example of the equations describing the growth of particles during their collisions, known as the Smoluchowski equations. They are used to describe a variety of natural phenomena and technological processes (from micro to macro scales). These include the description of blood clotting and the study of the content of toxic substances. A detailed description of the phenomena in question usually requires the use of very many equations, so finding solutions requires intensive and time-consuming calculations. The use of a special simplified structure with the help of the solution dimensionality reduction technique makes it possible to significantly speed up the calculations without losing the quality of the predictions.