Abstract <p>The article presents the architecture of the mathematical software of a distributed computing system with open source code for smartphones based on Android OS, united into a common network infrastructure. Building ex-scale systems based on mobile devices is a complex scientific task, since such systems must be potentially infinitely scalable, fault-tolerant, and must allow for a guaranteed scalability assessment when solving a specific problem. The BOINC system is the most well-known infrastructure for personal volunteer computing. However, it also has a number of shortcomings that must be eliminated when building a distributed computing system based on mobile devices with ex-scale-class performance. The proposed architecture allows taking into account the reconfiguration of the network of computing devices and constructing a guaranteed scalability assessment for heterogeneous distributed mobile computing systems. The work focused on the application of the developed computing system to solve problems of the collision of white dwarfs and the explosion of a thermonuclear supernova.</p>