The New Modification of the Approximating Functions Method for Cloud Computing

Abstract

The approach for building cloud-ready fault-tolerant calculations by approximating functions method, which is an analytical-numerical part of Volterra integral equation method for solving 1D+T nonlinear electromagnetic problems, is presented. The solving process of the original algorithm of the method is modified: it is broken down into the sequential chain of stages with a fixed number of sequential or parallel steps, each of which is built in a fault-tolerant manner and saves execution results in fault-tolerant storage for high availability. This economizes RAM and other computer resources and does not damage the calculated results in the case of a failure, and allows stopping and starting the calculations easily after manual or accidental shutdown. Also, the proposed algorithm has self-healing and data deduplication for cases of corrupted saved results. The presented approach is universal and does not depend on the type of medium or the initial signal. Also, it does not violate the natural description of non-stationary and nonlinear features, the unified definition of the inner and outer problems, as well as the inclusion of the initial and boundary conditions in the same equation as the original approximating functions method. The developed approach stress-tested on the known problems, stability checked and errors compared.