A parallel time-Schwarz domain decomposition method applied to an Euler-Bernoulli beam equation with constant coefficients

Abstract

In this work, we have developed and studied an algorithm based on a non-overlapping time Schwarz domain decomposition method applied to an Euler-Bernoulli beam equation with constant coefficients. We transformed our problem into a boundary value problem (BVP), and we applied a non-overlapping time Schwarz domain decomposition (T-SDDM). This approach allows us to break the computational sequentiality, which is a characteristic of most numerical methods for the resolution of non-stationary partial differential equations (PDEs), and it can be parallelized in a multi-processor or multi-core machine. We have studied the convergence of the proposed algorithm in the discrete case by using a finite difference scheme. Several numerical tests are achieved, which shows that T-SDDM preserves the properties of the numerical scheme and illustrates the theoretical result of the convergence. The numerical tests also show the efficiency and the good accuracy of the proposed algorithm T-SDDM in terms of the CPU time.