Search

The dynamic failure process of structures under extreme loadings is very common in many fields of engineering and science. The smoothed particle hydrodynamics (SPH) method offers inherent benefits in dealing with complex interfaces and large material deformations in extreme mechanics problems. However, SPH simulations for 3D engineering applications are time-consuming. To address this issue, we introduce MPI (Message Passing Interface) in our SPH scheme to reduce computational time. Some optimizations are adopted to ensure the massive computation of the SPH method. In particular, an optimized memory management strategy is developed to control the memory footprint. With the present MPI-based massive parallelization of the SPH method, several validation examples are tested and analyzed. By comparing the present numerical results with the reference data, the dynamic failure process of complex structures subjected to extreme loadings like explosive and impact loadings can be well captured. A large number of particles, up to 2.04 billion, are adopted in the present simulations. The scaling tests show that the scalability of the massively parallel SPH program achieves a maximum parallel efficiency of 97% on 10020 CPU cores. • A massively parallel SPH computing framework is proposed for extreme mechanics problems. • An optimized memory management strategy is developed to reduce memory footprint and achieve better scalability. • A non-blocking MPI point-to-point communications scheme with parallel IO is implemented for large-scale SPH simulations. • A series of numerical examples demonstrate the scalability and accuracy of the present parallel SPH framework. [ABSTRACT FROM AUTHOR]

• A hybrid computational scheme is developed assisted by spectral and finite difference methods. • Some novel operational matrices have been computed via shifted Gegenbauer polynomials. • Validation is being made through convergence and error-bound analysis. • Numerical simulations are performed for fractional time-dependent one, two, and three-dimensional Burger's equations. • Comparative analysis is presented to show the efficiency and reliability of the proposed scheme. • Method found a useful for nonlinear problems arising in Mechanics and engineering sciences. In this work, an innovative computational scheme is developed to compute stable solutions of time-fractional coupled viscous Burger's equation in multi-dimensions. To discretize the problem, the temporal derivative is approximated through a forward difference scheme whereas the spatial derivatives are approximated assisted by novel operational matrices that have been constructed via shifted Gegenbauer wavelets (SGWs). The piecewise functions are utilized to construct the operational matrices of multi-dimensional SGWs vectors although related theorems are offered to authenticate the scheme mathematically. The proposed computational algorithm converts the model understudy to a system of linear algebraic equations that are easier to tackle. To validate the accuracy, credibility, and reliability of the present method, the time-fractional viscous Burger's models are considered in one, two, and three dimensions. An inclusive comparative study is reported which demonstrates that the proposed computational scheme is effective, accurate, and well-matched to find the numerical solutions of the aforementioned problems. Convergence, error bound, and stability of the suggested method is investigated theoretically and numerically. [ABSTRACT FROM AUTHOR]