Efficient strategy for space-time based finite element analysis of vibrating structures

This paper presents an efficient parallel computing strategy to solve large-scale structural vibration problems. The proposed approach utilises a novel direct method that operates using simplex-shaped space-time finite elements and allows for the direct decoupling of variables during the assembly of global matrices. The method uses consistent stiffness, inertia and damping matrices and deals with non-symmetric matrices. One significant advantage of this approach is that the computational cost remains unaffected by the bandwidth of the matrix in the traditional sense because only non-zero coefficients are retained. The speed of computations demonstrates a noticeable increase as the number of nodes and the problem's dimensionality grow. To demonstrate the effectiveness of the parallel space-time approach, a comparison with a sequentially executed code was conducted. The results indicate that the proposed method enables calculations at least 20 times faster than those achieved using the classical finite element method. Furthermore, the parallelisation algorithm was successfully implemented to solve a dynamics problem involving a large-scale, three-dimensional railway structure subjected to a moving load. Remarkably, the problem was solved in a reasonable amount of time using a relatively low-cost personal computer.

Automated summary

This paper presents an efficient parallel computing strategy for solving large-scale structural vibration problems. The proposed approach uses a novel direct method with simplex-shaped space-time finite elements and allows for direct decoupling of variables during matrix assembly. The method uses consistent stiffness, inertia, and damping matrices and handles non-symmetric matrices. The results demonstrate that the proposed method enables calculations at least 20 times faster than the classical finite element method, and it can be applied to solve dynamics problems involving large-scale, three-dimensional structures on a personal computer.