Modal Analysis of Two-Dimensional Beams Using Parallel Finite Element Method

Modal analysis is the process of determination of the natural frequencies and mode shapes of structures. In practical problems, modal analysis may be repeated many times, which results in a huge amount of computations. Although parallel processing technique can reduce the analysis time, it is rarely implemented by civil engineers because it requires more programming skills as well as designing parallel algorithms. In the present paper, the Davidson algorithm is adapted for parallel modal analysis of two-dimensional beams. More precisely, the parallel version of the Davidson algorithm is implemented from scratch. A new proposed method, which is called "Modified Checkered Method" (MCM), is introduced, and four versions of the algorithm, are implemented. Two out of four versions use Row-wise and MCM in combination with Compressed Sparse Row algorithm, while the others utilize the aforesaid methods without matrix compression. It is shown that the speedup increases when the main matrix of the standard form of eigenvalue problem is not compressed. Moreover, the speedup will increase in comparison to the Row-wise division method when MCM is used. It is notable that the implemented Parallel Finite Element source code is capable of being used in companion with a wide variety of finite elements.