The Smoothed Finite Element Method (S-FEM) proposed by Liu G.R. can achieve more accurate results than the conventional FEM. Currently, much commercial software and many open-source packages have been developed to analyze various science and engineering problems using the FEM. However, there is little work focusing on designing and developing software or packages for the S-FEM. In this paper, we design and implement an open-source package of the parallel S-FEM for elastic problems by utilizing the Julia language on multi-core CPU. The Julia language is a fast, easy-to-use, and open-source programming language that was originally designed for high-performance computing. We term our package as juSFEM. To the best of the authors knowledge, juSFEM is the first package of parallel S-FEM developed with the Julia language. To verify the correctness and evaluate the efficiency of juSFEM, two groups of benchmark tests are conducted. The benchmark results show that (1) juSFEM can achieve accurate results when compared to commercial FEM software ABAQUS, and (2) juSFEM only requires 543 seconds to calculate the displacements of a 3D elastic cantilever beam model which is composed of approximately 2 million tetrahedral elements, while in contrast the commercial FEM software needs 930 seconds for the same calculation model; (3) the parallel juSFEM executed on the 24-core CPU is approximately 20× faster than the corresponding serial version. Moreover, the structure and function of juSFEM are easily modularized, and the code in juSFEM is clear and readable, which is convenient for further development.is to theoretical redesign the algorithm structure in combination with the characteristics of the S-FEM to improve the computational efficiency. The other is to utilize the parallelism on multicore CPU or many-core GPU. As a variation of the S-FEM, the edge-based smooth element method (ES-FEM) is parallelized on the GPU [9].Because the process of the S-FEM is quite similar to the FEM, most current S-FEM programs are modified on the basis of the FEM [10]. Reference [11] introduced an effective algorithm for establishing the smoothing domains, realizing the automation of 3D entity calculation and adaptive analysis. However, the current S-FEM program, which uses a programming language such as C/C++ or Fortran, usually requires high demand of programming skill, and the code is difficult to read and modify. For programs written in high-level languages such as Python and MATLAB, the code is readable but computationally inefficient [12].In summary, quite few efforts are dedicated to developing the open-source packages of the S-FEM by comprehensively considering the accuracy, efficiency, readability, and ease-ofdevelopment. To balance the program execution efficiency and the ease of implementing the program, in this paper, we design and implement an open-source package of parallel S-FEM for elastic problems by using the Julia language [13]. We term our package as juSFEM. To the best of the authors knowledge, juSFEM is the first package of p...
<p>The post-failure of landslide is a stage where large deformations are present. It is difficult to properly resolve such large deformations using traditional mesh-based numerical methods. Meshless methods, such as the material point method (MPM), can resolve such problems by reducing the dependence on the mesh. However, the time-consuming mapping procedure between the material points and background nodes exists at each time step of MPM, consequently, one needs an efficient implementation taking advantage of modern computer hardware architectures for a high-resolution computational model. In the present study, we develop a high-performance MPM simulation package using Julia language to simulate the landslide post-failure stage. We show both the 2D and 3D computation models. The parallel algorithm on the GPU version is based on the features of MPM through CUDA.jl, a library that natively supports CUDA computing in Julia. To validate the performance of the present simulation package, we perform benchmarks on both CPU and GPU versions of the package. Furthermore, we use the uniform Generalized Interpolation MPM (uGIMP) and apply it to resolve a real problem to demonstrate the capabilities of this package. &#160;The simulation result is in good agreement with the ground truth. HPC simulation is not only reproducing the run-out process but also provides us with a better understanding of the complex mechanisms involved in landslide movements.</p>
In this paper, a parallel Smoothed Finite Element Method (S-FEM) package epSFEM using incremental theory to solve elastoplastic problems is developed by employing the Julia language on a multicore CPU. The S-FEM, a new numerical method combining the Finite Element Method (FEM) and strain smoothing technique, was proposed by Liu G.R. in recent years. The S-FEM model is softer than the FEM model for identical grid structures, has lower sensitivity to mesh distortion, and usually produces more accurate solutions and a higher convergence speed. Julia, as an efficient, user-friendly and open-source programming language, balances computational performance, programming difficulty and code readability. We validate the performance of the epSFEM with two sets of benchmark tests. The benchmark results indicate that (1) the calculation accuracy of epSFEM is higher than that of the FEM when employing the same mesh model; (2) the commercial FEM software requires 10,619 s to calculate an elastoplastic model consisting of approximately 2.45 million triangular elements, while in comparison, epSFEM requires only 5876.3 s for the same computational model; and (3) epSFEM executed in parallel on a 24-core CPU is approximately 10.6 times faster than the corresponding serial version.
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