Papers by Keyword: Domain Decomposition Method

Abstract: This contribution reviews utilization of parallel computers in various engineering problems. First, parallel computers are classified and a very short review of the most powerful computers is presented. Then, engineering problems are sorted with respect to possible parallelization.Finally, two examples of different utilization of parallel computers are described. Domaindecomposition method based on the Schur complement method is the first example and a multi-scale analysis of masonry structure is the second one.

Abstract: This study investigates the computer simulation of fracture process in compressive failure of cross-ply laminate of composite materials. The purpose of this study is to establish the numerical analysis method to understand the fracture mechanism and predict the mechanical response of composite materials through the computer simulation. The stacking sequence of the simulated laminate is [0/90] s. The reinforcement fibers in 0-degree plies are modeled by circle cross-section beam elements to represent the three-dimensional effect in bending of fibers. Cohesive elements are inserted in the connection of beam elements to simulate the bending breaking of fibers. For the purpose of parallel computing, the domain decomposition method is applied, and for pre-conditioned conjugate gradient algorithm, incomplete Cholesky conjugate gradient method is applied. The simulated results show that in the initial state of the loading, the stress concentration occurs around the initial misalignment of fiber in 0-degree plies, and it also occurs around the area where fibers come close in 90-degree plies. At average applied strain 1.20 %, the fiber breaking damage initiates in 0-degree ply, and after this point the damage develops in the material. The simulated damage is close to the microscope picture of the actual composite materials obtained in the experiment. The current simulation is considered to correspond with the actual material deformation.

Abstract: It presents the coupling of Pseudo-spectral method (PS) and domain decomposition method (DDM) for the elastostatic problem. First, the original problem is decomposed into several sub-problems by DDM. Next combining the advantage of easy programming and high accuracy of Pseudo-spectral method, we can solve these sub-problems in parallel by PS. Finally the global numerical solution is obtained by the partition of unity approximation. Some numerical experiments illustrate the effectiveness and accuracy of our method.

Abstract: Based upon the Reissner-Naghdi-Berry’s shell theory, a domain decomposition method (DDM) is utilized to investigate the vibration characteristics of the combined cylindrical-spherical shell with different boundary conditions. The combined shell was first apart from prescribed-displacement boundary and then divided into some cylindrical and spherical shell subdomains, respectively. The boundary equations were introduced into the energy functional of the combined shell as well as the constraint equations derived from interface continuity conditions between two adjacent shell subdomains. Fourier series and Chebyshev orthogonal polynomials were employed as the admissible displacement functions for each shell subdomain in the circumferential direction and axial direction in order to obtain the discretization equations of motion of the combined shell. Exact free vibration solutions of the combined shell has been performed via the DDM and were compared with those obtained by the finite element software ANSYS to confirm the reliability and accuracy.

Abstract: Domain decomposition method for solving the discrete problem of the second kind of variational inequality is considered. The variational inequality is reformulated as an equivalent optimization problem. Then the overlapping domain decomposition method is proposed. The convergence of the methods is obtained.

Abstract: An efficient domain decomposition method (DDM) is employed to improve upon the efficiency and capability of the finite element-boundary integral (FE-BI) method for calculation of electromagnetic (EM) scattering from deep cavities. This method first subdivides the original cavity into many sub-domains along its depth and classifies these sub-domains into a few building blocks. It then employs the substructuring method to deal with the different types of sub-domains. The resulting Schur complement system is solved by a special method which has low memory requirements because the formation of the global Schur complement matrix is not necessary. Numerical results indicate that the presented method is an effective approach for scattering by deep cavities.

Abstract: To solve a large scale elasto-plastic dynamics analysis of a complicated structure, such as a seismic analysis of a nuclear power plant and a skyscraper, a new implementation strategy for a parallel finite element code, suitable on a parallel supercomputer with modern multi-core / many core scalar CPUs, has been required. In this work, we propose a new design and programming style to optimize the performance of a parallel finite element code based on the domain-decomposition method (DDM) on multi-core CPUs, considering their cache hierarchy. Instead of a traditional, memory access-intensive approach, DS (Direct solver-based matrix Storage), two new matrix storage-free approaches, DSF (Direct solver-based matrix Storage-Free) and ISF (Iterative solver-based matrix Storage-Free), are proposed. Our new DSF/ISF-based DDM solver is not only more efficient in memory usage but also comparable in computational time against existing DS-based DDM solvers on multi-core CPU architectures.

Abstract: Recently, applications of integrated large composite structures have been attempted to many structures of vehicles. In order to improve the cost performance and reliability, it is necessary to judge the structural integrity of composite structures. Fracture simulation techniques using FEM have been developed for the purpose. Since a number of iterations of finite element analysis are required in the fracture simulation, the simulation techniques consume many memory resources and much calculation time. In this study, a personal computer cluster (PC cluster) and the domain decomposition method were incorporated into a fracture simulation system. Calculations using a Windows PC cluster were carried out to confirm the efficiency of the proposed simulation system. As a result, it is concluded that adopting the domain decomposition method and the computer cluster is remarkably efficient to reduce calculation time.