A hybrid method between the Kriging model and the radial basis function (RBF) networks is proposed for robust construction of a response surface of an unknown function. In the hybrid method, RBF approximates the macro trend of the function and the Kriging model estimates the micro trend. Hybrid methods using two types of model selection criteria (MSC), i.e., leave-one-out cross-validation and generalized cross-validation for RBF were applied to three one-dimensional test problems. The results were compared with those of the ordinary Kriging (OK) model and the universal Kriging model. The accuracy of each response surface was compared by function shape and root mean square error. The proposed hybrid models were more accurate than the OK model for highly nonlinear functions because they can capture the macro trend of the function properly by RBF, while the OK model cannot. In addition, the hybrid models can find the global optimum with few sample points using the Kriging model approximation errors.

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In this paper, the authors' recent developments on the crack propagation analysis software system are presented. The system has been developed based on three main parts i) finite element model generation, ii) finite element analysis and iii) stress intensity factor computations. We adopt the quadratic tetrahedral finite element and the processes in the finite element model generation are fully automated by using the Delaunay tessellation technique. The stress intensity factors are evaluated by using the virtual crack closure-integral method (VCCM) for the tetrahedral finite element. In previous papers, the authors have presented the crack analysis software system for single crack cases. It is extended to deal with the propagations of multiple cracks and their coalescences. The net-section yield criterion is adopted to judge the coalescence of adjacent cracks. In this paper, a brief review on the exiting crack propagation analysis system is presented first and present developments for the multiple cracks with their coalescence are discussed in detail. Finally, some numerical examples are presented.

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One of the cavitation models for cavitating flow simulations is the bubble dynamics based method (bubble model). In a typical bubble dynamics based method, the Rayleigh-Plesset equation is solved for determining the volumetric motion of a bubble. It is derived for a single bubble in uniform fluid, and thus, is not adequate for a bubble in high void fraction fluid. Therefore, in the existing bubble dynamics based model, high void fraction fluid has not been treated as far as utilizing the Rayleigh-Plesset equation is concerned. In this paper, a bubble dynamics model treating high void fraction region is proposed. The present model has a threshold between low and high void fraction. Below the threshold, Rayleigh-Plesset equation is solved. Above the threshold, the second derivative of temporal difference of a bubble radius is set to be zero when the bubble is expanding, and Rayleigh-Plesset equation is again solved when the bubble is shrinking. For computational example, flow around Clark-Y11.7% and NACA0015 is calculated for validation of this approach and compared with experiment and the old bubble dynamics based method.

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A new method of Adaptive Plan system with Genetic Algorithm called APGA is proposed to reduce a large amount of calculation cost and to improve a stability in convergence to an optimal solution for multi-peak optimization problems with multi-dimensions. This is an approach that combines the global search ability of Genetic Algorithm (GA) and the local search ability of Adaptive Plan (AP). The APGA differs from GAs in handling design variable vectors (DVs). GAs generally encode DVs into genes and handle them through GA operators. However, the APGA encodes control variable vectors (CVs) of AP, which searches for local optimum, into its genes. CVs determine the global behavior of AP, and DVs are handled by AP in the optimization process of APGA. In this paper, we introduce some strategies using APGA to solve a huge scale of optimization problem and to improve the convergence towards the optimal solution. These methodologies are applied to several benchmark functions with multi-dimensions to evaluate its performance. We confirmed satisfactory performance through various benchmark tests.

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New solution algorithms of finite-difference systems for 1D and 2D Poisson's equations were obtained by modifying Gaussian elimination. Introduction of a new naming of row and column for coefficient matrices of the systems made it possible to derive the elimination algorithms explicitly. Since the finite-difference systems for Poisson's equations are diagonally dominant, solutions with high accuracy can be obtained with no use of pivoting in the present algorithm. The computer execution time for the present algorithm would appear to be one order smaller than the time for SOR with Chebyshev acceleration.

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To analyze large-scale problems by a domain decomposition method (DDM), it is important to accelerate the subdomain local solver. For utilizing cache memory effectively and for saving main memory usage, we employ the preconditioner of incomplete Cholesky factorization with threshold (ICT) optimized for the subdomain local solver of the DDM. Though the ICT preconditioner was originally proposed for ill-conditioned problems, we employ it in this study because it can freely control the number of nonzeros of the preconditioning matrix. By controlling the number of nonzeros, both the coefficient and the preconditioning matrices can fit on the cache memory. By using the cache memory effectively, the computation time of the ICT-based subdomain local solver becomes comparable to that of the direct LDL-based solver. In addition, when the number of degrees of freedom (DOFs) of an analysis model becomes very large, the LDL-based DDM solver suffers from overflow of the main memory whereas the ICT-based solver can complete the analysis. Using this solver, we succeeded in analyzing a structural problem of 64 million DOFs in 8 minutes on a parallel computing cluster of 8 nodes.

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This paper aims at practical Monte Carlo (MC) simulation by finite element method for a dynamic problem where the load condition includes uncertainty factors. A new sampling scheme is proposed to predict an extreme case with high stress by unexpected combination of load parameters, which is involved in the tail probability, to be used in the fatigue life estimation of structures. The proposed scheme, named as stepwise limited sampling (SLS), can provide the expected value of the stress with moderate accuracy and provide reliable results with extremely high stress. In the demonstrative example, the proposed method was computationally cost-effective than usual MC simulation. In addition, a model order reduction (MOR) technique is employed to reduce both the computational cost and the memory requirement. The latter contributed to the fast MC simulation by parallel processing.

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The multiphase field (MPF) method is recognized as a powerful numerical method to simulate microstructural evolutions, such as solidification, grain growth, recrystallization, and phase transformation, in various materials. However, because we need to solve the time evolution equations for multiple-order parameters derived from the total Gibbs free energy, MPF simulations are very computationally expensive. In this paper, we use a graphics processing unit (GPU) to accelerate the two-dimensional MPF simulation of austenite-to-ferrite transformation in a Fe-C alloy. This is an important phenomenon for predicting the morphology of multiphase microstructures in steel. To perform the MPF simulation on an NVIDIA GPU, the program code is developed in CUDA Fortran. Using this code, the acceleration performance of the GPU implementation is evaluated, and our results demonstrate that the GPU computation can powerfully accelerate the MPF simulation by introducing an active parameter tracking (APT) method, which is used to reduce the computational load and memory consumption. The performance of the GPU computation with APT achieves a speedup factor of 5 compared with the GPU computation without APT and a speedup factor of 15 compared with the basic CPU computation without the APT method.

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This paper is concerned with a novel proposal to determinate classification boundaries both in time and frequency domains based on the support vector machines (SVM) technique for diagnosis of ventricular septal defect (VSD). Firstly, two heart sound characteristic waveforms are extracted both from time-domain and frequency-domain. Four heart sound feature parameters both in time and frequency domains, [T₁₁, T₁₂] and [F_G, F_W], are obtained from the crossed points of the waveforms at the selected threshold values. Secondly, a novel algorithm to determine the classification boundaries surrounding the feature parameters is proposed with the aid of SVM technique for evaluating the performance of VSD auscultation. Finally, the classification labeling indexes based on the classification boundaries are introduced for diagnosis of VSD. A case study on the normal and VSD cases is demonstrated to validate the usefulness and efficiency of the proposed method; the classification accuracy (CA) is gained 98.4% for diagnosing VSD from the normal cases. Furthermore, the proposed method is applied to classify the sizes of the defect in VSD. The accuracies have been achieved at 94.9% for small, 93.6% for moderate and 95.8% for large VSD.

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