Multi-resolution MPS method is proposed in this paper. In order to consider difference of particle sizes, the weight function is calculated using not only distance but also particle sizes, and the incompressible condition is changed from the condition that the particle number density should be constant to the condition that the divergence of velocity field should be zero. Even though the particle sizes vary greatly, the dam break can be simulated very stably. The spatial resolution can be changed to split big particles and merge small particles. The simulation is as accurate as the traditional MPS method and the calculation cost is reduced greatly.

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In this paper, genetic algorithm with a stress-based crossover is improved to solve structural shape optimization problems. The design domain is well divided by finite element method. According to one initial topology, the boundary profile elements and the neighboring outside elements, which are design variables, are randomly set to “0” or “1” to generate the initial population. To keep the shape deforming gradually, a logical “OR” operation is applied on each child structure and a “mask” structure. Moreover, the material weight of child is adjusted dynamically. Three experiments were performed to verify the effectiveness of improved SX for structural shape optimization.

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The numerical accuracy and stability of the stabilized space-time finite element method based on GLS for shallow water flows is investigated in this paper. The numerical solutions obtained by the stabilized space-time finite element method are compared with the stabilized finite element solutions using the finite difference discretization (Crank-Nicolson method) in time. This paper also investigates the efficiency of the way using a variable time step size based on CFL condition for shallow water flow analysis.

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Stress-based crossover (SX) is a genetic operator for structural topology optimization using the information of stress. This paper discusses three types of SX parameter. First, generation alternation models are used to improve the search ability of genetic algorithms. Second, several different meshes are used to study the mesh dependency of SX. A comparison of evolutionary structural optimization (ESO) and SX is performed on the MBB beam problem. Third, element stress ranking method is adopted to study the impact of element stress on final topology. In addition, different domain division strategy for GA and FEM is introduced to further discuss the element stress in uence in SX.

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Thermoelectric heat control systems based on the Peltier effect offer highly attractive capabilities compared to conventional heat pump systems. Due to the absence of moving parts, such systems are essentially free of mechanical vibration and noise, are highly reliable, and can be easily miniaturized. This paper proposes a new topology optimization method for the design of heat transfer control systems composed of thermoelectric materials and heat conductors. First, a nonlinear finite element method is introduced to analyze the nonlinear coupling effect of thermal and electric fluxes. Next, the thermal conductor portion of the heat transfer control system is set as the design domain, and the homogenization method is used for its relaxation. A topology optimization problem is formulated based on the thermal potential energy concept, and an optimization algorithm is constructed using sequential linear programming. Finally, several numerical examples are presented to confirm the utility of the proposed method.

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An integration scheme for finite elements on the boundary of analysis domain in structured finite element analysis is proposed in this paper. In structured finite element analysis, the structured grid is adopted as finite elements and the inconsistency between boundary of finite elements and that of analysis domain occurs. For accurate integration of weak-formed governing equation, accurate numerical integration scheme, such as gauss integration, and appropriate evaluation of integration region must be incorporated. In this paper, Newton-Cotes integration technique with sub-cell evaluation of integration region is proposed and efficient integration of element stiffness matrices on the boundary of analysis domain is achieved.

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Epoxy resin is widely used for engineering components as adhesive and matrix materials due to its prior properties. However, pure epoxy resin is brittle. To improve the fracture toughness of the epoxy resin, rubber particles are mixed with epoxy resin. In this study, we measured the fracture toughness of unmodified epoxy resin and rubber-modified epoxy resin using single-edged notch bending specimens. The microstructure in damage zone was investigated, employing transmission electron microscopy (TEM). The distributions of strain around a crack tip were measured using a micro-video-scope and the digital image correlation method (DICM). The measured distribution of strain was compared with that estimated using the finite element method (FEM) in conjunction with Gurson’s model, which can well describe the yielding of porous materials such as rubber-modified epoxy resin. The measured distribution of strain around a crack tip was similar to that obtained by the three dimensional FEM with Gurson’s model.

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The conventional GPBi-CG method involves inherently instability of convergence rate. Even if the so-called preconditioning technique is adopted in the GPBi-CG method for reduction of difficulties of solving problems, the situation remains as it is. The fact that the GPBi-CG method computed in finite arithemetics has two variants of residual causes the instability. We refer to this situation as “split of residual”. On the other hand, in our proposed GPBiCG_AR method we does not almost meet with the above “split of residual” because of consistency of residual. In this paper, we introduce two kinds of the preconditioned GPBi-CG and GPBiCG_AR methods. Through numerical experiments, we demonstrate that the preconditioned GPBiCG_AR method performs well as compared with the preconditioned GPBi-CG method in view of stability of convergence and robustness of convergence for several problems.

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Using a parallel FE solver, a 3-D structural analysis, whose degrees of freedom may exceed 100 million, can be performed on a supercomputer such as the Earth Simulator, the IBM BlueGene/L, etc. To visualize the result data of such a huge scale analysis, a sort-last parallel rendering of polygons on a graphics cluster or a supercomputer is effective. In this paper, to remove the performance bottleneck in the sort-last parallel rendering, we try to accelerate an image composition stage by introducing fast and efficient image compression techniques based on the combination of run length and differential encoding methods. We applied the proposed techniques for the visualization of a huge-scale structural analysis, and the rendering speed of 170 millions triangles per second was obtained on a PC cluster.

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To solve the flow around the complex geometries is one of the difficult problems for Computational Fluid Dynamics (CFD). To overcome this problem, we have already proposed the method for solving the preconditioned compressible Navier-Stokes equations using an Immersed Boundary (IB) method and a Building-Cube Method (BCM). Although the method has several advantages, the solution convergence deteriorates while increasing number of cubes. In this paper, improvement of convergence is presented by applying an Implicit Residual Smoothing (IRS) for CFD with “multi-cube”. The reason of acceleration is considered as propagation of residual. Finally, improved algorithm for IRS is also proposed.

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This paper will introduce the novel concept of creative design to multi-objective topology optimization. Creative design in topology optimization involves allowing the optimization process to be influenced by specific designer inputs regarding topological properties and preferences. These inputs can be created very naturally within the level set framework. A new objective function using a signed least square error is also proposed to measure deviation from the designer inputs. The example presented here shows the trade-off that exists between deviation from desired designer inputs and performance metrics, such as compliance. If the designer inputs are aesthetic features, the interpretation of the creative design becomes one that searches for beauty and performance in topology.

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This paper discusses a new level set method-based topology optimization method using the discretization-based sensitivity with respect to the signed distance function. First, the basic concepts of structural optimization based on the level set method is briefly discussed, and the minimum compliance problem is formulated based on the level set method. Next, a level set function updating scheme using the discretization-based sensitivity with respect to the signed distance function is constructed. In this scheme, the normal velocity is determined by the discretization-based sensitivities of the mean compliance and the perimeter. By updating the level set function using the discretization-based sensitivities of the mean compliance and the perimeter, simple and appropriate optimal configurations can be obtained. Finally, several numerical examples are provided to confirm the validity of the proposed method.

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This paper presents the effective methodology of making most suitable configuration of block structures in a realistic time scale. In this method, the conventional scheme of the topology optimization is used as the optimization calculation. However, on each iterative process, the design parameters, which have the continuous values, are discretized on the basis of thresholds, which are set as the intermediate value between specific points. Therefore, the objective function and weight ratio change in a random manner. Thus all the solutions before convergence become the candidate of optimal solution. And they should be plotted on the weight-ratio compliance plane. As the result, the optimal solutions are obtained as the border line of plotted area. As the numerical example, the block configuration analysis of a XY-stage plate composed of four types of blocks is conducted.

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Computation efficiency of the balancing domain decomposition method is investigated in this paper. An iterative substructuring method with coarse grid correction is one of the most effective methods for parallel computing of large scale structural finite element analyses. In this study, a prediction curve of parallel computation cost of the balancing domain decomposition method is proposed, and the optimal number of subdomains is estimated. Numerical validation of the optimal number of subdomains is conducted and the measured computation time with the optimal number of subdomains shows better computation performance than those with other numbers of subdomains.

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We parallelize the density matrix renormalization group (DMRG) method, which is a groundstate solver for one-dimensional quantum lattice systems. The parallelization allows us to extend the applicable range of the DMRG to multiple leg ladders or quasi two-dimension cases. Such an extension is regarded to bring about several breakthroughs in quantum physics, chemistry, nano-device engineering, and so on. The parallelization requires an all-to-all communication which involves all processes. Such a communication is not suitable for multi-core clusters, which are presently the main stream of the parallel computer, because the network bandwidth should be shared by a large number of processes. Therefore, we propose a new communication strategy to eliminate the all-to-all communication by rearranging a data distribution. We evaluate performance of the new strategy on “SGI Altix 3700Bx2” (single-core system) and “T2K Open Supercomputer (Todai Combined Cluster)” (quad-core system) and confirm that the strategy is quite crucial for typical multi-core systems like T2K.

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Some users would like to continue their computation under a certain limitation such as available resources or their rules for computer resources when they execute their simulation programs required a considerable time. In order to construct a computational environment suited for the restricted situations, we develop a problem solving environment which consists of four components: a runtime for a computation, a job submitter, a monitoring/handling tool for self-management, and a class library for programs. The computation executed on the proposed system is able to move to or copy to other computers on user demand. As a result, the system allows users to use flexibly their computer resources. Through experiments, the system makes a computation running at any time with a little overhead under the condition of unpredicted runtime adding/releasing, and the system reduces turnaround time by the effect of mirroring computing.

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Many researchers who research stochastic simulations such as reinforcement learning algorithms have to run their programs many times to compare developing algorithms and find better sets of parameters for their programs. In order to reduce their working time, we build a problem solving environments (PSE) system to assist them. Our system has three sub-systems: a distributed computing system, a data management system and a graph generation system. We present a relationship between developing algorithms and the three sub-systems. Users automatically obtain results and compare them graphically using the system after they register their own programs in the system. We conduct experiments with human subjects. As a result, user obtained five times speed-up for his work time through executions, storing results and comparing algorithms.

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Recently, in the computational simulation of science and engineering, the size of a matrix to be solved is getting larger. Thus the high performance matrix solver for the larger matrix is desired. Although various new methods are proposed and commercial codes are developed, the speed-up of the solver by the single process is limited due to the clock speed saturation. Therefore, the parallel computation is inevitable. In such a background, in this study, we made a parallel implementation to the Residual Cutting Method based matrix solver developed by the authors group by using Algebraic Multi Grid as an inner solver. From the results of performance evaluation, we found that the developed matrix solver has good parallel performance.

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The purpose of this research was to establish a three-dimensional (3D) numerical modeling method for electromagnetic (EM) exploration problems, such as the magnetotelluric (MT) method, and to determine the iterative solver and preconditioner suitable for a system of linear equations of the 3D EM modeling. We developed a new numerical calculation code for solving Maxwell's equations based on EM potentials by a finite difference method incorporating the Lis (Library of iterative solvers for linear systems). The accuracy of the developed code was confirmed by comparing its results with those of the integral equation method using two synthetic geoelectrical models, which are typical for electromagnetic exploration. Thereafter, we used various Lis'iterative solvers and preconditioners to solve the system of linear equations. Calculation results indicate that a combination of FGMRES and ILU(0) is the best for the 3D finite difference modeling of the MT method.

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In this paper, we present a new interpolation method expressing an arbitrary discontinuous curve with a high accuracy based on the B-Spline interpolation. We call it “The Heaviside B-Spline interpolation method”. The idea of this method is to use the Heaviside step function to construct a high accurate discontinuous spline function being analogous to the enrichment of displacement discontinuous modeling, known as the eXtended FEM. The Heaviside B-spline interpolation method enables interpolating jump or discontinuous data in 1-D or 2-D plane by using a least square method : The method interpolates “The Heaviside Step function” with a high accuracy without Gibbs's phenomena. We obtain excellent results for several examples in which the data is given by a discontinuous function.

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In order to accelerate incompressible flow analysis, 2-dimensional Navior-Stokes equation is solved on GPU (Graphics Processing Unit). The code has been developed in CUDA and all the dependent variables are allocated on the global memory without communications between CPU and GPU memories. The SMAC algorithm is applied and the spatial derivatives are represented by the finite difference on Cartesian grid. The Red&Black Multigrid (MG) method improves the convergence of the SOR method for the pressure Poisson equation. The 3-stage Runge-Kutta method is applied to integrate in time for the advection term with 3rd-order upwind scheme. For the neighbor-grid accesses, we use the small-size shared memory as a software-managed cache. The overall performance of the incompressible flow calculation achieves 17 GFLOPS and about 14-times speed-up to compare with the 1-core CPU calculation. We carry out the computing for the flows around a circle and the Strouhal numbers of the GPU results are in good agreement with those obtained experimentally. It is found that the GPU computing has great contribution for incompressible flow analysis from the engineering view point.

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Scientific Concept Vocabulary (SCV) has been proposed to actualize Cognitive methodology based Data Analysis System: CDAS which supports researchers to analyze large scale data efficiently and comprehensively. In the information model of SCV, all semantic information is related to substantial data and algorisms. Consequently, SCV enables a data analysis system to process semantic information for physics and engineering. Using SCV, it is hoped that CDAS is able to extract semantic information from numerical simulation data. In this paper, the prototype of SCV has been constructed and applied to actual data of numerical simulation in order to confirm the implementability of the system.

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Microstructure formation and stress distribution during directional solidification are simulated using a phase field model for a binary alloy system. Nuclei are set as the initial condition, and the growth toward the liquid region is supposed. Cellular structure is formed as the crystal grows, and wavy pattern at the growing front is observed. Coalescence of the adjacent cells occurs under a certain condition, and then droplets and grooves of liquid phase are generated. The stress distributions in these complicated structures are then calculated, while only an elastic behavior is considered for simplicity. Relatively large tensile stress is generated in the interfacial region, and especially large stress concentration is observed when the droplets and grooves appear. When the stress dependency on the phase transformation is considered, the morphology is drastically varied. Also it reveals that the dependence of the chemical composition on the elastic constant affects the stress distribution.

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Thermal actuators are devices which can generate motion using amplified thermal expansion effects in certain portions of compliant structures, and such can be used in Micro-Electro Mechanical Systems (MEMS). In typical thermal actuators, the temperature increases are achieved by electrical resistive heating or use of external heat sources. This paper proposes a design method for a new kind of thermal actuator using thermoelectric devices as heat control systems. The thermoelectric devices enable us to utilize both heating and cooling effects so that complex actuator motion can be achieved. In this paper, first, the design requirements for thermal actuators using thermoelectric devices are clarified and a topology optimization problem for the thermal actuator design problem is formulated. Next, topology optimization using the level set method is applied to solve the optimization problem. Finally, several numerical examples of thermal actuator design problems using thermoelectric devices are presented to confirm the usefulness of the proposed method.

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