This paper describes the application of a radial basis function approximation for evaluating European stock option: The European stock option is evaluated with Black-Sholes equation and the bonundary condition related to the exercise. Price. The Black-Sholes equation is solved with Crank-Nicholsonm scheme and RBF-approximation. Finally, numerical results are compared with the theoretical solutions to discuss the validity of the formulation.

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With the microscopic phase-field model, the precipitation process of aged alloys was explored by computer simulation, which could help us clarify some discussional views on precipitation mechanisms of alloys. In this paper, the precipitation process of Ni_<75>Al_<2.5>V_<22.5> alloy was studied. From simulated microscopic behavior and calculated order parameters of different precipitates, it's found that θ ordered phase precipitated earlier than γ' ordered phase by congruent ordering + spinodal decomposition mechanism and thus produced a nonstoicheometric θ single ordered phase. Then, the nonstoicheometric γ' phase precipitated by a non-classical nucleation and growth, mechanism at the APBS of θ phases. Meanwhile, both of them transformed to stoicheometric ordered phases.

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Fundamental equations for the analysis of phase transformation process are derived by using the phase field model, in which the coupling effects among the phase, temperature and stress/strain are taken into account. Compared to the conventional phase field equation, the dependency of the phase-change factor on stress/strain is introduced as well as the constitutive equation including the thermal and transformation expansion. In order to numerically solve the coupled equations, the finite element analysis is applied, and a simple simulation for solidification problem is presented as a test-case result.

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A Higher-order accurate Adaptive Mesh Refinement method is developed for blood flow simulation. The method based on the Interpolated Differential Operator scheme has third-order accuracy for Poisson equation. We integrate. Navier-Stokes equation by second-stage implicit Runge-Kutta method for numerical stability. We demonstrate the blood flow simulation with many branches, and show the effectiveness of the method.

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The genesis and development of intracranial aneurysm have long been of interest but remain not understood. In the present study we simulate the progression of intracranial aneurysms by constructing a computational model of a curved artery. It is hypothesized that high local wall shear stress above a threshold value will lead to degeneration of the arterial wall mechanical properties. Our computer simulation shows that evenif the wall shear stress inside a saccular aneurysm is low, aneurysm development can occur due to degeneration of the wall distal and proximal to the aneurysm. The interaction between the geometry change and the wall degeneration is key to the development of aneurysms.

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A numerical methodology of evaluating the Eshelby stress and its related equations is examined by use of the mixed-hybrid finite element method. The equilibrium of Eshelby stress reveals the canonical form of the linear momentum in material space and applications have been made on fracture mechanics and electrodynamics. In order to clarify the Eshelby stress, the numerical algorithm is established such that the residual of the canonical momentum can be numerically estimated. The stress fields on notched effect and mode-I cracking are implemented and the differences from the Cauchy stress are discussed.

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In this paper, we introduce a new approach to surface mesh improvement problem. In contrast to previous methods we do not tend to preserve new mesh vertices on the original discrete surface. Instead our technique keeps mesh nodes very close to a smooth or piecewise-smooth surface approximated by an initial mesh. As a result, the algorithm is able to improve mesh quality while preserving essential surface characteristics and features. Proposed approach can be applied iteratively not only to polygonal meshes but also to 2D and 3D curves that allows to treat sharp edges and surface boundaries. We demonstrate effectiveness of our method using various triangular and quadrilateral meshes.

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Presented research concerns modeling of different mesh quality. Parameters for further improvement of the mesh elements. Basic case of triangulation is considered for producing the mesh elements with uniform distribution of the aspect ratio values. This approach allows creating different applicable to a mesh processing algorithms based on quasi-statistical modeling proposed at the preliminary step. Various formulas can be derived for calculation of new values of the mesh quality parameter. Vertex direction movement with the distribution taken in the modeling step is controlled.

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In this paper, we present mesh improvement algorithms based on quasi-statistical modeling. A mesh quality parameter is modeled as a random variable with the desirable distribution based on an initial topology of the mesh. The goal of the presented research is to improve the polygonal mesh by producing the mesh elements with a Gaussian (normal) distribution of the mesh quality parameter values.

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We have developed a parallel software general platform for various numerical schemes such as finite element method, finite difference method, and finite volume method as well as other numerical schemes, to assist a smooth shift to parallel computational world for non-specialists in parallel computations, which only requires ordinary input data and the subroutine to construct his stiffness matrix. The source codes and the detailed manuals in both Japanese and English versions are released at the AIST website: http://www.aist.go.jp/infobase/pcp/ to general users with free of charge. A major characteristic of this software platform is that it greatly assists users to parallelize his current numerical code in non-parallel computers with a high degree of parallel efficiency regardless of any types of disc retized numerical analysis technique used, and without advanced knowledge or experience in parallel computation required. The function of next version 1.2 is introduced in the presentation.

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[in Japanese]

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