Akira Tezuka

Finite Element and Finite Difference Methods

Finite element methods (FEM) and finite difference methods (FDM) are numerical procedures for obtaining approximated solutions to boundary-value or initial-value problems. They can be applied to various areas of materials measurement and testing, especially for the characterization of mechanically or thermally loaded specimens or components. (Experimental methods for these fields have been treated in Chaps. 7 and 8.)

A platform for parallel CFD FEM computations

It is a time consuming and very skilful task for researchers or developers in computational mechanics to modify a program, designed for a single processor, to one suitable for parallel computation. This is a serious bottleneck in parallel computation, even though a general-purpose parallel computational library, such as MPI, is applied to this modification. We have developed a parallel matrix solver platform, based on a domain decomposition method, for various numerical schemes such as the finite element method (FEM), the finite difference method and the finite volume method, to accelerate a smooth shift to the realm of parallel computation. Parallel software such as PETSc, Aztec, GEOFEM and ADVENTURE have already been developed, however these systems are more suitable for professionals in parallel computation and not valid for our purpose. In our platform, a user is merely required to call the platform at the stage of stiffness matrix calculation. GMRES and Bi-CGSTAB with several pre-conditioners are used as a basic matrix solver. The option of invoking a Lagrange-multiplier is also included. For partitioning, a fast graph generator for arbitrary elements and an interface with MeTis are provided. Our platform is valid for a variety of hardware, including a single processor based workstation, through the exchange of Makefilein. The effectiveness of our platform is evaluated with several examples in the area of finite element fluid dynamics in this paper.

Development of Common Software Platform on Parallel Computations for Discretized Numerical Schemes and its Application to Finite Element Fluid Dynamics

It is a time consuming and very skillful task for researchers or developers on computational mechanics to modify a program for a single processor to the one for parallel computation. This is a serious bottleneck for parallel computation, even though general-purpose parallel computational library such as MPI is applied in his modification. We developed a parallel matrix solver platform, called ‘Parallel Computing Platform/PCP, based on domain de composition scheme for various numerical schemes such as finite element method (FEM), finite difference method (FDM) and finite volume method (FVM) to accelerate a smooth shift to parallel computational world. Some parallel software such as PETSc, Aztec, GEOFEM and ADVENTURE had been developed, however, these are for professionals in parallel computations and not valid for our purpose. In our platform, what a user should do is just to call the platform at the stage of stiffness matrix calculation. GMRES and Bi-CGSTAB with some pre-conditioners are used as a basic matrix solver. The option of Lagrange-multiplier is also attached. For the partitioning, a fast graph generator for arbitrary elements and the interface with MeTis are equipped. Our platform is valid for a variety of hardware, including single processor based WS, by exchanging Makefile.in. The effectiveness of our platform is evaluated with several examples in finite element fluid dynamics.

A state reduction approach to interpretation of system behavior based on system simulation

System modeling and simulation techniques have been introduced to the early stage of model-based design in product development. Given a description of a system in terms of system components and connections, these techniques compute its numerical behavior by building and solving an equation system derived from the topology of system components. Currently, these techniques have a limitation in supporting designers to interpret the overall behavior of a system in terms of semantics rather than numerical values. To overcome the limitation, the paper briefly introduces a semi-automated procedure to support designers to validate a product model with system simulation results. The procedure reduces the dynamic state of a system by clustering the behavior of system components in terms of their parameters at discrete time intervals. It also generates the overall system behavior by computing clustering patterns and its transitions and identity relations across intervals in the entire simulation duration.