Unit name:Advanced Numerical Analysis Software Research Unit

Key words: numerical algorithms, sophisticated software, large-scale simulations, data analysis

Nowadays, the method of reproducing real-world phenomena on computers for their analysis and prediction is used in every research field. We often see the results of computer simulations presented as computer graphics (CG) on TV, which are obtained by numerical calculations. The research unit led by Professor Sakurai conducts research and development to help utilize the next generation of computers to perform efficient numerical calculations.

Mathematical approaches applied to natural science, industries, and many other fields

There are often multiple calculation methods to solve one mathematical question, and calculation procedures are referred to as algorithms. The research unit conducts research on sophisticated algorithms used to answer questions involving linear equations, or to find eigenvalues in particular.

Solving an eigenvalue problem refers to finding the vectors that characterize the changes of a multivariate function and finding the quantities of the changes. It may sound difficult. However, eigenvalue calculations are used to analyze many questions such as an appropriate shape of automobile components to reduce their vibrations as much as possible. Linear equations and eigenvalue calculations are also used in a variety of fields, including designs of ships and airplanes, seismic isolation for buildings, drug discovery, the development of semi-conductors, genetic and image analyses, and natural scientific studies, including cosmology and particle physics. The research unit conducts research in collaboration with researchers from these many different fields (Figure 1).

Figure 1: Research subjects of the research unit and their applications

For the effective use of high-performance computers of the next generation

There have always been improvements in the performance of computers. The better the performance of the computer is, the larger the number of eigenvalues it can calculate, and the faster its calculation speed becomes. However, it has become increasingly difficult for conventional numerical calculation algorithms to fully utilize the performance of current advanced computers.^*1 To effectively utilize the performance of the latest large-scale, parallel-type computers, it is necessary to develop new algorithms according to the structures of computers and technologies for the implementation of programs and software required to operate algorithms on computers. Our research unit has specialists in high-performance computation with sufficient knowledge of the structures of high-performance computers of the next generation. Our research unit also has researchers specializing in algorithms. They collaborate with each other to develop algorithms that can operate on super parallel-type computers of the next generation and high-performance, and to develop parallel-type calculation software (Figure 2).

Furthermore, we also try to improve our algorithm and software by providing researchers with them for their own researches and asking the researchers for feedback.
*1: The parallel-type, high-performance computer system, in which multiple computers are linked to each other through networks, is currently common. As the degree of parallel computation grows, the speed of such computer system grows.

Figure 2: Positioning of research conducted by the research unit

Interviewed on August 4, 2015