Simulation programs, such as those for predicting meteorological phenomena and finding new properties in material, are composed of multiple numerical algorithms, each of which is a procedure for numerical calculations. In order to realize the full computing potential of the K computer, it is necessary to review and modify the existing algorithms so that they work in a scalable manner on the K computer’s vast configuration of processor cores. Furthermore, it is also necessary to develop innovative algorithms that can deal with the unprecedented challenges raised by the K computer, as well as next-generation supercomputers. In addition to the review and development of such algorithms, we are investigating how to gather them into a numerical library that is open to all researchers. We expect this work will contribute greatly to improving the performance and expanding the scale of supercomputers.