On the research and development of fast solvers arising in scientific computation

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Progress is made in the study of vortex method, thin layer element method, wavelet, finite difference method. Okamoto published a survey paper on the fundamental solution method. Mr. K.Kobayashi develops, under the guidance of Okamoto, a new algorithm for computing the minimal surfaces. F.Sasaki considers a new application of wavelets to integral equations, in which the conventional wavelets are difficult to be applied because of the nonlocality of the integral equations. K.Murota and S.Iwata develop a unified theory for the mixed matrices. They write a program to compute the combinatorial canonical form of the mixed matrices and made it available through internet. M.Sugihara considers theoretical background of the fundamental solution method. In particular he proposes a new method of locating the singularities in three-dimensional domain. He also applies the double exponential transform to the Sinc method of functional approximation. His results show that the double exponential transform is of the optimal order in the Sinc method. Y.Iso considers a numerical method for inverse scattering problem. He shows that a certain high precision numerical software is very effective. T.Ikeda performs numerical experiments of the parallel computation for the reaction-diffusion equation. He clarifies some of the theoretical background of basic algorithms in the parallel computation, ] which has been only heuristically derived.