NONLINEAR LARGE SCALE COMPUTATION AND ITS VISUALIZATION

我们得到了以下结果：1.非线性系统的应用分析。(1)简化磁Benard系统的吸引子分析(H.Imai，Nakamura)(2)用变分不等式(Fujita，Kawa ada)建立具有摩擦型边界条件的粘性流体系统的数学形式(Fujita，Kawa ada)。(3)分析了非零出流条件下的N-S方程(Morimoto)。(4)用模糊方法分析形状设计问题(Natori，T.Hanada等)。演化系统的数值分析。(1)简化磁Benard系统(Imai，Nakamura)的数值模拟。(2)各种理想流动的数值分析(H.Okamoto，M.Shoji)。(3)发展方程的数值分析(Y.Chen)。(4)Stefan问题(花田)的数值分析。(4)Stefan问题(花田)的数值分析。计算算法的发展(1)电荷模拟法的算法(M.Katsurada，Okamoto)。(2)谱方法非线性计算算法(IMAI)。(3)可视化算法(IMAI)。

We obtain the following results.1. Applied analysis of nonlinear systems. (1) Analysis of attractors of simplified magnetic benard system (H.Imai, Nakamura) (2) Mathematical formulation of systems of viscous fluid with friction type boundary conditions by variational inequalities (Fujita, Kawarada). (3) Analysis do Navier-Stokes equations with non-vanishing outflow condition (Morimoto). (4) Analysis of shape design problem by the fuzzy method (Natori, T.Hanada, et.al).2. Numerical analysis of the evolution systems. (1) Numerical simulation of simplified magnetic Benard system (Imai, Nakamura). (2) Numerical analysis of various perfect flows (H.Okamoto, M.Shoji). (3) Numerical analysis of evolution equation (Y.Chen). (4) Numerical analysis of Stefan problem (Hanada). (4) Numerical analysis of Stefan problem (Hanada).3. Development of Computational algorithm (1) Algorithm of charge simulation method (M.Katsurada, Okamoto). (2) Nonlinear computation algorithm by spectral method (Imai). (3) Algorithm of visualization (Imai).