Finite element analysis for 3-dimensional large scale problem by using domain decomposition methods

A.用有限元法进行大规模磁问题的数值计算：首先，我们开发了时谐涡流问题和非线性静磁问题的计算代码。为了使代码的效率，那么我们已经考虑了减少其计算成本，并提高适用的问题，例如，一个永久磁铁或移动的障碍物。B。数值求解器的线性方程组的对称系数矩阵：我们已经考虑了收敛的MRTR方法的残差最小化的基础上。此外，我们还开发了几个预条件，来自鲁棒不完全Cholesky分解，并已通过应用于一些真实的问题显示了它们的效率。C.应用减结构方法离散Stokes方程：我们已经建立了一个粗略的空间的平衡预条件适用于离散Stokes方程。D.热对流问题的有限元方法的误差估计：本文建立了变系数热对流问题的一类有限元方法的误差估计。E.高效的有限元方法的实现大规模结构分析的BDD方法：我们发展了不完全BDD方法，提高了其并行效率，实现了约1000万自由度的非平稳结构分析。

A.Numerical computations of large scale magnetic problems by finite element method:First, we have developed computational codes for time-harmonic eddy current problems and nonlinear magnetostatic problems. To make the codes efficient, then we have considered the reduction of their computational costs, and the enhancement of applicable problems, for example, a permanent magnet or a moving obstacle.B.Numerical solver for linear systems with symmetric coefficient matrices:We have considered the convergence of MRTR method based on the minimization of residuals. Moreover, we have developed several precondisioners, which come from robust incomplete Cholesky factorization, and have shown their efficiency by appling to some real problems.C.Application of a substracturing method to discretized Stokes equations:We have established a coarse space of a balancing precondisioner for applying to discretized Stokes equations.D.Error estimates of finite element methods for thermal convection problems:We have established error estimates of a class of finite element methods for thermal convection problems with variable coefficients.E.Realization of highly efficient BDD methods for large scale structural analysis:We have developed incomplete BDD methods, improved its parallel efficiency, and realized nonstationary structural analysis with about 10 million DOF problems.