数值计算磁流体力学(MHD)存在奇强非线性性、不规则区域磁场非H^1和算法稳定性等诸多难点。为此，本项目拟利用单位分解、区域分解和两重网格的思想，设计可以在单元量级上实现并行的高效并行后处理算法，开展不规则区域上非定常不可压缩 MHD方程的可扩展高效并行有限元算法研究。包括:在全局粗网格上，构造磁场和人工压力项混合有限元格式获取磁场非H^1解，设计无条件或几乎无条件稳定的半隐或隐显全离散有限元算法，得到全局低频分量，并证明其稳定性和最优收敛性，然后在局部区域细网格上并行求解残量子问题，捕捉解的高频分量。利用自适应技巧对局部区域和子问题进行自适应加密和求解，构造全局连续的整体解。探索适合求解高哈特曼数问题的并行有限元亏量校正格式。算法允许时间大步长剖分和空间并行能高效、高精度、低代价求解MHD，该研究将会为MHD的大规模科学计算提供一类算法基础和理论支持。

One will be confronted with many difficulties when solving magnetohydrodynamics (MHD) numerically, such as tremendous nonlinearity, magnetic field with non H^1 space on irregular area, stability of the method and so on. Therefore, the project plans to use the ideas of partition of unity, domain decomposition and two-grid method, propose efficient post-processing algorithms which may be achieved in parallel on element level, carry out the research on extendable and efficient parallel finite element algorithms for the unsteady MHD equations on irregular domain. The project is to construct mixed finite element (FE) scheme with magnetic field and artificial pressure term to obtain magnetic non H^1 solution on global coarse grid mesh, design fully discrete semi-implicit or implicit/explicit schemes with unconditional (or almost unconditional) stability, obtain the global low frequency component of FE solution, prove their stability and optimal convergence, then find local fine grid corrections by residual sub-problems on local domains in parallel to capture the high-frequency component of the solution. Meanwhile, the adaptive skills are used to refine the local sub-domains and the corresponding local sub-problems are solved adaptively, and the globally continuous FE solutions are constructed. Explore parallel defect correction FE schemes to solve high Hartmann numbers problems. The algorithms proposed with allowing large time step portion and solving the problem in parallel on space are efficient, high-accuracy and low-cost. The project will provide a class of basic algorithms and theoretical supports for the MHD large-scale scientific computing.