时空有限元方法的高效计算

Efficient Computation of Space-Time Finite Element Method

为提高时空有限元方法求解二维瞬态不可压缩的Navier-Stokes方程的计算效率并降低对计算机内存的需求,用行格式存储法存储大型稀疏矩阵,用Newton-Raphson迭代法求解非线性代数方程组,用无填充不完全分解预处理方法以及重启型GMRES方法求解子迭代步的线性方程组.为验证该方法的可行性,对Reynolds数为100的圆柱绕流问题进行数值模拟.采用行格式存储法的存储空间仅为等带宽存储法的3.68%.

To improve the computational efficiency and reduce the requirement on memory in solving two-dimensional transient incompressible Navier-Stokes equations with space-time finite method, the compressed sparse row format was used to store the large-scale sparse matrix, Newton-Raphson method was adopted to solve the nonlinear equations and the restarted GMRES method with the zero fill-in incomplete triangle decomposition precondition was adopted to solve the linear equations during sub- iterations. To verify the feasibility of the proposed method, the problem of flow around a circular cylinder was numerically simulated at the Reynolds of 100. The required memory with the compressed sparse row format was 3.68% of that with equi-band-width storage method.