A direct finite element solver is considered for symmetric sparse matrices arising from the application of the finite element method to problems of structural mechanics and solid mechanics. The solver is based on the block Cholesky method generalized to indefinite matrices. A distinctive feature of the proposed method from other known approaches is the original algorithm for parallelizing the factorization procedure, as well as assembling the matrix of a system of linear and linearized algebraic equations, based on the analysis of the adjacency graph for the finite elements of the design model. All the proposed parallelization algorithms use dynamic mapping of computational tasks to threads and are based on a general idea that uses a dependency vector that controls the execution of computational tasks in a parallel region. This approach is relatively simple and at the same time demonstrates high efficiency. It was developed for solving nonlinear static and dynamic problems of structural mechanics, requiring multiple assembly and factorization of a sparse matrix, but can be successfully applied in other areas of computational mathematics.

对于将有限元方法应用于结构力学和固体力学问题而产生的对称稀疏矩阵，可以考虑使用直接有限元求解器。求解器基于泛化为不定矩阵的块Cholesky方法。与其他已知方法相比，该方法的一个显着特征是用于分解因式分解程序以及基于线性和线性代数方程组系统矩阵的原始算法，该算法基于对有限元的邻接图的分析。设计模型。所有提出的并行化算法都使用计算任务到线程的动态映射，并且基于使用依赖向量控制并行区域中计算任务执行的一般思想。这种方法相对简单，同时显示出很高的效率。它是为解决结构力学的非线性静态和动态问题而开发的，需要对稀疏矩阵进行多次组装和分解，但可以成功地应用于计算数学的其他领域。