Efficient Blocked Symmetric Compressed Sparse Column Method for Finite Element Analysis

In the field of finite element analysis (FEA), which is widely used in aerospace, automotive, and civil engineering, optimizing the storage of the global stiffness matrix and improving the efficiency of solving finite element equations are critical to handling large-scale and complex engineering problems. However, existing methods face significant limitations: adaptive mesh methods reduce computational costs by adjusting mesh density but require substantial resources for mesh generation and may sacrifice accuracy in coarse mesh regions. Assembly-free methods avoid explicit storage of the global stiffness matrix to save space but prolong solution time due to repeated recalculation of element stiffness matrices. Traditional sparse matrix compression storage methods (such as compressed sparse column (CSC) and compressed sparse row (CSR)) fail to fully leverage the blocked symmetry of the global stiffness matrix, leading to redundant memory usage and low computational efficiency in sparse