基于H - Matrices的结构特征值问题加速研究

提出遗传双重互易法，利用遗传矩阵结构（Hierarchical Matrices , H - Matrices）加速双重互易边界元法（DRBEM）结构特征值问题分析过程并压缩数据存储。通过自适应交叉拟合算法对遗传矩阵中的相容子块使用低阶秩块拟合，减少参与矩阵运算数据规模，降低计算消耗的内存空间。针对规模和效率的不同计算环境要求提出两种求解优化策略，即完全遗传双重互易法(PHDM)和混合遗传双重互易法(MHDM)，以求针对性提高数值计算效果。数值算例验证了所提方法的效率以及数据压缩效果。

Researchs on the Acceleration of Structure Eigenvalue Problem based on H – Matrices

The Hierarchical Dual Reciprocity Method (H - DRM) is proposed, which is applied for accelerating Dual Reciprocity Boundary Element Method (DRBEM) procedure and save computer memory during computation. Through applying low rank approximation with Adaptive Cross Approximation (ACA) algorithm for admissible blocks, the computer memory consumption will be saved significantly, and the scale of data involved in computation will diminish greatly. With respect to the different requirement about efficiency and scale, two different evaluation strategies are proposed --- pure hierarchical matrices method (PHDM) and mixed hierarchical matrices method (MHDM) --- to improve effect of H - DRM. Some numerical examples are presented in the last section for validation effect of the proposed methodology.