针对高频亥姆霍兹问题的𝒟ℋ2矩阵的内存高效压缩技术

IF 1.8 3区数学 Q1 MATHEMATICS

Numerical Linear Algebra with Applications Pub Date : 2024-07-05 DOI:10.1002/nla.2575

Steffen Börm, Janne Henningsen

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引用次数: 0

摘要

对于高频亥姆霍兹边界积分方程，定向插值是一种快速高效的压缩技术，但其原始形式需要非常大的存储量。代数再压缩可以大大减少存储需求，并相应加快求解过程。在重新压缩过程中，需要权重矩阵来正确衡量不同基向量对最终结果的影响，而对于高精度近似，这些权重矩阵比最终压缩矩阵需要更多的存储空间。我们提出了一种权重矩阵压缩方法，并证明这种方法只会给整体近似带来可控误差。数值实验表明，新方法显著降低了存储需求。

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Memory‐efficient compression of 𝒟ℋ2‐matrices for high‐frequency Helmholtz problems

Directional interpolation is a fast and efficient compression technique for high‐frequency Helmholtz boundary integral equations, but requires a very large amount of storage in its original form. Algebraic recompression can significantly reduce the storage requirements and speed up the solution process accordingly. During the recompression process, weight matrices are required to correctly measure the influence of different basis vectors on the final result, and for highly accurate approximations, these weight matrices require more storage than the final compressed matrix. We present a compression method for the weight matrices and demonstrate that it introduces only a controllable error to the overall approximation. Numerical experiments show that the new method leads to a significant reduction in storage requirements.

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来源期刊

Numerical Linear Algebra with Applications 数学-数学

CiteScore

3.40

自引率

2.30%

发文量

审稿时长

12 months

期刊介绍： Manuscripts submitted to Numerical Linear Algebra with Applications should include large-scale broad-interest applications in which challenging computational results are integral to the approach investigated and analysed. Manuscripts that, in the Editor’s view, do not satisfy these conditions will not be accepted for review. Numerical Linear Algebra with Applications receives submissions in areas that address developing, analysing and applying linear algebra algorithms for solving problems arising in multilinear (tensor) algebra, in statistics, such as Markov Chains, as well as in deterministic and stochastic modelling of large-scale networks, algorithm development, performance analysis or related computational aspects. Topics covered include: Standard and Generalized Conjugate Gradients, Multigrid and Other Iterative Methods; Preconditioning Methods; Direct Solution Methods; Numerical Methods for Eigenproblems; Newton-like Methods for Nonlinear Equations; Parallel and Vectorizable Algorithms in Numerical Linear Algebra; Application of Methods of Numerical Linear Algebra in Science, Engineering and Economics.