Compression method for boundary integral matrices with translation-invariant kernel functions

具有平移不变核函数的边界积分矩阵的压缩方法

• 批准号: 455431879
• 负责人: Professor Dr. Steffen Börm
• 金额: --
• 依托单位: Mathematisches Seminar
• 依托单位国家: 德国
• 项目类别: Research Grants
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/455431879?language=en
• 关键词: Compression; method; boundary; integral; matrices

The proposed project aims to develop numerical methods for boundary integral equations that can handle the very fine meshes that appear, e.g., when dealing with complicated geometries or high-frequency scattering.The project focuses on two approaches: first, we intend to take advantage of the translation-invariance of the kernel function to reduce the storage requirements. While this is common practice in the context of particle methods, e.g., for fast multipole methods, is appears to be rare in the field of boundary element methods, since the more complicated shapes of the supports of the basis functions make it difficult to use simple bisection techniques. Second, we aim to adapt algebraic recompression algorithms to allow them to also take advantage of translation-invariance. Particularly for more complicated kernel functions arising, e.g., for high-frequency scattering, these recompression algorithms are very important, since they reduce the storage requirements by more than two orders of magnitude and allow us to treat fine meshes on affordable hardware.Compared to existing methods, the new technique does not require specially structure meshes, but will be able to handle fairly general unstructured meshes that appear, e.g., when dealing with applications in electrostatics, magnetostatics, or scattering.

拟议的项目旨在为边界积分方程开发数值方法，这些方程可以处理出现的非常细的网格，例如，在处理复杂的几何形状或高频散射时。尽管这在粒子方法的背景下是常见的做法，例如，对于快速多极方法，在边界元素方法领域似乎很少见，因为基本函数支持的更复杂的形状使得难以使用简单的分配技术。其次，我们旨在调整代数循环算法，以使其还可以利用翻译不变性。特别是对于更复杂的内核功能，例如，对于高频散射，这些恢复算法非常重要，因为它们将存储需求降低了两个以上的数量级，并且可以使我们能够在现有方法上使用不可或缺的方法，但在适用于现有的方法上，新技术不需要通常的结构，但是ERE不得不在现有方法上进行处理。在静电，磁静态或散射中。