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.

拟议项目旨在开发边界积分方程的数值方法，这些方法可以处理出现的非常精细的网格，例如，当处理复杂的几何形状或高频散射。该项目集中在两个方法：第一，我们打算利用核函数的不变性，以减少存储需求。虽然这在粒子方法的上下文中是常见的实践，例如，对于快速多极方法，在边界元法领域中似乎是罕见的，因为基函数的支撑的更复杂的形状使得难以使用简单的二分技术。其次，我们的目标是适应代数再压缩算法，让他们也利用的不变性。特别是对于出现的更复杂的核函数，例如，对于高频散射，这些再压缩算法是非常重要的，因为它们将存储需求减少了两个数量级以上，并且允许我们在负担得起的硬件上处理精细网格。与现有方法相比，新技术不需要特殊结构的网格，但是将能够处理出现的相当一般的非结构化网格，例如，当处理静电学、静磁学或散射中的应用时。