多尺度偏微分方程的小波解法
The solution of multi-scale partial differential equations using wavelets
摘要：
波函数是一种强大的新的数学工具，它提供了以自然的方式处理以几个长度尺度为特征的量的可能性。在这篇文章中，我们将展示如何小波可以用来解决偏微分方程表现出广泛变化的长度尺度，因此很难访问其他数值方法。作为基准计算，我们求解了三维铀二聚体的泊松方程。在这种情况下，电荷分布的长度尺度变化了4个数量级。使用提升插值小波的迭代次数是独立的最大分辨率和计算工作量，因此严格线性缩放相对于系统的大小。
英文摘要：
Wavelets are a powerful new mathematical tool which offers the possibility to treat in a natural way quantities characterized by several length scales. In this article we will show how wavelets can be used to solve partial differential equations which exhibit widely varying length scales and which are therefore hardly accessible by other numerical methods. As a benchmark calculation we solve Poisson's equation for a 3-dimensional Uranium dimer. The length scales of the charge distribution vary by 4 orders of magnitude in this case. Using lifted interpolating wavelets the number of iterations is independent of the maximal resolution and the computational effort therefore scales strictly linearly with respect to the size of the system.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
