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Implicit Multi-Scale Plasma Simulations Using Low Cost Matrix-Free Methods for Partial Differential Equations

使用低成本无矩阵方法进行偏微分方程的隐式多尺度等离子体模拟

基本信息

批准号：
1912183
负责人：
Andrew Christlieb
金额：
$ 25万
依托单位：
Michigan State University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2019
资助国家：
美国
起止时间：
2019-08-01 至 2023-07-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1912183&HistoricalAwards=false
关键词：
Implicit Multi Scale Plasma Simulations

项目摘要

The Carrington event of 1859 was a massive solar flair that hit the earth and left large amounts of charged particles trapped in the earth's magnetic field. These charged particles created large currents that coupled to the telegraph wires via an inductive coupling, as what happens in transformers. The currents that were pushed through the telegraph wires were so large they caused the telegraph machines to explode. If this were to happen today, unless we know to turn off and disconnect the power grid, such an event would destroy modern power infrastructure. Yet solar flairs happen all the time, we can't simply turn off the power grid every time one happens. From the time of detection, it takes 3 days for a solar flair to travel the distance to the earth. Predicting if a solar flair will hit the earth is currently done with low resolution models, which are not particular good at predicting these events. Increasing the accuracy to include more physics in the calculation leads to bigger calculations that simply can't be done in three days, even on modern super computers with state of the art methods. This project centers on creating a new class of methods that could make these calculations possible. One way to begin to address the issues of simulating problems with a significant number of time scales is to use implicit solvers. These typically lead to large systems of implicitly coupled equations. The main bottleneck in scalable solvers for such systems is in the communication and large number of interactions that are needed to solve these systems. In this project we are pursuing a new paradigm that solves coupled systems of non-linear PDEs, it is important to note that the pieces of the operators are typically linear. We have developed a strategy of expanding these pieces of the operators as global convolutions that give unconditional stability when combined with explicit time stepping methods, but can be cheaply evaluated with three term recurrence relations and avoids iteration. This approach has led to unconditionally stable solvers for problems such as degenerate advection diffusion or the Hamilton Jacobi equations. Here we are working to extend these methods to systems of PDEs.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

1859年的卡林顿事件是一次巨大的太阳耀斑，它撞击了地球，留下了大量被困在地球磁场中的带电粒子。这些带电粒子产生了巨大的电流，通过电感耦合耦合到电报线，就像变压器中发生的那样。通过电报线的电流是如此之大，以至于导致电报机爆炸。如果这种情况发生在今天，除非我们知道关闭和断开电网，否则这样的事件将摧毁现代电力基础设施。然而，太阳耀斑一直在发生，我们不能简单地在每次发生时关闭电网。从被探测到的时间算起，太阳耀斑需要3天的时间才能到达地球。目前，预测太阳耀斑是否会袭击地球是通过低分辨率模型进行的，这些模型并不特别擅长预测这些事件。提高精度以在计算中包括更多的物理学导致更大的计算，即使在具有最先进方法的现代超级计算机上，也无法在三天内完成。这个项目的中心是创建一个新的方法类，可以使这些计算成为可能。开始解决具有大量时间尺度的模拟问题的一种方法是使用隐式求解器。这些通常导致隐式耦合方程的大系统。可扩展求解器的主要瓶颈是解决这些系统所需的通信和大量的交互。在这个项目中，我们正在追求一个新的范式，解决耦合系统的非线性偏微分方程，重要的是要注意，件的运营商通常是线性的。我们已经制定了一个战略，扩大这些作品的运营商作为全球卷积，提供无条件的稳定性时，结合显式时间步进方法，但可以便宜地评估与三项递归关系，并避免迭代。这种方法已经导致了无条件稳定的求解问题，如退化平流扩散或汉密尔顿雅可比方程。在这里，我们正在努力将这些方法扩展到PDE系统。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

项目成果

期刊论文数量（6）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

Order enhanced finite volume methods through non-polynomial approximation

通过非多项式逼近阶增强有限体积法

DOI：
10.1016/j.jcp.2023.111960
发表时间：
2023
期刊：
Journal of Computational Physics
影响因子：
4.1
作者：
Christlieb, Andrew J.;Sands, William A.;Yang, Hyoseon
通讯作者：
Yang, Hyoseon

A Kernel-Based Explicit Unconditionally Stable Scheme for Hamilton-Jacobi Equations on Nonuniform Meshes

DOI：
10.1016/j.jcp.2020.109543
发表时间：
2020-02
期刊：
ArXiv
影响因子：
0
作者：
A. Christlieb;William A. Sands;Hyoseon Yang
通讯作者：
A. Christlieb;William A. Sands;Hyoseon Yang

High-Order Semi-Lagrangian WENO Schemes Based on Non-polynomial Space for the Vlasov Equation

DOI：
10.1007/s42967-021-00150-5
发表时间：
2021-08
期刊：
Communications on Applied Mathematics and Computation
影响因子：
1.6
作者：
A. Christlieb;M. Link;Hyoseon Yang;Ruimeng Chang
通讯作者：
A. Christlieb;M. Link;Hyoseon Yang;Ruimeng Chang

Kernel Based High Order “Explicit” Unconditionally Stable Scheme for Nonlinear Degenerate Advection-Diffusion Equations

DOI：
10.1007/s10915-020-01152-w
发表时间：
2017-07
期刊：
Journal of Scientific Computing
影响因子：
2.5
作者：
A. Christlieb;Wei Guo;Yan Jiang;Hyoseon Yang
通讯作者：
A. Christlieb;Wei Guo;Yan Jiang;Hyoseon Yang

Parallel Algorithms for Successive Convolution

连续卷积的并行算法

DOI：
10.1007/s10915-020-01359-x
发表时间：
2021
期刊：
Journal of Scientific Computing
影响因子：
2.5
作者：
Christlieb, Andrew J.;Guthrey, Pierson T.;Sands, William A.;Thavappiragasm, Mathialakan
通讯作者：
Thavappiragasm, Mathialakan