Fast direct solver for Grad-Shafranov equation based on compact scheme

doi:10.16568/j.0254-6086.201801002

NUCLEAR FUSION AND PLASMA PHYSICS ›› 2018, Vol. 2 ›› Issue (1): 8-14.DOI: 10.16568/j.0254-6086.201801002

• Plasma Physics • Previous Articles Next Articles

Fast direct solver for Grad-Shafranov equation based on compact scheme

HU Jin-di1, 2, XIAO Bing-jia1, LUO Zheng-ping1, HUANG Yao1

(1. Institute of Plasma Physics, Chinese Academy of Science, Hefei 230031; 2. University of Science and Technology of China, Hefei 230026)

Received:2016-12-21 Revised:2017-10-22 Online:2018-03-15 Published:2018-03-15

基于紧致差分的Grad-Shafranov方程快速解法

胡金迪1, 2，肖炳甲1，罗正平1，黄耀1

(1. 中国科学院等离子体物理研究所，合肥230031； 2. 中国科学技术大学，合肥230031)

通讯作者: 罗正平(1983-)，男，安徽池州人，博士，主要从事等离子体控制研究。
作者简介:胡金迪(1991-)，男，安徽蚌埠人，硕士，主要从事CUDA并行计算研究。
基金资助:
国家磁约束核聚变发展研究专项(2014GB103000)；国家自然科学基金(11575245)

Abstract

Abstract:

In the process of iterative computation of plasma equilibrium reconstruction, it is needed to fast solve Grad-Shafranov (G-S) equation. A fourth-order compact scheme was constructed with discrete sine transform (DST) technique to solve G-S equation, and CUDATM was used to realize parallel acceleration. This method will be used in EAST plasma equilibrium reconstruction PEFIT code to fast solve G-S equation based on compact scheme. It turns out that in 65×65 mesh, if the right side current distribution is known, the time needed to solve G-S equation based on GPU is about 34μs.

Key words: Poisson equation, Grad-Shafranov equation, Solov’ev equation, Compact scheme, DST technique, CUDA

摘要：

在等离子体平衡重建迭代计算过程中，需要快速求解Grad-Shafranov方程(G-S方程)。构造了具有四阶精度紧致差分格式的离散方程，采用离散正弦变换技术对其进行快速求解并采用CUDATM实现GPU并行加速，将其应用到EAST等离子体平衡重建PEFIT代码中，实现基于紧致差分格式的快速G-S方程求解。结果表明，在65×65的网格下，给定方程右端项电流分布的前提下，使用GPU求解G-S方程所需时间为大约34μs。

关键词: 泊松方程；Grad-Shafranov方程；Solov&rsquo, ev方程；紧致差分格式；DST技术；CUDA

CLC Number:

TL61+2.3

HU Jin-di, XIAO Bing-jia, LUO Zheng-ping, HUANG Yao. Fast direct solver for Grad-Shafranov equation based on compact scheme[J]. NUCLEAR FUSION AND PLASMA PHYSICS, 2018, 2(1): 8-14.

胡金迪1, 2，肖炳甲1，罗正平1，黄耀1. 基于紧致差分的Grad-Shafranov方程快速解法[J]. 核聚变与等离子体物理, 2018, 2(1): 8-14.

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Fast direct solver for Grad-Shafranov equation based on compact scheme

基于紧致差分的Grad-Shafranov方程快速解法

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