本文選題：Grad-Shafranov方程　切入點(diǎn)：平衡重建　出處：《中國(guó)科學(xué)技術(shù)大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：在等離子體平衡重建迭代過(guò)程中,我們需要快速求解Grad-Shafranov(G-S)方程。在目前的EAST等離子體平衡重建PEFIT代碼中,采用五點(diǎn)差分方法通過(guò)離散正弦變換(DST)在65×65網(wǎng)格中進(jìn)行快速求解,當(dāng)網(wǎng)格進(jìn)一步擴(kuò)展到更精細(xì)的129x129或257x257時(shí),其需要耗費(fèi)的時(shí)間將成倍增長(zhǎng),將嚴(yán)重影響等離子體平衡重建的實(shí)時(shí)性。本文開(kāi)展了多種改進(jìn)算法的研究,并采用具有四階精度的緊致差分格式離散化G-S方程,并在此基礎(chǔ)上通過(guò)DST方法快速求解,獲得更好的加速比,并成功應(yīng)用到PEFIT代碼中。本文首先描述了低網(wǎng)格下基于GPU的多重網(wǎng)格方法加速,在串行條件下,多重網(wǎng)格方法要優(yōu)于DST方法,但多次實(shí)踐證明,在使用GPU加速后多重網(wǎng)格算法并沒(méi)有提供好的加速比。通過(guò)經(jīng)驗(yàn)總結(jié),證明多重網(wǎng)格算法無(wú)法滿足實(shí)時(shí)要求。本文著重描述了如何構(gòu)造具有四階精度的緊致差分格式的Grad-Shafranov離散方程,并使用DST技術(shù)進(jìn)行快速求解,實(shí)現(xiàn)基于緊致差分格式的快速G-S方程求解。結(jié)果表明,在65 × 65網(wǎng)格下,在給定方程右端項(xiàng)電流分布的前提下,使用GPU求解G-S方程所需時(shí)間大約為34μs。此外,本文還提出了一種擴(kuò)展網(wǎng)格剩余節(jié)點(diǎn)值的估算方法。目前Grad-Shafranov方程用于實(shí)時(shí)算法是在二維空間下進(jìn)行的,而Grad-Shafranov方程屬于線性橢圓偏微分方程的一種,本文嘗試了將離散正弦變換技術(shù)應(yīng)用到規(guī)則區(qū)域內(nèi)三維空間下橢圓偏微分方程的快速求解方法中,并使用了 CUDA進(jìn)行了加速。
[Abstract]:In the iterative process of plasma equilibrium reconstruction, we need to solve the Grad-Shafranov-G-S) equation quickly. In the current EAST plasma equilibrium reconstruction PEFIT code, the five-point difference method is used to solve the problem in 65 脳 65 grids by discrete sinusoidal transform. When the grid is further extended to the finer 129x129 or 257x257, the amount of time it takes will increase exponentially, which will seriously affect the real-time performance of plasma equilibrium reconstruction. The G-S equation is discretized by a compact difference scheme with fourth-order accuracy. On this basis, a better speedup can be obtained by solving the G-S equation quickly by the DST method. And successfully applied to PEFIT code. Firstly, this paper describes the acceleration of multigrid method based on GPU in low grid. Under serial condition, multigrid method is superior to DST method, but it has been proved by practice many times. The multigrid algorithm with GPU acceleration does not provide a good speedup. It is proved that the multigrid algorithm can not meet the real-time requirements. This paper mainly describes how to construct Grad-Shafranov discrete equations with fourth-order precision compact difference scheme, and use DST technique to solve them quickly. The fast solution of G-S equation based on compact difference scheme is realized. The results show that under the condition of 65 脳 65 grid and given current distribution at the right end of the equation, the time required to solve G-S equation using GPU is about 34 渭 s. In this paper, a new method for estimating the residual node value of extended grid is proposed. At present, the Grad-Shafranov equation is used in two dimensional space, and the Grad-Shafranov equation is a kind of linear elliptic partial differential equation. In this paper, the discrete sinusoidal transform technique is applied to the fast solution of elliptic partial differential equations in three dimensional space, and CUDA is used to accelerate it.
【學(xué)位授予單位】：中國(guó)科學(xué)技術(shù)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O241.8;O53

【參考文獻(xiàn)】

相關(guān)期刊論文 前9條

1 張一鳴;曾麗萍;沈欣媛;張利;丁亞清;肖成馨;康衛(wèi)紅;王海;;ITER計(jì)劃與聚變能發(fā)展戰(zhàn)略[J];核聚變與等離子體物理;2013年04期

2 魯晶津;吳小平;Klaus Spitzer;;三維泊松方程數(shù)值模擬的多重網(wǎng)格方法[J];地球物理學(xué)進(jìn)展;2009年01期

3 葛永斌;田振夫;馬紅磊;;三維泊松方程的高精度多重網(wǎng)格解法[J];應(yīng)用數(shù)學(xué);2006年02期

4 李傳亮,孔祥言;線性橢圓型方程的數(shù)值網(wǎng)格生成方法[J];水動(dòng)力學(xué)研究與進(jìn)展(A輯);2000年02期

5 田振夫;求解泊松方程的高精度緊致差分方法[J];黃淮學(xué)刊(自然科學(xué)版);1998年S4期

6 吳小平,徐果明,李時(shí)燦;利用不完全Cholesky共軛梯度法求解點(diǎn)源三維地電場(chǎng)[J];地球物理學(xué)報(bào);1998年06期

7 田振夫;泊松方程的高精度三次樣條差分方法[J];西北師范大學(xué)學(xué)報(bào)(自然科學(xué)版);1996年02期

8 王殿輝;;三維Poisson方程的差分解[J];鞍山鋼鐵學(xué)院學(xué)報(bào);1988年04期

9 郭雯;三維Poisson方程的直接解法[J];福州大學(xué)學(xué)報(bào);1982年04期

相關(guān)碩士學(xué)位論文 前2條

1 郭曉天;科大反場(chǎng)箍縮實(shí)驗(yàn)裝置（KTX）誤差場(chǎng)主動(dòng)控制系統(tǒng)原型設(shè)計(jì)[D];中國(guó)科學(xué)技術(shù)大學(xué);2016年

2 羅正平;托卡馬克中等離子體平衡計(jì)算[D];合肥工業(yè)大學(xué);2007年

，

本文編號(hào)：1581419