Implementation of the fast multipole expansion technique in the higher order bem 快速多極子展開技術(shù)在高階邊界元方法中的實(shí)現(xiàn)
Here are some references for nrqcd & nrqed : renormalization group scaling in nonrelativistic qcd on the multipole expansion , the qcd heavy quark potential to order v * * 2 : one loop matching conditions on matching calculations 11下面是非相對(duì)論性量子色動(dòng)力學(xué)和非相對(duì)論性量子電動(dòng)力學(xué)的一些參考資料:關(guān)于多極展開的非相對(duì)論性量子色動(dòng)力學(xué)中的重整化群定標(biāo),關(guān)于匹配計(jì)算的v * * 2階的量子色動(dòng)力學(xué)重夸克勢(shì):?jiǎn)稳ζヅ錀l件。
After solution of radiational and diffractional fluid field of asymmetrical sections by applying the multipole expansion method , wave loads on damaged ships are calculated by the linear strip theory under the non - upright floating condition , taking the effect on the heel angle and trimming angle caused by the damaged tank inundation below waterline into account 然后采用線性切片理論,計(jì)及水線以下破損后船舶由于艙室進(jìn)水產(chǎn)生的橫傾角與縱傾角的影響,利用多級(jí)展開法求解非對(duì)稱剖面的二維輻射和繞射流場(chǎng),計(jì)算了破損船體非正浮狀態(tài)條件下的波浪載荷。
The major work is as follows : solution of two dimensional radiation or diffraction fluid field . this thesis extends multipole expansion method to adapt to disturbed fluid fields of 2d floating bodies with asymmetric forms , which is applied with symmetric forms originally . and given the solution of potential velocity and hydrodynamic pressure of radiation and diffraction fluid fields , which is incited by a 2d arbitrary form , actual application field of the multipole expansion method has been enlarged 關(guān)于二維擾動(dòng)流場(chǎng)的求解:將通常僅適宜求解具有對(duì)稱形狀二維物體擾動(dòng)流場(chǎng)的多極展開法(保角變換方法)擴(kuò)展至非對(duì)稱形狀二維物體,給出了任意形狀二維物體的輻射和繞射流場(chǎng)的速度勢(shì)及水動(dòng)壓力的頻域解,進(jìn)一步擴(kuò)大了多極展開法的實(shí)際應(yīng)用范圍。
Secondly , proportional arc length method is used to conformal mapping process of asymmetry sections so as to solute the 2d radiation problem with the method of multipole expansion . on the basis of above , 3d hydrodynamic coefficients are given and motions of the container ship flokstra are predicted considering the initial heel 然后,采用比例弧法對(duì)全剖面進(jìn)行保角變換并在此基礎(chǔ)上用多極展開法計(jì)算非對(duì)稱剖面的輻射流場(chǎng),進(jìn)而采用切片理論合成全船的水動(dòng)力系數(shù)并對(duì)flokstra集裝箱船進(jìn)行了考慮橫傾影響的運(yùn)動(dòng)響應(yīng)預(yù)報(bào)。
百科解釋
A multipole expansion is a mathematical series representing a function that depends on angles ? usually the two angles on a sphere. These series are useful because they can often be truncated, meaning that only the first few terms need to be retained for a good approximation to the original function.