1、21211221()()dmin(),()xxyJ y xl y xxy xyy xyyB(x2,y2)dsdxxA(x1,y1)Oy21122212()dmin()0,()xxygyJ y xxy xy xy 21()(,)dminxxJ y xF x y yx122()0,()y xy xy 21(,)(,)dxxJJ yyJ yF x yy yyF x y yx 2122222221!()()22dxxFFFFFyyy yyyyyyy yyx 23JJJJ0()(0)0 0()(0)0 21(),(,),(,)dxxF x y xy xx 21,(,)(),(,)(,)xxyF x y
2、xy xy x ,(,),(,)(,)dyF x y xy xy xx21,(),()(),(),()()dxyyxF x y xy xxFx y xy xxx0()(0)0 0()21d0 xxFFyyyyx21d0 xxFFyyyyx21d xxFFyyyyx21d0 xxFFyyx21d0 xxFFyyyyxdd0()FFyyx 122()0,()y xy xy()(,)d0()()xyzvsbJ uFu uu uvufrrrrr()(,)dminxyzvJ uFu u uuvrr()()sbufrrr0()()()()()()xyzsbFFFFuxyzvufuuurrrr()(,)d(
3、,)dminxyzvsJ uFu uu uvBusrrr 0()0()cos(,)cos(,)cos(,)()()()nxnynzyzyzxxFFFFuxuyuzuFFFBuuuuvsrre ee ee e图5-2 场域D的三角元剖分示意图DyxOLi(xi,yi)m(xm,ym)j(xj,yj)Lee 的前提下，的前提下，()e()()(,)11zDAAzzJ y22AA0(,)()LbAzA r20122 d d2d d()DDLbJ AzzAABJAr 123(,)eeeAzNAz(x,y)ez 或或()e，则由则由y)(11AAzzJ 11ZZzAyAxxyJ 1AJ121212012
4、(,)()()LLLLLbLbx yDuuxxyyuunnunfuuuuqrr 0210d1()d dd ddmin()BDLDLbB BJ ux yfu x yqu luu r0210d1()d dd ddmin()BDLDLbB BJ ux x yfu x yqu luu rK(u)u=P 图5-6 规则平面域的自动剖分xy1201191 2118117116115114113112111110109108107106711416 223610152128125 10491636(15,0)(5,0)2627282930(20,0)图5-7 圆形域的自动剖分mmijji自动细分str图5-
5、8 三角元的一次细分24681357(a)mjiji细分细分jmirstmjirst(b)图5-9 (a)原始规范化的剖分 (b)、两类单元mm12234131345 556677889910101111121213141414151516161719201832313132(a)mm图5-10 (a)一次细分后的形态 (b)规范化后的一次细分1sAjAJ 1sAAtJ 22112()2d dsDJ AAjAJ Ax y KAjAPT()d d1eeijDeeeejjiiNNNNxxyyKx yd deeeeijijDTN Nx yd deeelslDPJ Nx y222220 xy 22zz
6、HH 2zk H 22zzEk E 222220(,)00LLx yDxyn 对于TE波：对于TM波：22212()d d(,)d dxyDDJx yfx yx y 2222()()d dmin12DxyJx y 2 KTd d()eeijDeeeejjiiNNNNxxyyKx yd deeeeijijDTN Nx y2cf 2c11221()11eiiiijjmmxyNab xc yxyxy1211iijjmmxyxyxy 122iieiSSNjejSNmemSN1,0eeeijmNNNOxm(xm,ym)j(xj,yj)i(xi,yi)P(x,y)SiSjSm三角元eNi=Si/Ni=0Ni=1 单元形状函数Nse(x,y)的几何意义1eeeijmNNN(0,0)(1,0)(0,1)e 局部坐标系图示eiNejN01,01eeejijNNN 2,()(),1124eeiieejjiijjeeijNNx yNNxyNNxyabab,()(),2eeijx yNN
