sphere.edp

FreeFem++可以生成高质量的有限元网格。可以用于流体力学

mesh Th=square(10,20,[x*pi-pi/2,2*y*pi]);  //  $]\frac{-pi}{2},frac{-pi}{2}[\times]0,2\pi[ $
//  a paratrization of a sphere 
func f1 =cos(x)*cos(y);
func f2 =cos(x)*sin(y);
func f3 = sin(x);
//  de  partiel derivatrive of the parametrization DF
func f1x=sin(x)*cos(y);   
func f1y=-cos(x)*sin(y);
func f2x=-sin(x)*sin(y);
func f2y=cos(x)*cos(y);
func f3x=cos(x);
func f3y=0;
// $  M = DF^t DF $
func m11=f1x^2+f2x^2+f3x^2;
func m21=f1x*f1y+f2x*f2y+f3x*f3y;
func m22=f1y^2+f2y^2+f3y^2;

func perio=[[4,y],[2,y],[1,x],[3,x]];  // to store the periodic condition 

// the intial mesh
savemesh(Th,"sphere",[f1,f2,f3]);

real hh=0.1;
real vv= 1/square(hh);
verbosity=2;
Th=adaptmesh(Th,m11*vv,m21*vv,m22*vv,IsMetric=1,inquire=1,periodic=perio);
plot(Th,wait=1);
Th=adaptmesh(Th,m11*vv,m21*vv,m22*vv,IsMetric=1,periodic=perio);
plot(Th,wait=1);
Th=adaptmesh(Th,m11*vv,m21*vv,m22*vv,IsMetric=1,periodic=perio);
plot(Th,wait=1);
Th=adaptmesh(Th,m11*vv,m21*vv,m22*vv,IsMetric=1,periodic=perio);
savemesh(Th,"sphere-a",[f1,f2,f3]);
plot(Th,wait=1);
exec("ffmedit sphere-a");