| Author | Message | ||
     Ole Tar (oletar) New member Username: oletar Post Number: 1 Registered: 05-2007 |
Dear Sir, I'm a novice in FlexDDE. I'm trying to solve a problem related to the movement of sodium ions in glass under applied high voltage. It seems that the program (see text below) requires a huge amount of nodes, and I cannot solve it on my Pentium 4, 2 Ghz, 512 Mb RAM notebook. Could you help me to introduce some trick to decrease the number of nodes. Thanks, oletar TITLE 'Electric field and Na+ ion distribution: in a fiber with hole' SELECT errlim=1e-3 SMOOTHINIT = ON VARIABLES U NNa NO DEFINITIONS r0=62.5e-6 a=25e-6 b=15e-6 {dimensions, mkm} U_el=5000 {Applied voltage, V} mueNa=1e-15 {mobility of sodium ions} kb=1.38e-23 Temper=523 q=1.6e-19 eps=3.78 eps0=8.854e-12 Ni=8e21 {initial concentration of sodium ions} mueNO=0 mesh_spacing=1e-6 Ex=-dx(U) Ey=-dy(U) E=-grad(U) Em=magnitude(E) INITIAL VALUES NNa=ramp(sqrt(x**2+(y+25e-6)**2)-15e-6-0.5e-6,0,Ni,1e-6) NO=ramp(sqrt(x**2+(y+25e-6)**2)-15e-6-0.5e-6,0,Ni,1e-6) U=0 EQUATIONS U: div(grad(U))=-(q/(eps*eps0))*(NNa-NO) NNa: dt(NNa)=(mueNa*kb*Temper/q)*div( grad( NNa))+mueNa*DOT(grad(NNa),grad(U))-mueNa*NNa*(q/(eps*eps0))*(NNa-NO) NO: dt(NO)=0 BOUNDARIES region 'fiber' start 'electrode_2' (b,-a) value(U)=U_el*(1-exp(-5*t))**1 arc( center=0,-a) angle=360 start 'perimeter' (r0,0) value(U)=0 arc( center=0,0) angle=360 feature { a "gridding feature" to help localize the activity } start (0.02e-6,-a) arc( center=0,-a) angle=360 TIME from 0 to 100 FRONT(NNa-Ni/2,8e21) PLOTS for t=0 by 1 to 100 contour( U) painted contour( NNa) painted !surface( NNa) !contour( Em) painted surface( Em) elevation( NNa,-NO,NNa-NO) from (0,-10e-6) to (0,10e-6) elevation( U) from (0,-10e-6) to (0,10e-6) elevation( Ey) from (0,-10e-6) to (0,10e-6) !elevation( Em) on 'electrode_1' elevation( Em) on 'electrode_1' !vector( E) norm END | ||
| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 844 Registered: 06-2003 |
You have defined MESH_SPACING=1e-6. It takes about 25,000 cells to fill your figure with cells this size. If you don't want that many, don't ask for them. Because you have a very steep front propagating from the central hole, you should probably retain your MESH_SPACING=1e-6, but move it to a point after "Start 'electorde+2' (b,-a)" This will apply the mesh control only on the boundary of the hole, and not throughout the domain. Also, NO is unchanging (dt(NO)=0), so there is no point in treating it as a variable. Move the definition of NO to the DEFINITIONS section. Your "Feature" seems to be inside the inner circle, and is excluded, so you might as well remove it. With these changes, your problem runs with about 5000 nodes and uses about 18MB RAM. It still runs quite slowly, but this is probably because of the exponential shape imposed on U and the nonlinearity of the system. | ||
| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 845 Registered: 06-2003 |
PS The problem seems to run much more quickly with some hysteresis on U. I used for the U equation U: dt(U) = div(grad(U))-(q/(eps*eps0))*(NNa-NO) I don't know if this affects the solution. |