convergence problem when using the weak constraint on Dirichlet boundary

Thu, 02 Sep 2010 23:28:41 +0000

Hi,

I am recently building a semiconductor device model (similar but not identical to the MOSFET model in the library), which include the poisson equation and diffusion equation. I set the voltage at certain boundary (Dirichlet), and try to get the current. According to the manual, the lagrangian multiplier in a weak constraint would be an accurate representation of the flux. But when I try to use the weak constraint and solve the lagrangian multiplier, the model does not converge. The log file would be something like below:

Iter ErrEst Damping Stepsize #Res #Jac #Sol
1 1.2e-005 1.0000000 43 101 56 153
2 6.3e-006 1.0000000 1.2e-005 102 57 155
3 5.8e-006 1.0000000 6.3e-006 103 58 157
4 4.9e-006 1.0000000 5.8e-006 104 59 159
5 4.7e-006 1.0000000 4.9e-006 105 60 161
6 3.6e-006 0.2422812 4.7e-006 107 61 164
7 2.9e-006 0.1835810 3.6e-006 109 62 167
8 2.5e-006 0.1498790 2.9e-006 111 63 170
9 2.2e-006 0.1274153 2.5e-006 113 64 173
10 1.9e-006 0.1111807 2.2e-006 115 65 176
11 1.7e-006 0.1000000 1.9e-006 117 66 179
12 1.6e-006 0.1000000 1.7e-006 119 67 182
13 1.4e-006 0.1000000 1.6e-006 121 68 185
14 1.3e-006 0.1000000 1.4e-006 123 69 188
15 1.1e-006 0.1000000 1.3e-006 125 70 191
16 1e-006 0.1000000 1.1e-006 127 71 194
17 9.2e-007 0.1000000 1e-006 129 72 197
18 8.3e-007 0.1000000 9.2e-007 131 73 200
19 7.5e-007 0.1000000 8.3e-007 133 74 203
20 6.7e-007 0.1000000 7.5e-007 135 75 206
21 6.1e-007 0.1000000 6.7e-007 137 76 209
22 5.5e-007 0.1000000 6.1e-007 139 77 212
23 4.9e-007 0.1000000 5.5e-007 141 78 215
24 4.4e-007 0.1000000 4.9e-007 143 79 218
25 4e-007 0.1000000 4.4e-007 145 80 221

Errest keeps decreasing but does not stop. If I increase the MaxIter, the ErrEst will go to even 1e-10 but it still not converge. If I do not use weak constraint, the model has no problem to converge. I tried to manually scale the lagrangian multiplier, since the order of magnitude of lm is much different from other varibles, but still no success. I am wondering anyone has seen similar convergence problem when using the weak constraint before? Any solution to this problem?

Thanks,

Wei

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convergence problem when using the weak constraint on Dirichlet boundary