[petsc-users] floating region help

[Gong Ding]

On Wed, Sep 21, 2011 at 05:51, Gong Ding<gdiso at ustc.edu> wrote:
The background of this problem is the single event upset simulation of CMOS unit circuit, i.e. SRAM, latch, flip-flop.
They all very big, ~ 1M mesh nodes. Direct method is too slow and memory consuming.
Some stupid commercial code needs more than one week to simulate one particle event.
 People usually need 100-1000 events to determine the circuit behavior!    
Fortunately，the problem is in time domain. the transport equation of carrier has a d/dt term which helps stable.
The most difficult part comes from metal connection. Just use above inverter, when both NMOS and PMOS are closed,
 the metal connection region has only displacement current from semiconductor region as eps*dE/dt, while metal region
the current can be written as sigma*E. The current conservation here is the boundary condition at the metal-semiconductor interface.
 (Since E is \frac{\partical phi}{\partical n}, here phi is the independent variable)
How much does the time step help? Given the description, I'd expect not much unless it's unreasonably short.
For a PNPN structure, the condition number in DC simulation is about 1e20.
A transient simulation with 1 us time step can reduce the condition number to 1e6. 
As a result, the floating problem of semiconductor region can simply be conqured with transient mode
My problem is a poisson's equation with highly heterogeneous conductance.
 
 
Obviously, sigma >> eps/T, the governing equation of phi has a large jump parameter at the metal/semiconductorinterface.
 The eigen value analysis confirmed that the number of samllest eigen value equals to the number of floating metal region.
And theeigen vector is exactly the floating region. 
Hmm, with a single low-energy mode, could you just start the Krylov method with a nonzero initial guess and make the initial guess exactly this mode. That would ensure that the Krylov space captures it exactly, and further iterations should all come from picking up the rest of the modes. Alternatively, you could formulate a modified system for which this mode was removed analytically.
For some paper I see that the balancing neumann neumann preconditioner also helps.
Can you give some suggestion?
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