Dear All,
I met the exactly same problem as you described.
I am working on 3 coupled PDEs, two from the Joule heating, one PDE form diffusion-drift equation.
The domain is a rectangle.
The boundary condition for the Diffusion-Drift is Zero flux on all edges.
The initial condition for the diffusion-drift is 1E27 [m^-3] in the left half domain and 0 for the right half.
The solver is time dependent with constant damping factor Newton's method and a MUMPS linear solver.
The issue:
Negative concentration keeps to present.
The approaches I have tried:
(1) C=if(c<0,eps,c). No problems caused by negative ion concentration. However, there is a time step within which the maximum iterations of (constant damping) newton's method has been reached. (Resolved by C=if(c<0,1E25,c))
(2) Ultra dense mesh+Boundary mesh layer. Problem "NaN or Inf found" in the linear MUMPS solver. And the speed is so slow that I believe segregated solver has to be implemented.
(3) As the diffusion drift equation is implemented in the PDE interface, there is no stabilization option, although the Joule heating equations are of available stabilization options.
(4) Put a background ion concentration for the right half domain. However, when time increases, there will be negative ion concentration in some regions of the left-half domain.
Can any one help? Many many thanks in advance.
I met the exactly same problem as you described.
I am working on 3 coupled PDEs, two from the Joule heating, one PDE form diffusion-drift equation.
The domain is a rectangle.
The boundary condition for the Diffusion-Drift is Zero flux on all edges.
The initial condition for the diffusion-drift is 1E27 [m^-3] in the left half domain and 0 for the right half.
The solver is time dependent with constant damping factor Newton's method and a MUMPS linear solver.
The issue:
Negative concentration keeps to present.
The approaches I have tried:
(1) C=if(c<0,eps,c). No problems caused by negative ion concentration. However, there is a time step within which the maximum iterations of (constant damping) newton's method has been reached. (Resolved by C=if(c<0,1E25,c))
(2) Ultra dense mesh+Boundary mesh layer. Problem "NaN or Inf found" in the linear MUMPS solver. And the speed is so slow that I believe segregated solver has to be implemented.
(3) As the diffusion drift equation is implemented in the PDE interface, there is no stabilization option, although the Joule heating equations are of available stabilization options.
(4) Put a background ion concentration for the right half domain. However, when time increases, there will be negative ion concentration in some regions of the left-half domain.
Can any one help? Many many thanks in advance.