I am trying to solve a multiphase cahn hilliard equation with an obstacle potential. So I have an energy functional. However, the linear inequality arises when I eliminate one of the phase variables. So, the variables are phi1,phi2, phi3 , mu1,mu2 and mu3. with ,0<phi1,phi2,phi3<1 and phi1+phi2+phi3 =1 . If I get rid of phi3 and mu3, I get an additional constraint 0 < phi1+phi2 < 1 , which I just added to the lagrangian with a multiplier.
> From: [email protected] > To: [email protected]; [email protected] > CC: [email protected] > Subject: Re: [petsc-users] Extending PETSC-SNES-VI to linear inequality > constraints, > Date: Mon, 23 Dec 2013 21:27:57 -0700 > > subramanya sadasiva <[email protected]> writes: > > > Hi, Is it possible to extend PETSC-SNES VI to handlie linear > > inequality constraints. My problem has 4 variables . 2 of them have > > bounds constraints, as well as a linear inequality. At present I've > > implemented an augmented lagrangian method to handle the linear > > inequality and I let SNES VI handle the bounds constraints. However, > > the convergence of this method is very poor. I'd like to know if there > > was an easy way to get SNES VI to handle the linear inequalities as > > well. Thanks, > > This would be a useful extension, though I think nonlinear inequality > constraints may ultimately be necessary. We are integrating TAO as a > module in PETSc, which will help with problem formulation. > > Does your problem have an "energy" or objective functional, or is it a > general variational inequality?
