Re: [petsc-users] Preconditioning of Liouvillian Superoperator

2024-02-01 Thread Barry Smith
> On Feb 1, 2024, at 6:57 AM, Niclas Götting > wrote: > > Thank you very much for the input! > > I've spent a lot of time to compress the linear system to a quarter of its > size. This resulted in a form, though, which cannot be represented by > Kronecker products. Maybe I should return

Re: [petsc-users] Preconditioning of Liouvillian Superoperator

2024-02-01 Thread Niclas Götting
Thank you very much for the input! I've spent a lot of time to compress the linear system to a quarter of its size. This resulted in a form, though, which cannot be represented by Kronecker products. Maybe I should return to the original form.. The new structure of the linear system is as

Re: [petsc-users] Preconditioning of Liouvillian Superoperator

2024-01-31 Thread Barry Smith
For large problems, preconditioners have to take advantage of some underlying mathematical structure of the operator to perform well (require few iterations). Just black-boxing the system with simple preconditioners will not be effective. So, one needs to look at the Liouvillian

Re: [petsc-users] Preconditioning of Liouvillian Superoperator

2024-01-31 Thread Matthew Knepley
On Wed, Jan 31, 2024 at 8:21 AM Mark Adams wrote: > Iterative solvers have to be designed for your particular operator. > You want to look in your field to see how people solve these problems. > (eg, zeros on the diagonal will need something like a block solver or maybe > ILU with a particular

Re: [petsc-users] Preconditioning of Liouvillian Superoperator

2024-01-31 Thread Mark Adams
Iterative solvers have to be designed for your particular operator. You want to look in your field to see how people solve these problems. (eg, zeros on the diagonal will need something like a block solver or maybe ILU with a particular ordering) I don't personally know anything about this

[petsc-users] Preconditioning of Liouvillian Superoperator

2024-01-31 Thread Niclas Götting
Hi all, I've been trying for the last couple of days to solve a linear system using iterative methods. The system size itself scales exponentially (64^N) with the number of components, so I receive sizes of * (64, 64) for one component * (4096, 4096) for two components * (262144, 262144) for