Linked Questions

52
votes
4answers
8k views

What guidelines should I follow when choosing a sparse linear system solver?

Sparse linear systems turn up with increasing frequency in applications. One has a lot of routines to choose from for solving these systems. At the highest level, there is a watershed between direct (...
23
votes
1answer
12k views

Why is Newton's method not converging?

I am using PETSc's nonlinear solver package SNES to solve a system of nonlinear equations obtained by discretizing a partial differential equation. How can I determine why the solver is not converging ...
15
votes
3answers
835 views

What is a scalable preconditioner for high-frequency Helmholtz?

Standard multigrid and domain decomposition methods do not work, but I have large 3D problems and direct solvers are not an option. What methods should I try? How are my choices affected by the ...
13
votes
2answers
2k views

Which preconditioners (and solver) in PETSc for indefinite symmetric systems should I use?

My system is a symmetric FE problem with lagrange multipliers (e.g. incompressible Stokes' flow): \begin{pmatrix}A & B^T \\ B & C\end{pmatrix} where $C = 0$ is the typical case (I have even ...
15
votes
1answer
4k views

How can I estimate the condition number of a large sparse matrix using PETSc?

I have a PETSc Mat and would like to estimate its condition number.
3
votes
1answer
860 views

Full Multigrid convergence is too slow. What could possibly be causing it?

I've coded full multigrid in Matlab and it doesn't seem to be converging fast enough. When I increase the number of grids or the number of iterations, it converges to the analytical solution. But FMG ...
11
votes
1answer
458 views

How to establish that an iterative method for large linear systems is convergent in practice?

In computational science we often encounter large linear systems which we are required to solve by some (efficient) means, e.g. by either direct or iterative methods. If we focus on the latter, how ...
5
votes
1answer
409 views

Intersection of hyperplanes

A very basic question but i couldn't find another post about it: Given $p$ non parallel hyper-plane in $\mathbb{R}^p$: $\left(\begin{array}{cccc} c_{11} & a_{11} & .... & a_{1p} \\ ... &...
3
votes
2answers
1k views

Solving Newton-Raphson step with ill-conditioned sparse matrix

I am trying to build a complex simulator for the transport of mass & heat in porous media. I am currently following coarsely the algorithm laid out in an older software and have got the simulator ...
3
votes
1answer
366 views

Limitations of Domain Decomposition Method (DDM) in Finite Element Analysis (FEA)?

The use of DDM in FEA makes parallel solution of the whole analysis e.g. assembly, solver etc possible. DDM splits the model in domains and runs them in parallel. Since there are interconnected nodes ...
2
votes
1answer
99 views

What method to solve a sparse complex symmetric (non-Hermitian) system?

I have a sparse system (about 78% of zero entries) that is complex and symmetric (but not Hermitian). The following figure shows the structure of the problem. The off-diagonal blocks are incidence ...
2
votes
1answer
149 views

Number of GMRES iterations increase when stepping forward in time, using the Newton method

I am solving a system of nonlinear time-dependent equations using the Newton method in a finite-element-setting, i.e. first I create the jacobian matrix for the current time, and afterwards I try to ...
1
vote
1answer
87 views

Debugging Shell matrix

I am trying to solve complex valued Poisson equation $$(C + \nabla. D \nabla )u = f \text{ ;where C, D, u and f are complex numbers.} $$ I am breaking this eqn into real valued problem, which is of ...