9k 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 (...
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15k 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 ...
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947 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 ...
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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 ...
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### 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.
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1k 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 ...
579 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} \\ ... &...
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### 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 ...
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507 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 ...
492 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 ...
345 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 ...
632 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 ...
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1 vote
365 views

### Python libraries for larges scale optimization/rootfinding

I have been dealing with the standard libraries of scipy.optimize for rootfinding and optimization problems, but the problems i want to solve are very large, which makes the standard solvers run out ...
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1 vote
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 ...