For questions about finding saddlepoints, critical points of a function which are not local extrema.

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### Matrices that achieve worst-case $LDL^T$ element growth

Matrices that achieve the worst case $\rho_n = 2^{n-1}$ element growth in LU factorization with partial pivoting are known; see e.g. Theorem 9.7 in Higham, Nicholas J., Accuracy and stability of ...
346 views

### Distributed Lagrange multiplier approach to impose constraint in Poisson equation

I'm trying to understand how Lagrange multipliers are applied in order to impose constraints in PDEs. Consider $B \subset \Omega$. For instance, a square inside another square domain $\Omega$. Let's ...
248 views

1 vote
37 views

### constrained zero-sum two person game

Finding the saddle point of a constrained zero-sum two-person game is equivalent to a resolution of primal-dual programs (with bi-linear objective function). I am looking for a free solver to compute ...
1 vote
133 views

### Parallelisation strategies for mixed FE formulations

Mixed FE formulations with LBB-stable elements require two different meshes for the primary and the constraint variables, for example, displacement and pressure. With continuous approximation for the ...
66 views

### Some formulations of domain coupling lead to saddle point problems. Is this merely an artifact?

Background I wanted to learn how to couple FEM and BEM (for the Poisson equation), because I wanted to better understand how open boundary conditions look like. Therefore I worked through the relevant ...
170 views

### Solving saddle point problem having non-invertible top-left block with a PETSc nested matrix

My system is a symmetric FE problem with lagrange multipliers: $Z=\begin{pmatrix}A & C^T \\ C & 0\end{pmatrix}$ The matrix $A$ is positive semi-definite, non-invertible. The whole matrix is ...
367 views

### Iterative linear solver for "ugly" saddle point system

I am a graduate student majoring scientific computing. The numeric model I made caused a very ugly-looking saddle-point linear system. It is not symmetric at all and I will attach the sparsity pattern ...
1 vote
155 views

### Simplest way to precondition Uzawa iteration

I have a diffusion problem with an internal circular dirichlet constraint and a side condition which shall enforce a certain global volume integral. $\nabla(D \nabla u(x)) = 0$ outer boundary ...
Given two Hilbert spaces $X$ and $Y$ and $a \colon X \times X \to \mathbb{R}$ as well as $b \colon X \times M \to \mathbb{R}$, both being continuous bilinear forms with $a(\cdot, \cdot)$ being ...
I am interested in numerically solving the following constrained minimization problem; Find the value of $x\in \mathbb{R}^n$ that minimizes $f$ where $f\colon \mathbb{R}^n\to \mathbb{R}$ is defined ...