# Tagged Questions

Questions related to whether the sequence of iterates generated by an iterative method has one or more limit points, and if those limit points have the correct properties.

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### Interpreting convergence study results, fixed CFL

I am trying to determine the order of my numerical method for resolving a fluid-structure interaction problem using the immersed boundary method. I am using Crank-Nicolson to resolve the fluid ...
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### Dynamic Successive Over/under Relaxation (SOR) with several variables

I am solving a partial differential algebraic equation (PDAE) system which has the following dependent variables: $f=f(X,T)$ and $g=g(T)$, along with a few others My current method for coupling is ...
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### Finite element error for second order ODE at nodes equal to zero

I coded a finite element method with linear basis elements for the problem $$-u'' = f(x), x\in[0,1], u(0) = u(1) = 0$$ The nodes are uniformly spaced and I will denote them as $x_i$. I initially ...
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### Linear stationary iteration method

Suppose you are attempting to solve $Ax = b$ using linear stationary iteration method defined by $$x_k = G x_{k-1} + f$$ that is consistent with $Ax = b$, i.e., for which $f = (I - G)A^{-1}b$. Suppose ...
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### Efficient solution of large systems of non linear algebraic equations

I have quite simple problem of FEM solution of 1D differential non-linear equation. Altough the problem itself is simple, the numerical solution of the arising system of non-linear algebraic equations ...
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### Manufacturing a solution for non-smooth coefficients in elliptic problems

This question is a continuation of this answer (I can't comment) If we were going to manufacture a solution for a problem with discontinuous coefficients, I understand that the solution should have ...
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### slow convergence in displacement using newton method in nonlinear FEM

I have been running a code on crack propagation using phase-field, and viscosity is considered. My code works okay for low viscosity but runs into some converging issue when viscosity becomes high. ...
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### DIIS method to accelerate SCF convergence for stretched geometries

I am implementing from scratch an Hartree-Fock calculation in the STO-3G basis set to perform Born-Oppenheimer molecular dynamics. I have a Restricted Hartree-Fock procedure that can reproduce very ...
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### maltab ode solver- user defined criteria to stop calculations

is there a way to add a user defined convergence criteria to an ode solver so that the solution is stopped? I know that Matlab uses absolute and relative tolerances but would that suffice in solving ...
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### How to choose the number of random points in Monte Carlo simulations?

I am struggling with convergence criteria when performing a Monte carlo simulation on a uniform distribution. Any help would be much appreciated ! Say I want to sample uniformly a 1D interval (for ...
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### Finding rate of convergence by curve fitting in Matlab

I have some data: number of nodes $N$ and error in energy norm corresponing to it. I have seen in some references that the rate of convergence is reported by $$\| u-u_h\| _E=CN^{\alpha}$$ How can ...
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### Application of vector extrapolation methods to convergence to a steady state solution

I'm working on a fluid solver using dual-time stepping and everything works really well, except the convergence in pseudo-time is slow. I'd like to accelerate the convergence. I know multigrid methods ...
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### Temperature dependent 1-d conduction in Python?

I'm trying to write a Python code that is a numerical solver for 1-d heat conduction (using FVM) with a temperature dependent thermal conductivity. The solver has three functions I need to iterate ...
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### What are some reasons that Conjugate Gradient iteration does not converge?

I would greatly appreciate it if you could share some reasons the Conjugate Gradient iteration for Ax = b does not converge? My matrix A is symmetric positive definite. Thank you so much! Edit with ...
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### How to test convergence of an algorithm for constrained optimization

I am applying an iterative method (projected newton) to an optimization problem. Theoretically, the method should converge linearly. I would greatly appreciate it if you could share how should I test ...
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### Finite element convergence rates for mixed problems

I've coded up a Stokes Flow problem using finite elements and am in the process of verifying that it works. I'm just not sure what convergence rate I should be expecting as I globally refine the mesh. ...
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### Stationary phase approximation for an integral with infinity saddle points?

I need a hand with the numerical evaluation, in Mathematica, for this integral: $$f(t)=\int_{-\infty}^\infty Exp\{it(\omega_H-\omega_l-\omega_k) - \sum _{j\neq(l,k)} S_j [1-e^{-it\omega_j}]\}\, dt$$ ...
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### BFGS Fails to Converge

The model I'm working on is a multinomial logit choice model. It's a very specific dataset so other existing MNLogit libraries don't fit with my data. So basically, it's a very complex function ...