# Questions tagged [numerics]

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### Remez algorithm convergence

I have implemented the Remez algorithm in Python where all calculations were done with the Python mpmath library. I have noticed that sometimes the $|E_{max}|$ and $|E_{min}|$ do not monotonically ...
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### Ill-condioned Linear System and Gaussian Elimination

Suppose that I have a linear system $Ax=b$ such that $A$ is ill-conditioned. Can I say that it is dangerous to find a solution with Gaussian Elimination for this system, or does there exist some class ...
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### How can I practice multivariable root-finding?

Recently, I've been reading up on various root-finding / optimization algorithms such as the Levenberg-Marquardt method, Gauss-Newton, Conjugate Gradient, trust-region and trust-region-dogleg. I've ...
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### Imposing pressure variation instead of Dirichlet boundary conditions on Finite Element Method

I always see Finite Element codes solving PDE with Dirichlet or Neumann boundary conditions. But, I have a problem now consisting of a straight cylinder with a circular base (a simple 3D tube), with ...
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### Solution of Cahn-Hilliard equation

I need to solve the Cahn-Hilliard equation $$\frac{\partial u}{\partial t} = \Delta(f(u) - \epsilon^2\Delta u), \hspace{.5cm}(x, t)\in \Omega\times(0, T],$$ using mixed formulation \...
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### Norm estimates if adjoints can't be computed

Assume that you have two linear maps $A$ and $V$. For a given $x$ (of appropriate dimension) you can compute $Ax$ numerically, and for any $y$ (of appropriate dimension) you can calculate $V^Ty$ ...
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### Accurate and efficient computation of the logarithm of the ratio of two sines

For exploratory work related to special function implementations, I need to compute $\log \frac{\sin y}{\sin x}$, where $0 \le x \le y \le 2x < \frac{\pi}{2}$. Cases with $x \approx y$ in ...
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### Parity for artificial dissipation term in a finite-difference solution

I have a doubt regarding the signal of the dissipative term in a finite difference solution for an equation of the form $$\frac{\partial u}{\partial x}+f(x)=0, u(0)=0$$ In which $f$ is an odd ...
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### numerical solution to pde on an ellipse

Looking for advice on discretization (preferably finite difference) schemes for pdes on curves in general, but in this case it is an ellipse (so given by $(a\cos(r), b\sin(r)$). The problem is the ...
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### Is Romberg integration method implemented as weighted function values numerically correct?

I have to integrate expression f(x) * g(x) for many different functions f but just one g. I ...
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The Gauss-Kuzmin distribution gives the probability of an integer appearing as a partial denominator in the continued fraction of a real number $x$ as $$P(a_k = k) = -\log_2\left(1 - \frac{1}{(k+1)^2}... 0answers 64 views ### Numerical calculation of the Berry connection I'm doing some numerical calculations involving Hermitian matrices, and derivatives of the eigenvectors. Essentially, I have an n x n, Hermitian matrix H(x), which is dependent on some continuous ... 1answer 113 views ### Accurately Computing a Positive Vector in the Nullspace of a Matrix I'm sure this question has been asked before yet after many hours of searching I am unable to find a definitive answer. The problem at hand is solving the linear system:$$A \mathbf{x} = \mathbf{0}$$... 1answer 146 views ### Red flags for numerical computing? I've learnt the hard way that you should avoid: computing small numbers as the difference of two large numbers evaluating chaotic functions with imprecise inputs. Are there any other red flags a ... 0answers 30 views ### At what l/d ratio will a frame element start to behave as a shell element? I'm working in ETABS. There are few columns of dimension 300mmx1400mm. The height of building is 36.6 meter above ground level and the dimension of building is 26mx68m. I'm getting the time period of ... 0answers 145 views ### A parallelized GMRES solver? My application calls for solving a dense, 40,000 x 40,000, ill-conditioned linear system. The native SciPy GMRES solver with preconditioning has worked well for my application and solving a single ... 0answers 81 views ### How to construct a Fortin Operator for Crouzeix-Raviart Element? I want to prove the LBB condition for the Stokes Equations discretised by the Crouzeix-Raviart element. The continuous Stokes Equation in the weak formulation is Find u \in H_0^1(\Omega, \mathbb{R}^... 0answers 36 views ### Simulating the response of nonlinear system with stiff differential equations I want to simulate the response of a nonlinear system given in the following form:$$ \dot{x_1} = f_1(\bar{x_1})+g_1(\bar{x_1})x_2, \ x_1(0) = 0.2  \dot{x_2} = f_2(\bar{x_2})+g_2(\bar{x_2})x_3, \...
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Abstract I have the next equation to find a force, for my problem: $$U=-\int \vec{m}\small{(x)}\times \vec{B}(x)dV$$ $$\vec{F}=-\nabla U$$ Considering 3-dimensional space with x,y,z coordinates, ...