# All Questions

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### Pivoted Cholesky vs Modified Cholesky

I am solving nonlinear least squares problems with the normal equations approach, so on each iteration, I need to solve: $$J^T J \delta = -J^T f$$ for the step $\delta$, where $J$ is a large (...
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### Relation between Stress/Strain and normal derivative of displacement

I calculated the stress $\sigma$ and strain $\varepsilon$ for a solid plate with dirichlet boundary conditions $u = g$, where $u$ is the displacement. With these I want to calculate $\nabla_n u = t$ ...
36 views

### Stokes Equation fails to converge for an ellipse

This might be because of the mesh, but the following code blows up for all values of b not 1. Does anybody have any experience working with the ellipse mesh in Fenics? ...
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### identifying peaks in data

I have data with peaks on some background, for example: The two prominent peaks at ~390 and ~450, as well as the much smaller peak at ~840. What are some options to programmatically find the position ...
83 views

### Plug-and-go Clebsch-Gordan computation in python?

I started a little project in python, under the assumption that it would be easy to find a routine for numerically computing Clebsch-Gordan coefficients in some library such as scipy. When it came ...
78 views

### Finite difference methods

I am currently applying the finite difference method to the solution of the diffusion equation. I think that a problem has occurred, and is as follows, my explicit method is the most accurate when ...
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### Single-variable multimodal derivative-free optimization (for a well-behaved function)

Are there well-established approaches to single-variable multimodal optimization? Given $f:\mathbb{R}\rightarrow\mathbb{R}$ that: has several local minima within a given range of interest $[a,b]$ is ...
47 views

### Numerically Approximating the Jacobian and Comparing the Eigenvalues With Analytical Form

I am trying to study the stability of numerical discretization schemes using the Jacobian matrix of the residues with respect to the vector of conserved variables. For a simple diffusion equation ...
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### How to use MeshFunction in FEniCS (dolfin)?

I'm a beginner user of FEniCS and still struggling with some of the basics. Specifically, I have some issues doing the tutorials in the Langtangen-Logg book Solving PDEs in Python - The FEniCS ...
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### Changing geometry scale breaks simulation

I'm trying to find the capacitance matrix for a small array of metal boxes in air using Comsol 5.4. The geometry presented here is a simple geometry that recreates the problem I'm experiencing. ...
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### Stability of SVD, Eigendecompositions, and pseudoinverse procedures in modern LAPACK routines

I have proposed an optimisation algorithm which I claim has improved upon the previous algorithm in a number of ways. One of these claims is that my proposed solution requires no explicit SVD and ...
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### How to add extra constraints to a linear system for probabilities？

Background： I have an equation which looks like as follows: $W \times P = R$ \left[\begin{array} &{1}&{0}&{0}&-\frac{w_{1}}{w_{o1}} &\dots &{0} &-\frac{w_{1}}{w_{0} } \...
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### How to justify using available code (in different language) for comparing algorithms

I have proposed an algorithm for a scheduling problem in a submitting paper. In the revision, the reviewer asked us to compare with another algorithm from the literature. Our algorithm is in MATLAB, ...
66 views

### User friendly scipy optimize wrapper package?

I'm creating too much throw away code for interfacing with the scipy optimize package in a user friendly way. (See code below for example of interruptible optimization that keeps last optimization ...
Please consider the assignment I have uploaded on the picture. I am confused about the functions $g_L(t)$, $g_R(t)$ and $\eta(x)$. What are they and how do I find them... My question: Is it possbile ...
I am trying to find the solution of linear advection equation of the form: $\frac {\partial c}{\partial t}+u\frac {\partial c}{\partial x}=0$ $c(x,0)=0$ \$c(0,t)=\{c_0 \ \text{for}\ t \leq t_1 \text{...