Top new questions this week:
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I have a matrix of the form: $M:=\begin{pmatrix} S_1 & & & \\\ Q_1 & S_2 & & \\\ & … & … & \\\ & & Q_n & S_n\end{pmatrix}$ where the blocks …
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I am currently trying to familiarise myself with (Pseudo-)Spectral Methods for solving differential equations. Now, I am struggling to understand some obviously crucial concept of this approach. The …
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I am using backtracking linesearch to globalize a (semismooth) newton solver to minimize a (strongly semismooth) strongly convex function , and I am observing something strange (which may be a bug). …
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I’ve made a previous question here and also in SO wondering why only the fsolve solver converges for the simple one dimensional unsteady conduction problem $$ \frac{\partial T}{\partial t} = \alpha \…
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I am looking for an element for FEM that is piecewise $C^1$ continuous across triangles (i.e. $C^1$ continuous on the edge separating 2 triangles of the mesh). I have heard about the Bell element: …
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Suppose I’m solving $Ax=b$ for dense $m\times d$ matrix $A$. For which $A$ is this hard to do? More concretely, is there any work on estimating the error after $k$ steps of iterative solver, $k\le d$, …
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I am trying to solve the following differential equation in the domain of $\theta \in [0, 2 \pi]$ using finite differences scheme: For $0< \theta \leq \pi$ \begin{align} \rho_i^{n+1}=\rho_i^{n}+D\…
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Greatest hits from previous weeks:
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As I understand it, since a solution to a linear program always occurs at a vertex of its polyhedral feasible set (if a solution exists and the optimal objective function value is bounded from below, …
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According to Nocedal & Wright’s Book Numerical Optimization (2006), the Wolfe’s conditions for an inexact line search are, for a descent direction $p$, Sufficient Decrease: $f(x+\alpha p)\le f(x)+…
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I tried to solve a simple Kepler problem numerically. I have discrete time steps, a starting position $(x_0,y_0)$ and starting velocity $(u_0, v_0)$. I used this iteration by calculating the forces …
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Suppose $$\begin{align*} \min A &\mathrm{vec}(U) \\ &\text{subject to } U_{i,j} \leq \max\{U_{i,k}, U_{k,j}\}, \quad i,j,k = 1, \ldots, n \end{align*}$$ where $U$ is a symmetric $n\times …
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I am a mechanical engineer, intermediated/advanced level in MATLAB and MATHEMATICA, and beginner in Python. I intend to get a PhD in aeroelasticity (FEM + CFD) and coding my own program. I intend to …
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Suppose I have two VTK files, both in structured grid format. The structured grids are the same (they have the same list of points, in the same order), and there is a field, call it “Phi”, in each VTK …
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What is the preferred and efficient approach for interpolating multidimensional data? Things I’m worried about: performance and memory for construction, single/batch evaluation handling dimensions …
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Can you answer this question?
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I’m interested in extending the concept of a staggered grid (commonly used to solve the incompressible Navier-Stokes equations) to a linear stability analysis context. For example, we can consider …
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