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1500 questions
8
votes
3 answers

Arbitrary Precision Optimization Libraries?

Are there any well-known optimization libraries (ideally with Python bindings or even in Python) supporting (unconstrained) minimization (of $f:\mathbb{R}^n \to \mathbb{R}$ for $n$ for $n\sim 10^1,10^2$) with support for arbitrary precision…
not all wrong
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8
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1 answer

How fast is automatic differentiation?

I asked this question earlier on StackOverflow, but it's obviously better suited for SciComp: While there seem to be lots of references online which compare automatic differentiation methods and frameworks against each other, I can't seem to find…
gilgamec
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Eigenvalue-like problem with coupled ODEs

I am looking at the following system of ODEs: \begin{array}{r}{\left[c_{2}(k)-\partial_{\tau}^{2}\right] \varphi_{2}\left(\tau \right)=f_{21}(\tau) \varphi_{1}\left(\tau \right)} \\ {\left[c_{1}(k)-\partial_{\tau}^{2}\right] \varphi_{1}\left(\tau…
KartMan
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1 answer

Do computational scientists typically also become domain experts?

Let's say I'm interested in fluid dynamics, specifically in fluid-structure interactions -- and I want to get into modeling, simulations and experiments. I am a mathematics student by training, having taken yearlong courses in introductory…
user32645
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8
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2 answers

Is there one general approach to build a projection methods for different problems?

My question is probably going to be too general to answer it with a couple words. Could you please suggest a good reading in that case. Projection methods are used to reduce size of the solution space for the problems. And there are at least two…
danny_23
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Why not use the preconditioned residual as termination criterion for preconditioned CG?

I have a Poisson equation with wildly varying material parameters (1 .. 1000), wildly varying element sizes (5 nm .. 100 um) and some quite anisotropic (tetrahedral) elements (100 nm x 100 um). I use (a C++ port of) Dan Spielman's approxChol as a…
Thomas Klimpel
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0 answers

What are some good debugging habits for numerical simulation?

I'm currently writing a lid drive cavity CFD code on python. Currently, my code has some issues (values jumping bear b.c). I was wondering what are some good habits in debugging numerical codes. Hopefully, I would be able to learn some which I may…
Kelvin Loh
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1 answer

Open-source, thread-safe implementation of convex optimization solvers in C/C++?

Is there an open-source, thread-safe implementation of convex optimization solvers in C/C++? Some libraries such as NLopt, Ipopt, OPT++ don't meet my requirements. OPT++ and Ipopt aren't thread-safe, and NLopt doesn't seem to have a…
Tianyang Li
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8
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2 answers

Octree cubes to tetrahedrons

I'm trying to learn more about volume meshing and have decided to try to implement a simple volume mesher. The strategy I have chosen is to subdivide my space using an octree, refined based on some criteria. I have made sure that my octree is…
WesDec
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1 answer

Should we always expect FEM error plots to be straight lines?

The error estimates in FEM are usually of the form $$||u^h-u||\leq Ch.$$ Taking logarithm on both sides, we obtain $$\log ||u^h-u||\leq \log C + \log h.$$ This estimate implies that the error lies below the straight line given by $\log y=\log C +…
Thangachelli Debopritama
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How to construct an effective preconditioner for this particular problem

A quick introduction to my problem I am currently developing a method for simulation of water waves in three dimensions based on potential flow theory. The computational bottleneck of the method is to solve the equation \begin{equation} f(x,y) =…
Mathias Klahn
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1 answer

$L^\infty$ stability property of an ODE

Suppose we have the initial-value problem on $(0,L)$: $$ \frac{d u(x)}{d x} = f(x) u(x),\, \qquad x\in\Omega,\,~~ u(0) = u_0, $$ I am reading a claim that says if we multiply the ODE by $u$ and integrate over $(0,L)$, we have $$…
user3482876
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1 answer

How reproducible are conda environments?

I am aiming at keeping my scientific studies and analyses reproducible: I am automating them as much as possible, I am sharing them, and I sharing them together with the execution environment(s) I've used to run the analyses. This is to make it…
Tim Tröndle
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8
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4 answers

(How) do you take into account memory fragmentation?

I use an example from finite element theory, but anybody who maintains a large datastructure and successively extends it will find something similar. Suppose I have an unstructured mesh of points and triangles, where the points are given by…
shuhalo
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8
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Fourier transform for Neumann boundary condition

I need to solve system of two coupled partial differential equations numerically. \begin{align} \frac{\partial x_1}{\partial t} &= c_1\nabla ^2 x_1 + f_1(x_1,x_2)\\ \frac{\partial x_2}{\partial t} &= c_2\nabla ^2 x_2 + K\frac{\partial…
chatur
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