What I found amazing about FEM is not the detail of how to implement it in code, but all the PDE theory & approximation theory -- how you can express the original continuous-domain infinite dimensional problem in a weak form using an infinite dimensional space of test functions, then approximating the weak form of the original problem with a finite dimensional Galerkin approximation, using a finite dimensional space of test functions, and use that to define a finite dimensional system of equations to solve. Then the theory for under what conditions you can guarantee that approximate solutions obtained from your finite dimensional approximation converge toward the true solution, as you increase the mesh resolution, and how fast the convergence rate will be.
Some of this is summarised in this paper in 2. model problem & 3. Galerkin discretisation of the problem, but not in a way that will communicate the mathematical ideas to anyone who hasn't already taken a course on the theory -- probably need a couple of courses on real analysis & a course on PDE as pre-reqs.
Yup. I'm trying to learn computational fluid dynamics for fun, and realised it's basically all numerical methods for PDEs, with some fluid dynamics-specific shortcuts. I know I've previously seen this stuff in relation to pricing derivatives in finance.
It's clear the underlying techniques are very powerful any time you have a thing whose rate of change varies as other things change. Once I understand everything better I will try it on e.g. capacity planning cloud resources and such.
Curious why both of you need linked lists in Python? Are you doing a lot of list insertion operations or something & allocations are bringing it to a crawl?
I'm quite tickled by the idea that you need a linked list because your allocator is spending too much time - traversing a linked list.
I thought one of the advent of code challenges needed a linked list, but other than that, I have never needed one.
I was just surprised as I thought it was a basic structure, so it just seemed like there ought to be a `from collections import linkedlist` because python just feel like the kind of language where you just do that without even consulting the docs.
Yeah for sure. I think your intuition is almost right. Python does have a "batteries included" philosophy, but it's also not usually clear or documented what data structures something is using. Like I presume that Python's sets are syntactic sugar over dictionaries where the values are None, but when I skimmed the docs just now I didn't find any mention of the implementation details.
Python doesn't want you thinking in terms of data structures, just in terms of functionality. Which I think is unfortunate and limiting.
Correct (actually a linked list of blocks[1]). It supports insertion and removal from both ends in O(1), which is very useful. However, it does not support insertion and removal from the middle (via an iterator) in O(1), so it's not a complete replacement for doubly-linked lists.
Imagine your brain being basically dead from lack of oxygen, medical danger like HAPE.
It looks like it there are even (? fully ?) vertical fixed rope pitches and going up actual technical climbing one article says a 5.9 offwidth ?!?! In -50F windy winter conditions wearing giant bulky winter suits.
If you've ever been sport climbing can you image descending multiple miles on a rope, even if kind of crawling backwards using feet/hands?
Climbers forget to tie knots in the end ALL THE TIME. Brad Gobright was one of the best climbers who was known for free soloing here in the Front Range (e.g. no ropes at all, like Honnold up El Cap) recently died on a rope descent.
Imagine on multiple miles of roped descent many knots, transfers, while you can't think from no oxygen. It's an truly impressive almost inhuman feat.
On one hand, I am truly inspired by the feat of achievement of this caliber, at the same time it leaves me with feeling of mournful contempt like a Gladiator fight where someone is going to die.
Location: Spain.
Willing to relocate: to the UK (London).
Remote: Yes
Technologies: Python: Numpy, Pandas, Django, FeniCS; MATLAB; Java;
Résumé: BsC in Industrial Engineering, MsC in Applied Mathematics, PhD in applied mathematics and mechanics (bioengineering). Interested in tech, looking for an opportunity in this field.
Complete CV: https://t.ly/qVTj
Email: inside CV.
