What do these dimension decide? What does increasing/decreasing these dimensions change?
Just kidding PPP is still best.
I'm looking for an efficient algorithm to calculate matrix exponentials to evaluate the solutions of ODEs. For now, I would prefer to evaluate the exact analytical solution using matrix exponentials rather than integrated the ODE directly because then my solution is independent of time step. I could revisit this preference if it becomes necessary.
So far, I've been using Matlab's expm function. This has worked well for smallish problems on the order of 1e3 DoF and smaller. When I get to 1e4 DoF, it becomes too expensive. Ideally I'd like to get to ~1e6 DoF, but now I'm not sure how feasible that will be.
I think the problem is that the Matlab expm algorithm might be fairly efficient for a single evaluation, but at each time point the full calculation has to be repeated. For this reason, I think I want a method that evaluates the action of the matrix. I have looked at "Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later” and there are clearly lots of options. In their update, they indicated that Krylov subspace methods have recently become more popular (but that was almost 20 years ago now). I found a paper from 2012 that lays out an algorithm for a Krylov space method: “A short guide to exponential Krylov subspace time integration for Maxwell’s equations” (Botchev). I'm also looking at another paper which uses a scaling and squaring method to compute the action of the exponential, using a Taylor series approximation: “Computing the Action of the Matrix Exponential, with an Application to Exponential Integrators” (Al-Mohy and Higham). I think either one of these might be better for my application, but clearly this is a pretty large field on its own and there might be something better or more recent that I should use.
Does anybody have suggestions for where I should look? Or should I just go ahead with the Krylov subspace method that I mentioned? Or, do you think I should ditch evaluation of the exact solution, and integrate the ODEs numerically? Will I need parallelization to get to 1e6 DoF?
Thanks in advance.
Do your worst!
For context I'm a Refuse Driver (Garbage man) & today I was on food waste. After I'd tipped I was checking the wagon for any defects when I spotted a lone pea balanced on the lifts.
I said "hey look, an escaPEA"
No one near me but it didn't half make me laugh for a good hour or so!
Edit: I can't believe how much this has blown up. Thank you everyone I've had a blast reading through the replies 😂
It really does, I swear!
I'm surprised it hasn't decade.
They’re on standbi
Buenosdillas
Hi!
I'm really curious about mathematics and want to get a better understanding of it. Lately my curiosity mainly has been towards numerical methods for differential equations and in the process of exploring that curiosity I found a lot of interesting information, some of which was fairly accessible to me and had clear parallels with my experience as a programmer.
But of course, vast majority of literature on the subject depends on more advanced topics that I'm quite far from understanding. Some examples would be calculus of variations used in Finite Element Method, Sobolev spaces, Krylov subspaces...
Unfortunately, I don't have a formal training and due to various circumstances only have an option to study mathematics on my own. I don't expect it to be easy or to end up doing any actual research math, my goal is just satisfying some of my curiosity and getting a better background, so that I'm able to explore more.
I have basic understanding of proofs, know some calculus and a bit of linear algebra. I can read, say, a book on numerical methods for differential equations and be able to understand and implement (simpler) methods explained there, though I have to skip more complex details and proofs.
What would be a good approach to move forward? I'm considering starting from Spivak's Calculus and Evan Chen's Infinitely Large Napkin, but I'd really appreciate some suggestions. I find it easier to work through books that are fairly terse and "formal" (as in, less "wordy" and more focused on the subject).
I'd also appreciate any suggestions on problem books and online lectures etc.
Thanks and sorry if my post is out of place here.
Pilot on me!!
Dad jokes are supposed to be jokes you can tell a kid and they will understand it and find it funny.
This sub is mostly just NSFW puns now.
If it needs a NSFW tag it's not a dad joke. There should just be a NSFW puns subreddit for that.
Edit* I'm not replying any longer and turning off notifications but to all those that say "no one cares", there sure are a lot of you arguing about it. Maybe I'm wrong but you people don't need to be rude about it. If you really don't care, don't comment.
When I got home, they were still there.
What did 0 say to 8 ?
" Nice Belt "
So What did 3 say to 8 ?
" Hey, you two stop making out "
I won't be doing that today!
You take away their little brooms
This morning, my 4 year old daughter.
Daughter: I'm hungry
Me: nerves building, smile widening
Me: Hi hungry, I'm dad.
She had no idea what was going on but I finally did it.
Thank you all for listening.
There hasn't been a post all year!
[Removed]
It’s pronounced “Noel.”
After all his first name is No-vac
What, then, is Chinese rap?
Edit:
Notable mentions from the comments:
-
Spanish/Swedish/Swiss/Serbian hits
-
French/Finnish art
-
Country/Canadian rap
-
Chinese/Country/Canadian rock
-
Turkish/Tunisian/Taiwanese rap
There hasn't been a single post this year!
(Happy 2022 from New Zealand)
Nothing, it just waved
Bob
Just to clarify, 12345678
So that I could frequently say, "I am going to walk 5 miles now."
Edit: My most popular post on Reddit! 😀 Thank you for the awards.
Me grabbing a soda from my (what I thought was) half full 12pk...
Notices there's only 2;
Me: "Awe man... This is a damn bird box!" Her: "What the hell does that mean?!" Me: (Pulls both cans out & shows them to her) "It's only got Toucans."
I'm not ashamed to admit the look on her face was glorious.
I was just sitting there doing nothing.
