Poisson's Equation
mattferraro.dev
Poisson's Equation
1–10 of 167 posts
Re: Poisson's Equation
#2Since you have written it as a symmetric, positive definite, sparse linear system, why don't use a standard solver like CHOLMOD which is available in Julia? (and behind octave's anti-slash operator). It should be faster than the ad-hoc single-scale Gauss-Seidel.
Re: Poisson's Equation
#3Sorry but can there be more context to why it is a powerful tool?
Re: Poisson's Equation
#4Great post, one nitpick -- I wouldn't say that a matrix is a "sparsely defined" function, but rather a function defined on a finite grid. It might also be worth pointing out that same approach works for any graph, not just a grid.
Re: Poisson's Equation
#5Since you have written it as a symmetric, positive definite, sparse linear system, why don't use a standard solver like CHOLMOD which is available in Julia? (and behind octave's anti-slash operator). It should be faster than the ad-hoc single-scale Gauss-Seidel.
At the end the author mentions there are a large number of methods available for solving. Also mentions there are a much larger set of applications that those discussed.
Re: Poisson's Equation
#6This was a very interesting read even as someone who probably has no practical use for these tools.
Re: Poisson's Equation
#7Since you have written it as a symmetric, positive definite, sparse linear system, why don't use a standard solver like CHOLMOD which is available in Julia? (and behind octave's anti-slash operator). It should be faster than the ad-hoc single-scale Gauss-Seidel.
At the end the author mentions there are a large number of methods available for solving. Also mentions there are a much larger set of applications that those discussed.
Sure! But it's a bit surprising that they do not use the language-provided linear solver and write simply f=A\b
Re: Poisson's Equation
#8Earlier quoted context omitted.
At the end the author mentions there are a large number of methods available for solving. Also mentions there are a much larger set of applications that those discussed.
Sure! But it's a bit surprising that they do not use the language-provided linear solver and write simply f=A\b
Wow! It seems you have the magical capacity to ingest the reference to an equation and instantly derive an intuition for how it works and what it's useful for. Learning technology this advanced has never been seen before by humankind, I hope you share it with the rest of us!
Re: Poisson's Equation
#9Sorry but can there be more context to why it is a powerful tool?
This is a typical issue with HN posts.
Some poor soul wrote a somewhat competent and maybe even lengthy blog post / article about something they really care about and are knowledgeable about. It may be directed at a specific audience, or maybe just screaming into the void to record down some insight they had for themselves to read again later, or similar. And they use a more-than-necessary general title like "the best tool you'll ever see" with "you" meaning either just themselves or a narrow target audience or so.
And then somebody comes along who finds it interesting, submits it to HN, it makes front page, and now it looks like the poor author with their more-general-than-needed title is making a general statement about sth for the changed audience which is the HN crowd, but which is distinctly different from the original target audience.
Case in point: The articles author self describes as: "I'm an aerospace engineer that writes software. I love math and science, and I have two cats."
For an aerospace engineer this all makes a lot of sense and is a super great tool, I'm sure. It's just not for the overall HN crowd. And it's not the authors fault.
Re: Poisson's Equation
#10Earlier quoted context omitted.
At the end the author mentions there are a large number of methods available for solving. Also mentions there are a much larger set of applications that those discussed.
Sure! But it's a bit surprising that they do not use the language-provided linear solver and write simply f=A\b
The goal of the article is educate on the mathematics, not a tutorial on how best to do mathematical modelling with Julia. An article like that is better served explaining the inner workings of the Black Box, rather than just using the Black Box.