The article explain clearly. Made a toy canvas to play with poisson https://github.com/beenotung/poisson-canvas
Poisson's Equation
161–167 of 167 posts
Re: Poisson's Equation
#162"you should know that Laplace's Equation has a close cousin called the Biharmonic Equation...
Which is widely used in modeling quantum mechanics. "
Can someone elaborate on that? The Wikipedia article (https://en.wikipedia.org/wiki/Biharmonic_equation) does not mention anything about quantum mechanics use cases for the biharmonic equation.
Re: Poisson's Equation
#163Earlier quoted context omitted.
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.
But they should mention the black box after the educational part.
Re: Poisson's Equation
#164Beautifully done. Everything was clear and intelligible. I have a CS background, but no physics/aerodynamics background. What are the minimum additional steps beyond this tutorial which could produce an aerodynamically correct 2D wing simulator? (With turbulence, not a steady-state solution.) I've come back to tackle this topic intermittently but have never cracked it. To anyone with expertise here who could share an…
There are many different ways to do what you'd like. The easiest starting point would probably be this tutorial: https://github.com/barbagroup/CFDPython But that won't handle turbulence. The real "turbulence problem" is that computing actual turbulent flows requires enormous computational resources. So instead of solving the Navier-Stokes equations, related equations with lower computational cost are solved. Because…
The CFD Online site is a great resource that I had missed before. Thank you for the links.
Re: Poisson's Equation
#165You can also use it to solve labyrinths. Just put a high pressure at the beginning and a low pressure at the end. Solve the Poisson equation. The path through the labyrinth is always the steepest slope. In [1] you can see a small implementation of the idea. [1] https://simulationcorner.net/maze/
More generally, I believe this is exactly the same as flow-field pathfinding, which conveniently has the property that you end up with a solution to the whole map -- so you've solved all pathfinding for all entities anywhere in the map, in one shot. Great for hosting a ridiculous amount of entities on a static (or slow-changing) map.
Brogue's creator also "invented" djikstra maps, which I believe is also exactly the same[0][1], to handle AI strategic pathfinding (e.g. avoid hazards while reaching treasure).
In Game AI Pro (I forget which article/book), someone suggests taking AI preferences (e.g. hunger, health) and computing a flow-field per preference (e.g. a food-map, a danger-map, etc), and multiplying the values against the preference to act as a weight (so food-map * %hunger, danger-map * %health), and summing the maps together to produce the final map used for pathfinding. Notably, the food-map can be shared by all entities consuming the same kind of food -- only the weight has to be re-calculated, and the final sum.
[0] http://www.roguebasin.com/index.php?title=The_Incredible_Pow...
[1] http://www.roguebasin.com/index.php/Dijkstra_Maps_Visualized
Re: Poisson's Equation
#166Earlier quoted context omitted.
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.
But they should mention the black box after the educational part.
Why? The goal of the article is not to be a Julia tutorial. Julia is just a convenient demonstrator. Better to make the code as language independent as possible.
Re: Poisson's Equation
#167Hiện tại hệ thống VayHay đang tuyển nhân viên Telesale khu vực cần thơ và các tỉnh thành khác toàn quốc làm việc 8h/ngày và có hỗ trợ vay tiêu dùng toàn quốc không thế chấp kì hạn và các gói vay linh hoạt, truy cập VayHay.vn để biết thêm thông tin