Comments (3)
Interesting suggestion, and it's it looks certainly easy to implement. Would expect the continuation to stop once a milestone is reached, or to continue?
from pacopy.
For natural parameter continuation, an obvious use-case is a strictly monotonic list of λ at the end of which the job's done.
In the general, e.g. arc-length, case, it's much less clear. I can't see as much practical call for milestones, except in making a figure like Farrell's, where one probably would like λ to have a nice round value to keep the caption tidy and to facilitate reproducibility. Stopping at milestones is going to be trickier when the parameter isn't monotonic. Maybe defer that case; I don't really need to reproduce figure 1.1 but do need to sweep Reynolds number.
On the question of termination, what I did to stop the 1-d Bratu arclength continuation after the curve had left the frame was raise an exception from the callback based on the norm. This sped things up a bit. kinnala/scikit-fem#126
from pacopy.
I came across a good motivation for stopping at milestones in natural parameter continuation in the literature:
The backward step flow was formulated and solved as a steady flow problem. In order to obtain a solution for the specified Re of 800, a series of steady state solutions were obtained at intermediate Re-values of 200, 400 and 600. Zeroth-order continuation was used to advance from one Re solution to another. The indicated sequence of steps in Re does not represent an optimized path to the final required state but was selected for convenience and with a view towards comparing solutions at other standard conditions.
- Gartling, D. K. (1990). A test problem for outflow boundary conditions—flow over a backward‐facing step. International Journal for Numerical Methods in Fluids, 11, 953–967. doi: 10.1002/fld.1650110704
from pacopy.
Related Issues (12)
- add fenics example
- support for simple 1d bifurcations HOT 3
- Complex-Ginsburg-Landau HOT 7
- Add very simple examples for beginners HOT 4
- reproduce Gross-Pitaevskii results
- stop when <u, u> = 0
- readme dump HOT 1
- no code in main branch HOT 1
- This version of pacopy is outdated. Please upgrade. HOT 2
- default maximum parameter stepsize HOT 2
- version bump for pacopy.natural.milestones HOT 2
Recommend Projects
-
React
A declarative, efficient, and flexible JavaScript library for building user interfaces.
-
Vue.js
🖖 Vue.js is a progressive, incrementally-adoptable JavaScript framework for building UI on the web.
-
Typescript
TypeScript is a superset of JavaScript that compiles to clean JavaScript output.
-
TensorFlow
An Open Source Machine Learning Framework for Everyone
-
Django
The Web framework for perfectionists with deadlines.
-
Laravel
A PHP framework for web artisans
-
D3
Bring data to life with SVG, Canvas and HTML. 📊📈🎉
-
Recommend Topics
-
javascript
JavaScript (JS) is a lightweight interpreted programming language with first-class functions.
-
web
Some thing interesting about web. New door for the world.
-
server
A server is a program made to process requests and deliver data to clients.
-
Machine learning
Machine learning is a way of modeling and interpreting data that allows a piece of software to respond intelligently.
-
Visualization
Some thing interesting about visualization, use data art
-
Game
Some thing interesting about game, make everyone happy.
Recommend Org
-
Facebook
We are working to build community through open source technology. NB: members must have two-factor auth.
-
Microsoft
Open source projects and samples from Microsoft.
-
Google
Google ❤️ Open Source for everyone.
-
Alibaba
Alibaba Open Source for everyone
-
D3
Data-Driven Documents codes.
-
Tencent
China tencent open source team.
from pacopy.