Zero Dissipation ERK6(5) #1033

utkarsh530 · 2020-02-14T23:08:21Z

Hi, I have currently implemented RK6(5) based on the paper (It does not account for zero dissipation yet, some basic changes needs to be done) here which is the basis of paper mentioned in #867. However, since this is my first attempt, I may have made some errors and sim tests are failing. Can anyone help where to possibly search for errors. Thanks.

coveralls · 2020-02-14T23:55:05Z

Coverage increased (+0.07%) to 86.797% when pulling c15a279 on utkarsh530:FRK65 into 46b4763 on JuliaDiffEq:master.

ChrisRackauckas · 2020-02-15T00:14:32Z

What does the convergence plot look like?

utkarsh530 · 2020-02-15T10:53:22Z

1-D out of place

2-D in place

codecov · 2020-02-15T10:59:27Z

Codecov Report

Merging #1033 into master will decrease coverage by 41.11%.
The diff coverage is 0%.

@@             Coverage Diff             @@
##           master    #1033       +/-   ##
===========================================
- Coverage   76.74%   35.62%   -41.12%     
===========================================
  Files          95       95               
  Lines       30621    30044      -577     
===========================================
- Hits        23500    10704    -12796     
- Misses       7121    19340    +12219

Impacted Files	Coverage Δ
src/OrdinaryDiffEq.jl	`100% <ø> (ø)`	⬆️
src/caches/low_order_rk_caches.jl	`34.67% <0%> (-61.07%)`	⬇️
src/algorithms.jl	`44.25% <0%> (-39.63%)`	⬇️
src/alg_utils.jl	`7.39% <0%> (-20.1%)`	⬇️
src/perform_step/low_order_rk_perform_step.jl	`67.93% <0%> (-30.63%)`	⬇️
src/caches/rkn_caches.jl	`0% <0%> (-100%)`	⬇️
src/iterator_interface.jl	`0% <0%> (-100%)`	⬇️
src/caches/symplectic_caches.jl	`0% <0%> (-100%)`	⬇️
src/caches/prk_caches.jl	`0% <0%> (-100%)`	⬇️
src/tableaus/rkc_tableaus.jl	`0% <0%> (-100%)`	⬇️
... and 66 more

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ChrisRackauckas · 2020-02-15T15:09:52Z

This isn't even converging. Do the b_i sum to 1? To the rows of a_i sum to c_i?

ChrisRackauckas · 2020-02-15T15:10:52Z

src/perform_step/low_order_rk_perform_step.jl

+  @unpack t, dt, uprev, u, f, p = integrator
+  @unpack α21, α31, α41, α51, α61, α71, α81, α91, α32, α43, α53, α63, α73, α83, α54, α64, α74, α84, α94, α65, α75, α85, α95, α76, α86, α96, α87, α97, α98, β1, β4, β5, β6, β7, β8, β1tilde, β4tilde, β5tilde, β6tilde, β7tilde, β8tilde, β9tilde, c2, c3, c4, c5, c6, c7, c8, c9 = cache
+  alg = unwrap_alg(integrator, true)
+  omega = alg.omega


looks like omega isn't used?

Actually, I am testing for convergence of paper I mentioned in my earlier comment, which had constant variables. The paper for zero dissipation requires only to change b4 b5 b6 to a function of omega which I will implement after this just to be sure that original coefficients are leading to convergence or not.

src/caches/low_order_rk_caches.jl

kanav99 · 2020-02-15T19:02:24Z

Hey! The b_i coefficients were bad. Check the tests now with the suggestions

utkarsh530 · 2020-02-15T23:00:53Z

Yep, I corrected another coefficient a_i & btilde_i. The 2-D in place plot looks like this:

Order estimate:
1-D out of place
Expression: ≈(sim3.�est[:l∞], 6, atol=testTol) Evaluated: 2.7735194214179764 ≈ 6 (atol=0.2)
2-D in place:
Expression: ≈(sim3.�est[:l∞], 6, atol=testTol) Evaluated: 2.865412492134244 ≈ 6 (atol=0.2)
Coefficients are for Periodic IVPs and hence result does not follow?

ChrisRackauckas · 2020-02-15T23:12:59Z

Make the dts a little bit larger: it's saturating at floating point epsilon.

utkarsh530 · 2020-02-15T23:25:57Z

Yep, that worked, thanks! I will add code for zero dissipation coefficients.

Co-Authored-By: Kanav Gupta <[email protected]>

utkarsh530 · 2020-02-21T06:45:54Z

I have added zero-dissipation fitted coefficients.
Question: should we set omega = 0 if not specified? (It coincides with RK6(5))

ChrisRackauckas · 2020-02-21T09:29:33Z

Question: should we set omega = 0 if not specified? (It coincides with RK6(5))

sure

utkarsh530 · 2020-02-21T10:43:15Z

Made required changes to struct FRK65. Please review.

ChrisRackauckas · 2020-02-21T10:55:53Z

src/algorithms.jl

  lazy::Bool
  Vern9(;lazy=true) = new(lazy)
 end
+struct FRK65 <: OrdinaryDiffEqAdaptiveAlgorithm


Parameterize this

ChrisRackauckas · 2020-02-21T10:56:02Z

src/algorithms.jl

  lazy::Bool
  Vern9(;lazy=true) = new(lazy)
 end
+struct FRK65 <: OrdinaryDiffEqAdaptiveAlgorithm


Suggested change

struct FRK65 <: OrdinaryDiffEqAdaptiveAlgorithm

struct FRK65{T} <: OrdinaryDiffEqAdaptiveAlgorithm

ChrisRackauckas · 2020-02-21T10:56:11Z

src/algorithms.jl

  Vern9(;lazy=true) = new(lazy)
 end
+struct FRK65 <: OrdinaryDiffEqAdaptiveAlgorithm
+  omega::Float64


Suggested change

omega::Float64

omega::T

utkarsh530 · 2020-02-21T17:05:46Z

Made the required changes.

ChrisRackauckas · 2020-02-21T20:05:45Z

test/algconvergence/ode_convergence_tests.jl

-  sim3 = test_convergence(dts4,prob,FRK65(0)) #standard value for non zero-dissipation tests
-  @test sim3.𝒪est[:l∞] ≈ 6 atol=testTol
+  sim3 = test_convergence(dts4,prob,FRK65())
+  @test sim3.𝒪est[:l∞] ≈ 6 atol=testTol1


instead, make this 6.5 and keep the same testtol. Looks like super convergence. What does plot(sim3) look like?

Here's the plot:

sim3.�est[:l∞]=6.547286289246398

sim3.�est[:l∞]=5.862512678209683
A test is failing if setting it to 6.5 and same testtol.

huh, that's weird. Instead of defining at testTol1, just put the larger value right in the code there and I'll accept.

Done. By the way, what is super convergence?

utkarsh530 force-pushed the FRK65 branch from 4e12c7a to bf24a11 Compare February 14, 2020 23:27

utkarsh530 changed the title ~~Zero Order Dissipation ERK6(5)~~ Zero Dissipation ERK6(5) Feb 14, 2020

utkarsh530 force-pushed the FRK65 branch from bf24a11 to cfdd844 Compare February 15, 2020 10:59

ChrisRackauckas reviewed Feb 15, 2020

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kanav99 reviewed Feb 15, 2020

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src/caches/low_order_rk_caches.jl Outdated Show resolved Hide resolved

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utkarsh530 and others added 4 commits February 21, 2020 10:16

Add FRK65 Butcher Table and basic performstep implementation

304840e

WIP: Add Adaptive EEST and sim tests

51d4f37

Update src/caches/low_order_rk_caches.jl

a5fa042

Co-Authored-By: Kanav Gupta <[email protected]>

Update src/caches/low_order_rk_caches.jl

17c83f3

Co-Authored-By: Kanav Gupta <[email protected]>

utkarsh530 force-pushed the FRK65 branch 3 times, most recently from 945f1ae to 17c83f3 Compare February 21, 2020 06:40

Add zero-dissipation fitted coefficients

c2e67de

Add def value to omega

a4e0642

ChrisRackauckas reviewed Feb 21, 2020

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ChrisRackauckas approved these changes Feb 21, 2020

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utkarsh530 force-pushed the FRK65 branch from 24f7ea9 to 421efc0 Compare February 21, 2020 17:04

ChrisRackauckas reviewed Feb 21, 2020

View reviewed changes

utkarsh530 force-pushed the FRK65 branch from 421efc0 to 3491d10 Compare February 21, 2020 21:52

Add parameterisation to FRK65 and update convergence tests

c15a279

utkarsh530 force-pushed the FRK65 branch from 3491d10 to c15a279 Compare February 21, 2020 21:56

ChrisRackauckas merged commit 75ec5dd into SciML:master Feb 22, 2020

ChrisRackauckas mentioned this pull request Aug 12, 2024

docs v7 rework #2317

Merged

	struct FRK65 <: OrdinaryDiffEqAdaptiveAlgorithm
	struct FRK65{T} <: OrdinaryDiffEqAdaptiveAlgorithm

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Zero Dissipation ERK6(5) #1033

Zero Dissipation ERK6(5) #1033

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