WIP: 2nd order pde #434

valentinsulzer · 2021-08-09T20:45:38Z

Trying to add functionality for 2nd order PDE such as the wave equation (inspired by #421 )
Not obvious why the test is failing, am I missing something obvious? Equations look sensible:

julia> equations(sys)
30-element Vector{Equation}:
 Differential(t)(Differential(t)(u₂(t))) ~ -(85.21111544320605u₁(t) + 85.21111544320605u₃(t) - (170.4222308864121u₂(t)))
 Differential(t)(Differential(t)(u₃(t))) ~ -(85.21111544320605u₂(t) + 85.21111544320603u₄(t) - (170.42223088641208u₃(t)))
 Differential(t)(Differential(t)(u₄(t))) ~ -(85.21111544320605u₃(t) + 85.21111544320608u₅(t) - (170.42223088641214u₄(t)))
 Differential(t)(Differential(t)(u₅(t))) ~ -(85.21111544320608u₄(t) + 85.2111154432061u₆(t) - (170.4222308864122u₅(t)))
 Differential(t)(Differential(t)(u₆(t))) ~ -(85.21111544320607u₅(t) + 85.21111544320603u₇(t) - (170.42223088641208u₆(t)))
 Differential(t)(Differential(t)(u₇(t))) ~ -(85.21111544320604u₆(t) + 85.21111544320613u₈(t) - (170.42223088641217u₇(t)))
 Differential(t)(Differential(t)(u₈(t))) ~ -(85.21111544320614u₇(t) + 85.21111544320604u₉(t) - (170.4222308864122u₈(t)))
 Differential(t)(Differential(t)(u₉(t))) ~ -(85.21111544320613u₁₀(t) + 85.21111544320604u₈(t) - (170.42223088641217u₉(t)))
 ⋮
 Differential(t)(Differential(t)(u₂₄(t))) ~ -(85.211115443206u₂₃(t) + 85.211115443206u₂₅(t) - (170.422230886412u₂₄(t)))
 Differential(t)(Differential(t)(u₂₅(t))) ~ -(85.21111544320617u₂₄(t) + 85.21111544320651u₂₆(t) - (170.42223088641268u₂₅(t)))
 Differential(t)(Differential(t)(u₂₆(t))) ~ -(85.21111544320652u₂₅(t) + 85.21111544320618u₂₇(t) - (170.4222308864127u₂₆(t)))
 Differential(t)(Differential(t)(u₂₇(t))) ~ -(85.211115443206u₂₆(t) + 85.211115443206u₂₈(t) - (170.422230886412u₂₇(t)))
 Differential(t)(Differential(t)(u₂₈(t))) ~ -(85.211115443206u₂₇(t) + 85.211115443206u₂₉(t) - (170.422230886412u₂₈(t)))
 Differential(t)(Differential(t)(u₂₉(t))) ~ -(85.211115443206u₂₈(t) + 85.211115443206u₃₀(t) - (170.422230886412u₂₉(t)))
 u₁(t) ~ exp(-t)
 u₃₀(t) ~ -exp(-t)

julia> equations(ode_order_lowering(sys))
58-element Vector{Equation}:
 Differential(t)(u₂ˍt(t)) ~ -(85.21111544320605u₁(t) + 85.21111544320605u₃(t) - (170.4222308864121u₂(t)))
 Differential(t)(u₃ˍt(t)) ~ -(85.21111544320605u₂(t) + 85.21111544320603u₄(t) - (170.42223088641208u₃(t)))
 Differential(t)(u₄ˍt(t)) ~ -(85.21111544320605u₃(t) + 85.21111544320608u₅(t) - (170.42223088641214u₄(t)))
 Differential(t)(u₅ˍt(t)) ~ -(85.21111544320608u₄(t) + 85.2111154432061u₆(t) - (170.4222308864122u₅(t)))
 Differential(t)(u₆ˍt(t)) ~ -(85.21111544320607u₅(t) + 85.21111544320603u₇(t) - (170.42223088641208u₆(t)))
 Differential(t)(u₇ˍt(t)) ~ -(85.21111544320604u₆(t) + 85.21111544320613u₈(t) - (170.42223088641217u₇(t)))
 Differential(t)(u₈ˍt(t)) ~ -(85.21111544320614u₇(t) + 85.21111544320604u₉(t) - (170.4222308864122u₈(t)))
 Differential(t)(u₉ˍt(t)) ~ -(85.21111544320613u₁₀(t) + 85.21111544320604u₈(t) - (170.42223088641217u₉(t)))
 ⋮
 Differential(t)(u₂₄(t)) ~ u₂₄ˍt(t)
 Differential(t)(u₂₅(t)) ~ u₂₅ˍt(t)
 Differential(t)(u₂₆(t)) ~ u₂₆ˍt(t)
 Differential(t)(u₂₇(t)) ~ u₂₇ˍt(t)
 Differential(t)(u₂₈(t)) ~ u₂₈ˍt(t)
 Differential(t)(u₂₉(t)) ~ u₂₉ˍt(t)
 u₁(t) ~ exp(-t)
 u₃₀(t) ~ -exp(-t)

valentinsulzer · 2021-08-10T17:05:48Z

Initial conditions also look correct:

julia> sys.defaults
Dict{Term{Real, Nothing}, Float64} with 60 entries:
  Differential(t)(u₂₀(t)) => 0.468408
  u₈(t)                   => 0.725995
  Differential(t)(u₂(t))  => -0.994138
  Differential(t)(u₃₀(t)) => 1.0
  Differential(t)(u₉(t))  => -0.647386
  Differential(t)(u₂₅(t)) => 0.856857
  u₁₄(t)                  => 0.161782
  Differential(t)(u₁₄(t)) => -0.161782
  u₁₃(t)                  => 0.267528
  u₃(t)                   => 0.976621
  Differential(t)(u₁₁(t)) => -0.468408
  u₃₀(t)                  => -1.0
  ⋮                       => ⋮

valentinsulzer added 6 commits August 6, 2021 18:45

trying wave equation

c3ab858

update test

f44988d

update test

3ad8f5e

update test

7066f42

fix NonlinearProblem

142690d

Merge branch 'master' into 2nd-order-pde

45e7282

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WIP: 2nd order pde #434

WIP: 2nd order pde #434

valentinsulzer commented Aug 9, 2021

valentinsulzer commented Aug 10, 2021

WIP: 2nd order pde #434

Are you sure you want to change the base?

WIP: 2nd order pde #434

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valentinsulzer commented Aug 9, 2021

valentinsulzer commented Aug 10, 2021