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Add time offset for LowStorageIntegrator #1151

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merged 12 commits into from
Aug 26, 2024
Merged

Add time offset for LowStorageIntegrator #1151

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5afd98e
add time offset for LowStorageIntegrator
pbrady Aug 9, 2024
f1506f3
Merge branch 'develop' into ptb/add-low-storage-time
pgrete Aug 14, 2024
8ea6f87
Add docs for `c` in `LowStorageIntegrator`
pbrady Aug 14, 2024
8a29cda
Merge branch 'develop' into ptb/add-low-storage-time
pbrady Aug 14, 2024
4d2bc60
Fix math expressions in docs
pbrady Aug 14, 2024
2d8d12e
Merge branch 'develop' into ptb/add-low-storage-time
pgrete Aug 22, 2024
8cf2a6a
add notebook for sparse time levels
pbrady Aug 23, 2024
9a1fff2
Merge branch 'develop' into ptb/add-low-storage-time
pbrady Aug 23, 2024
412b9b8
Remove binary content from notebook
pgrete Aug 26, 2024
d2df5c5
Merge remote-tracking branch 'origin/develop' into ptb/add-low-storag…
pgrete Aug 26, 2024
02b0bb4
Oops. Fixed mixed files.
pgrete Aug 26, 2024
e1e832e
Merge branch 'develop' into ptb/add-low-storage-time
pgrete Aug 26, 2024
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19 changes: 19 additions & 0 deletions src/time_integration/low_storage_integrator.cpp
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Original file line number Diff line number Diff line change
Expand Up @@ -57,67 +57,79 @@ LowStorageIntegrator::LowStorageIntegrator(const std::string &name)
beta.resize(nstages);
gam0.resize(nstages);
gam1.resize(nstages);
c.resize(nstages);

delta[0] = 1.0;
beta[0] = 1.0;
gam0[0] = 0.0;
gam1[0] = 1.0;
c[0] = 0.0;
} else if (name_ == "rk2") {
nstages = 2;
nbuffers = 2;
delta.resize(nstages);
beta.resize(nstages);
gam0.resize(nstages);
gam1.resize(nstages);
c.resize(nstages);

delta[0] = 1.0;
beta[0] = 1.0;
gam0[0] = 0.0;
gam1[0] = 1.0;
c[0] = 0.0;

delta[1] = 0.0;
beta[1] = 0.5;
gam0[1] = 0.5;
gam1[1] = 0.5;
c[1] = 1.0;
} else if (name_ == "vl2") {
nstages = 2;
nbuffers = 2;
delta.resize(nstages);
beta.resize(nstages);
gam0.resize(nstages);
gam1.resize(nstages);
c.resize(nstages);

delta[0] = 1.0;
beta[0] = 0.5;
gam0[0] = 0.0;
gam1[0] = 1.0;
c[0] = 0.0;

delta[1] = 0.0;
beta[1] = 1.0;
gam0[1] = 0.0;
gam1[1] = 1.0;
c[1] = 0.5;
} else if (name_ == "rk3") {
nstages = 3;
nbuffers = 2;
delta.resize(nstages);
beta.resize(nstages);
gam0.resize(nstages);
gam1.resize(nstages);
c.resize(nstages);

delta[0] = 1.0;
beta[0] = 1.0;
gam0[0] = 0.0;
gam1[0] = 1.0;
c[0] = 0.0;

delta[1] = 0.0;
beta[1] = 0.25;
gam0[1] = 0.25;
gam1[1] = 0.75;
c[1] = 1.0;

delta[2] = 0.0;
beta[2] = 2.0 / 3.0;
gam0[2] = 2.0 / 3.0;
gam1[2] = 1.0 / 3.0;
c[2] = 0.5;
} else if (name_ == "rk4") {
// Classic 5-stage SSPRK(5)4 in low-storage form
// ceff = 0.377
Expand All @@ -128,31 +140,38 @@ LowStorageIntegrator::LowStorageIntegrator(const std::string &name)
beta.resize(nstages);
gam0.resize(nstages);
gam1.resize(nstages);
c.resize(nstages);

delta[0] = 1.0;
beta[0] = 0.357534921136978;
gam0[0] = 0.0;
gam1[0] = 1.0;
c[0] = 0.0;

delta[1] = 0.0;
beta[1] = 2.364680399061355;
gam0[1] = -3.666545952121251;
gam1[1] = 4.666545952121251;
c[1] = 0.357534921136978;

delta[2] = 0.0;
beta[2] = 0.016239790859612;
gam0[2] = 0.035802535958088;
gam1[2] = 0.964197464041912;
c[2] = 1.0537621812245777;
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Is a time offset >1 allowed?

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That is unexpected. I observed the expected order of convergence so I assumed it was correct but am not an expert in SSP RK methods.

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I couldn't find any restrictions c so I experimented with changing c[2] <- 1.0 and the result was a loss of accuracy (to 1st order).


delta[3] = 0.0;
beta[3] = 0.498173799587251;
gam0[3] = 4.398279365655791;
gam1[3] = -3.398279365655790;
c[3] = 0.05396714924417825;

delta[4] = 0.0;
beta[4] = 0.433334235669763;
gam0[4] = 0.770411587328417;
gam1[4] = 0.229588412671583;
c[4] = 0.7355363985311864;

} else {
throw std::invalid_argument("Invalid selection for the time integrator: " + name_);
}
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1 change: 1 addition & 0 deletions src/time_integration/staged_integrator.hpp
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Expand Up @@ -55,6 +55,7 @@ class LowStorageIntegrator : public StagedIntegrator {
std::vector<Real> beta;
std::vector<Real> gam0;
std::vector<Real> gam1;
std::vector<Real> c; // time offset of each stage
};

// TODO(JMM): Should this be named ButcherTableauIntegrator?
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