TS: add support for transient variables in BDF

This feature enables conservative time integration even when using
nonconservative state variables. The formulation, which requires only
the definitio

TS: add support for transient variables in BDF

This feature enables conservative time integration even when using
nonconservative state variables. The formulation, which requires only
the definition of transient (conservative) variables C(U) as a
function of the state variable U, is appropriate for linear multistep
methods for ODE and DAE.

This technique could be extended to Runge-Kutta methods by creating an
index-1 DAE by augmentation with the equation C = C(U). The stage
equations in diagonally implicit methods generally ask to solve for Y:

F(Y, alpha Y + Z) = 0

where Y = [C, U] and Z is known from prior stages. With the augmented
equation, this decouples to

C - C(U) = 0
f(U, alpha C + C_z) = 0

This commit includes an example demonstrating loss of conservation in
chain rule primitive-variable IFunction, while preserving it for
pure-conservative variables and the transient variable formulation.

Resolves #547

Requested-by: Gautam Bisht <gautam.bisht@pnnl.gov>
Thanks-to: Hong Zhang <hongzhang@anl.gov>

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ESSL: reorganize code that handles PETSC_MISSING_LAPACK by using PetscMissingLapack()

And sync the missing function list with missing functions in current ESSL

If we find more LAPACK symbols missin

ESSL: reorganize code that handles PETSC_MISSING_LAPACK by using PetscMissingLapack()

And sync the missing function list with missing functions in current ESSL

If we find more LAPACK symbols missing in commonly used LAPACK impls,
we can add them back in the new format.

src/ksp/pc/impls/bddc/bddcprivate.c has alternate code for
PETSC_MISSING_LAPACK_GESVD. This code is retained for now [in case we
need to add this flag back in]

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Merge remote-tracking branch 'origin/maint'

fix memory leak in TSInterpolate_Sundials

Remove usage of PETSC_HAVE_FORTRAN_STDCALL, PETSC_BLASLAPACK_STDCALL, HAVE_FORTRAN_MIXED_STR_ARG flags - as Compaq f90 compiler is no longer supported

Fix more typos and add missing examples

added petsc maxord option

Merge remote-tracking branch 'origin/dalcinl/test-ts'

Minor fix for TSStep and tests for TSRK types

See merge request petsc/petsc!2462

TSRK: Add TSRKGetOrder()

TSRK: add tableau getter

TSRK: remove dead declaration

TSARKIMEX: add getter for fully implicit flag

Update test outputs

Merge remote-tracking branch 'origin/maint'

TSAlpha: fix spelling "Algoritmic" -> "Algorithmic"

Merge remote-tracking branch 'origin/maint'

Double CHKERRQ

Recompute shift and stage time if the step is rejected

Funded-by:
Project:
Time:
Reported-by: Stefano Zampini
Thanks-to:

Clean up the use of shift

This commit is intended to improve the code readability.

- Remove unnecessary changes to the shift field
- Make it more obvious that a TLM step does not alter the shift fi

Clean up the use of shift

This commit is intended to improve the code readability.

- Remove unnecessary changes to the shift field
- Make it more obvious that a TLM step does not alter the shift field when exit
- Use local variables as much as possible

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Merge branch 'knepley/fix-ts-theta-snes-eval' into 'master'

TS: SNESTSFormFunction/Jacobian_Theta() needs to recalculate the shift

See merge request petsc/petsc!2170

Replace use of 1 with appropriate error code; use PetscObjecComm() instead of PETSC_COMM_SELF for errors when appropriate

Commit-type: error-checking, testing-fix, style-fix, examples