Implicit stepping methods from the TimeStepping-namespace for large sparse matrices

[Maxi Miller]

As far as I understand all implicit time-stepping methods in the TimeStepping-namespace take a function which invert the jacobian matrix and the mass matrix (combined). This is done using a sparse solver (UMFPACK). Is it that still possible for a larger system (10kk DoFs), or do I have to resort to other methods, after inverting the sparse matrix will result in a dense matrix (which likely will overflow my memory)?

[Daniel Arndt]

Maxi,

The interface for TimeStepping::evolve_one_time_step is:

virtual double

  evolve_one_time_step(

  std::vector<std::function<VectorType(const double, const VectorType &)>>

  & F,

  std::vector<std::function<

  VectorType(const double, const double, const VectorType &)>> &J_inverse,

  double t,

  double delta_t,

  VectorType & y);

and does not depend on UMFPACK at all. You just need to provide a function-type object that can be used for evaluating the inverse of the Jacobians and the right-hand side.

You might also want to have a look at the test base/time_stepping_01 (https://github.com/dealii/dealii/blob/master/tests/base/time_stepping_01.cc).

Best,

Daniel

Am Mo., 15. Juli 2019 um 15:04 Uhr schrieb 'Maxi Miller' via deal.II User Group <dea...@googlegroups.com>:

As far as I understand all implicit time-stepping methods in the TimeStepping-namespace take a function which invert the jacobian matrix and the mass matrix (combined). This is done using a sparse solver (UMFPACK). Is it that still possible for a larger system (10kk DoFs), or do I have to resort to other methods, after inverting the sparse matrix will result in a dense matrix (which likely will overflow my memory)?

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[Maxi Miller]

If I understand it correctly, that is equivalent to solving Ax = b, with A and b given, and x returned?

Am Montag, 15. Juli 2019 22:03:46 UTC+2 schrieb Daniel Arndt:

Maxi,

The interface for TimeStepping::evolve_one_time_step is:

virtual double

  evolve_one_time_step(

  std::vector<std::function<VectorType(const double, const VectorType &)>>

  & F,

  std::vector<std::function<

  VectorType(const double, const double, const VectorType &)>> &J_inverse,

  double t,

  double delta_t,

  VectorType & y);

and does not depend on UMFPACK at all. You just need to provide a function-type object that can be used for evaluating the inverse of the Jacobians and the right-hand side.

You might also want to have a look at the test base/time_stepping_01 (https://github.com/dealii/dealii/blob/master/tests/base/time_stepping_01.cc).

Best,

Daniel

Am Mo., 15. Juli 2019 um 15:04 Uhr schrieb 'Maxi Miller' via deal.II User Group <dea...@googlegroups.com>:

As far as I understand all implicit time-stepping methods in the TimeStepping-namespace take a function which invert the jacobian matrix and the mass matrix (combined). This is done using a sparse solver (UMFPACK). Is it that still possible for a larger system (10kk DoFs), or do I have to resort to other methods, after inverting the sparse matrix will result in a dense matrix (which likely will overflow my memory)?

--
The deal.II project is located at http://www.dealii.org/
For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en
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