Summer of Code - Getting Started: Difference between revisions

Summer of Code - Getting Started (edit)

Revision as of 17:43, 18 June 2013

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→‎Improve a multi-dimensional solver based on Spectral Variational Integrators

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 Details on the methods to be implemented can be found in [http://dx.doi.org/10.1145/502800.502801 this paper] on bvp4c and [http://www.jnaiam.net/new/uploads/files/014dde86eef73328e7ab674d1a32aa9c.pdf this paper] on bvp5c. Further details are available in [http://books.google.it/books/about/Nonlinear_two_point_boundary_value_probl.html?id=s_pQAAAAMAAJ&redir_esc=y this book].
-=== Improve a multi-dimensional solver based on Spectral Variational Integrators ===
+=== Geometric integrators for Hamiltonian Systems ===
-The goal here is to implement some missing functionalities of a solver, already implemented and working, that uses Spectral
+[http://openlibrary.org/books/OL9056139M/Geometric_Numerical_Integration | Geometric (AKA Symplectic) integrators] are useful for
-Variational Integrator methods to find the solutions in multi-dimensional classical mechanics problems. You can find more details
+multi-dimensional classical mechanics problems and for molecular dynamics simulations.
-on these methods [http://arxiv.org/abs/1211.4534 here] or [http://www.math.ucsd.edu/~mleok/pdf/HaLe2012_SVI.pdf here]. This solver will be included in a package with other solvers used for the same type of problems. Some functionalities to implement would be the polynomial order adaptivity and the possibility to use the Jacobian in the function that solves the nonlinear problem at each iteration.
+The odepkg package has a number of solvers for ODE, DAE and DDE problems but none of them is currently
+specifically suited for second order problems in general and Hamiltonian systems in particular.
+Therefore a new package for geometric integrators would be a useful contribution.
+This could be created as new package or added as a set of new functions for odepkg.
+The function interface should be consistent throughout the package and should be modeled to follow
+that of other functions in odepkg (or that of DASPK and LSODE) but will need specific  extensions to accommodate for specific options that only make sense for this specific class of solvers.
+An initial list of methods to be implemented includes (but is not limited to)
+* Symplectic Euler methods
+* Störmer-Verlet method
+* Velocity Verlet method
+* Spectral Variational Integrator methods, see [http://arxiv.org/abs/1211.4534 here] or [http://www.math.ucsd.edu/~mleok/pdf/HaLe2012_SVI.pdf here]
+For this latter there is an existing code which is already working but needs to be improved, posted on the patch tracker (TODO)
+Furthermore, methods to implement solutions of problems with rigid constraints should be implemented, e.g.
+* SHAKE
+* RATTLE
 == GUI ==