Re: [Quantlib-dev] fd questions ctd...

[Klaus S. <kl...@sp...>]

Hi Peter,

I'm going to integrate the time dependent Dirichlet bc into QL 1.2 and SVN 
now. Might be that I need to come back to you in case I have additional 
questions.

regards
Klaus

On Saturday 12 May 2012 19:24:55 Peter Caspers wrote:
> Hi Klaus,
>
> yes, I totally agree. Concerning the time dependent Dirichlet bc I guess
> one should insert a
>
> bc->setTime( t );
>
> before each call of applyAfterApplying(Array&),
> applyAfterSolving(Array&) or applyAfterApplying(Real,Real) to ensure
> that valueOnBoundaryTimeDep_ / valuesOnBoundaryTimeDep_ are correctly
> set. No?
>
> Concerning the Neumann bc, I was too optimistic about what has to be
> done to adapt the existing operators. You are right, it is not enough to
> provide discretizations for the base operators in the general case. It
> works fine in my toy example but it is useless otherwise. Sorry I should
> have spent some more thoughts on this.
>
> I will be happy if you find the Dirichlet bc extension useful and add it
> to the SVN. I will also continue to think about the Neumann bc and try
> to send more useful code next time ;-)
>
> thank you again and regards
> Peter
>
> Am 10.05.2012 23:16, schrieb Klaus Spanderen:
> > Hi Peter,
> >
> > cool stuff. The Dirichlet bc was introduced to implement barrier options
> > only. Your time dependent code the right step forward..and yes, the
> > implementation of the schemes is based on either free bc's or non time
> > dependent Dirichlet bc's. This is also the main reason why
> > FdmBoundaryConditionSet is linked to FdmDirichletBoundary instead of
> > OperatorTraits<FdmLinearOp>::bc_set. One think we still need to do is to
> > make
> >
> > FdmDirichletBoundary::applyAfterApplying(Real x, Real value) const;
> >
> > time dependent as well.
> >
> > As you have written It's difficult to implement the Neumann bc in a
> > general manner for the multi dimensional framework. In the one dim.
> > framework all linear operators are tridiagonal operators and the Neumann
> > bc is "doable". I have no idea how to translate this idea into the multi
> > dimensional case except implementing the Neumann bc for all 10+ operators
> > individually. (hmm.. I don't think it is enough to do this for the three
> > basis operators alone).
> >
> >> Needless to say that I am totally not sure if I did that correctly.
> >
> > good question. I haven't seen much in the literature on the topic
> > "Neumann bc and operator splitting". I think we'll also at least need to
> > call applyBeforeSolving in the schemes for the Neumann bc case.
> >
> > IMO the Neumann bc task will take a bit longer. Shall we first lift the
> > time dependent Dirichlet bc to the QL 1.2 file structure and add this to
> > SVN?
> >
> > regards
> >   Klaus
> >
> > On Sunday 06 May 2012 21:24:39 Peter Caspers wrote:
> >> Hallo Klaus,
> >>
> >> thanks a lot for your answers. I implemented a Neumann condition for the
> >> multidimensional case. I tested the new class against known solutions
> >> for the 1d heat equation with Neumann and mixed lower Dirichlet / upper
> >> Neumann conditions using some of the existing multidim schemes. The
> >> results suggest that the implementation is ok. Also, the testsuite runs
> >> without problems which is good I guess.
> >>
> >> However, I could not see how to implement the condition by changing the
> >> final operator directly as done in the 1d framework. Instead I added
> >> functionality to change the discretization of multidim operators from
> >> default = FreeBoundary to Neumann by adding a method
> >>
> >> void FdmLinearOp::discretization(Size direction, Discretization d);
> >>
> >> The enum DiscretizationType in the same class can be used to specify a
> >> Neumann discretization together with the side (using bitwise or; this
> >> could be extended for other boundary conditions later). The method calls
> >> another protected virtual method changeDiscretization(...) which should
> >> be implemented by user defined operators. I did not do that for the
> >> existing operators yet (in case I am on the wrong road with my
> >> approach), but rather added a test operator FdmHeat1dOp (representing
> >> the pde u_t = \alpha u_xx) which demonstrates the principle. The
> >> required extension of operators can easily be done being supported by
> >> extended constructors of the 'basis' operators (first, second and mixed
> >> second derivatives) allowing for Neumann discretization now. I think I
> >> did that discretization in the standard way, but it should be cross
> >> checked.
> >>
> >> I amended the scheme implementations w.r.t. their calls to the
> >> apply...() methods having the impression that these accounted for the
> >> Dirichlet case only so far. Needless to say that I am totally not sure
> >> if I did that correctly. Since I also extended the Dirichlet condition
> >> to the time (and spatial) dependent case, I inserted the needed
> >> setTime() calls in the schemes accordingly. In the Dirichlet condition
> >> itself I implemented the applyBeforeSolving() method because I think it
> >> is necessary for the time dependent case (and comparisions to known 1d
> >> heat equation solutions do confirm this).
> >>
> >> I removed the FdmBoundaryConditionSet typedef from the multidim
> >> Dirichlet condition, instead refering to
> >> OperatorTraits<FdmLinearOp>::bc_set in the schemes, solvers, engines and
> >> operators now. There is a applyAfterApplying(Real,Real) method in the
> >> Dirichlet condition (used in some engine I think) which I added to the
> >> general interface (by default throwing an exception to ensure that only
> >> the implementation in the Dirichlet boundary is actually used).
> >>
> >> Finally I amended the concentrating1dmesher once again because I noted
> >> that it throws an exception when QL_EXTRA_SAFETY_CHECKS are enabled and
> >> the concentrating point is equal to one of the endpoints (this having to
> >> do with an extra check concerning the strict order of x values in
> >> interpolation.hpp).
> >>
> >> I attach my changes (zips with changed files as per directory and new
> >> files attached directly, all based on ql 1.1) and would be happy if you
> >> could have a look.
> >>
> >> Thank you
> >> Peter
>
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