Dear PETSc Team, May I request your opinion of the development proposal in the following mail. This work has been carried out in the framework of a PhD thesis ; besides the scientific goals, the proposed features are intended to be integrated in the open-source software Code_Aster, a general purpose finite element solver developed at EDF R&D, in particular for nuclear safety assessment. In order to ensure the perennity of the development, their integration within PETSc is crucial.
This is why I gently request your position on their integration in PETSc. Let us know your policy on the subject and do not hesitate to request for extra integration work if needed. Best regards, Nicolas [cid:[email protected]] Nicolas Tardieu Head of the Rotating Machinery Group EDF - R&D [email protected] Tél. : +33 1 47 65 39 05 ---------- Forwarded message ---------- From: Sylvain Mercier <[email protected]<mailto:[email protected]>> Date: 2015-11-03 17:09 GMT+01:00 Subject: [petsc-dev] Contribution proposal about the computation of (harmonic) Ritz pairs within GMRES To: [email protected]<mailto:[email protected]> Hi everyone, During my phd thesis, I have worked on solving sequences of linear systems with slowly varying matrices using GMRES(restart). In particular, I have developed a preconditioning technique to improve the action of an existing "first-level preconditioner". This new method is defined using Ritz or harmonic Ritz vectors obtained at the end of the solution of a linear system. Then I have developed two routines in PETSc (that I've called KSPSetComputeRitz and KSPComputeRitz) in order to compute the (harmonic) Ritz pairs associated to the smallest or largest (harmonic) Ritz values in modulus computed from the Hessenberg matrix of the last complete cycle in GMRES. Beyond the application to the preconditioning technique that I have developed, this routine can be used to recover approximated eigenpairs (and not only eigenvalues as already available in PETSc) of the preconditioned matrix at the end of a solution with GMRES. That is why I propose this contribution. Two new routines has been developed, similarly to the existing routines KSPSetComputeEigenvalues and KSPComputeEigenvalues. The first one is called KSPSetComputeRitz and sets a flag so that the last complete Hessenberg matrix computed with GMRES(restart) will be stored. Here is the synopsis of the current version (located in src/ksp/ksp/interface/itfunc.c) PetscErrorCode KSPSetComputeEigenvalues(KSP ksp,PetscBool flg) Input Parameters ksp - iterative context obtained from KSPCreate() flg - PETSC_TRUE or PETSC_FALSE The second routine aims at computing the Ritz or harmonic Ritz associated to the smallest or largest values in modulus. Here is the synopsis of the current version (located in src/ksp/ksp/impls/gmres/gmreig.c) PetscErrorCode KSPComputeRitz(KSP ksp,PetscBool ritz,PetscBool small,PetscInt *nrit,Vec S[],PetscReal tetar[],PetscReal tetai[]) Input Parameter ksp - iterative context obtained from KSPCreate() ritz - PETSC_TRUE or PETSC_FALSE to compute Ritz pairs and harmonic Ritz pairs, respectively small - PETSC_TRUE or PETSC_FALSE to compute pairs associated to smallest or largest values in modulus, respectively Input/Output parameter n - The number of required and recovered pairs Output Parameters S[] - a multidimensional PETSc vector to store the (harmonic) Ritz vectors, provided by user with a dimension of at least n tetar - real part of computed (harmonic) Ritz values, provided by user with a dimension of at least n tetai - imaginary part of computed (harmonic) Ritz values, provided by user with a dimension of at least n This routine has been developed whithin GMRES for real-valued linear systems. Then the (harmonic) Ritz pairs are possibly complex-valued and conjugated. In this case, two successive columns of S are equal to the real and the imaginary parts of the vectors. Finally, the routine KSPSolve_GMRES (located in src/ksp/ksp/impls/gmres/gmreig.c) has been modified in order to store the Hessenberg matrix and the basis vectors of the Krylov subspace as soon as a complete cycle has been performed. To conclude, I propose to contribute to PETSc with these developments (I have followed the conventions detailed in the developer guide). Please find attached a patch and the modified files. Regards, Sylvain Ce message et toutes les pièces jointes (ci-après le 'Message') sont établis à l'intention exclusive des destinataires et les informations qui y figurent sont strictement confidentielles. Toute utilisation de ce Message non conforme à sa destination, toute diffusion ou toute publication totale ou partielle, est interdite sauf autorisation expresse. 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Ritz_routines.tar.gz
Description: Ritz_routines.tar.gz
