From: Martin Kronbichler Date: Tue, 25 Aug 2009 12:16:39 +0000 (+0000) Subject: Provide an implemention for a Chebyshev polynomial preconditioner. X-Git-Tag: v8.0.0~7231 X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=66f46520cc8e17899ba6bb7876e212ff76425999;p=dealii.git Provide an implemention for a Chebyshev polynomial preconditioner. git-svn-id: https://svn.dealii.org/trunk@19337 0785d39b-7218-0410-832d-ea1e28bc413d --- diff --git a/deal.II/lac/include/lac/precondition.h b/deal.II/lac/include/lac/precondition.h index bcab1dc28b..1707b0f450 100644 --- a/deal.II/lac/include/lac/precondition.h +++ b/deal.II/lac/include/lac/precondition.h @@ -16,9 +16,10 @@ // This file contains simple preconditioners. #include -#include #include #include +#include +#include DEAL_II_NAMESPACE_OPEN @@ -96,7 +97,7 @@ class PreconditionIdentity : public Subscriptor * * In Krylov-space methods, this preconditioner should not have any * effect. Using SolverRichardson, the two relaxation parameters will - * be just multiplied. Still, this class is usefull in multigrid + * be just multiplied. Still, this class is useful in multigrid * smoother objects (MGSmootherRelaxation). * * @author Guido Kanschat, 2005 @@ -814,7 +815,216 @@ class PreconditionedMatrix : public Subscriptor }; - + +/** + * Preconditioning with a Chebyshev polynomial for symmetric positive + * definite matrices. This preconditioner is similar to a Jacobi + * preconditioner if the degree variable is set to one, otherwise some + * higher order polynomial corrections are used. This preconditioner needs + * access to the diagonal of the matrix its acts on and needs a respective + * vmult implemention. However, it does not need to explicitly know + * the matrix entries. + * + * This class is useful e.g. in multigrid smoother objects, since it is + * trivially %parallel (assuming that matrix-vector products are %parallel). + * + * @author Martin Kronbichler, 2009 + */ +template , class VECTOR=Vector > +class PreconditionChebyshev : public Subscriptor +{ +public: + /** + * Standardized data struct to + * pipe additional parameters + * to the preconditioner. + */ + struct AdditionalData + { + /** + * Constructor. + */ + AdditionalData (const unsigned int degree = 1, + const double smoothing_range = 0., + const bool nonzero_starting = false, + const unsigned int eig_cg_n_iterations = 8, + const double eig_cg_residual = 1e-2); + + /** + * This determines the degree of the + * Chebyshev polynomial. The degree + * of the polynomial gives the number + * of matrix-vector products to be + * performed for one application of + * the vmult() operation. + */ + unsigned int degree; + + /** + * This sets the range between the + * largest eigenvalue in the matrix + * and the smallest eigenvalue to be + * treated. If the parameter is zero, + * an estimate for the largest and + * for the smallest eigenvalue will + * be calculated + * internally. Otherwise, the + * Chebyshev polynomial will act in + * the interval + * $[\lambda_\mathrm{max}/ + * \tt{smoothing\_range}, + * \lambda_\mathrm{max}]$, where + * $\lambda_\mathrm{max}$ is an + * estimate of the maximum eigenvalue + * of the matrix. A choice of + * smoothing_range between 5 + * and 20 is useful in case the + * preconditioner is used as a + * smoother in multigrid. + */ + double smoothing_range; + + /** + * When this flag is set to + * true, it enables the + * method vmult(dst, src) to + * use non-zero data in the vector + * dst, appending to it the + * Chebyshev corrections. This can be + * useful in some situations + * (e.g. when used for high-frequency + * error smoothing in a multigrid + * algorithm), but not the way the + * solver classes expect a + * preconditioner to work (where one + * ignores the content in + * dst for the + * preconditioner application). + */ + bool nonzero_starting; + + /** + * Maximum number of CG iterations + * performed for finding the maximum + * eigenvalue. + */ + unsigned int eig_cg_n_iterations; + + /** + * Tolerance for CG iterations + * performed for finding the maximum + * eigenvalue. + */ + double eig_cg_residual; + }; + + PreconditionChebyshev (); + + /** + * Initialize function. Takes the + * matrix which is used to form the + * preconditioner, and additional + * flags if there are any. This + * function works only if the input + * matrix has an operator + * el(i,i) for accessing all + * the elements in the + * diagonal. Otherwise, use the other + * initialize function to + * manually provide the diagonal. + * + * This function calculates an + * estimate of the eigenvalue range + * of the matrix weighted by its + * diagonal using a modified CG + * iteration. + */ + void initialize (const MATRIX &matrix, + const AdditionalData &additional_data = AdditionalData()); + + /** + * Second initialize function. Takes + * the matrix which is used to form + * the preconditioner, a vector + * containing the inverse of + * the diagonal of the input matrix, + * and additional flags if there are + * any. + */ + void initialize (const MATRIX &matrix, + const VECTOR &diagonal_inverse, + const AdditionalData &additional_data = AdditionalData()); + + /** + * Computes the action of the + * preconditioner on src, + * storing the result in + * dst. + */ + void vmult (VECTOR &dst, + const VECTOR &src) const; + + /** + * Resets the preconditioner. + */ + void clear (); + +private: + + /** + * A pointer to the underlying + * matrix. + */ + SmartPointer matrix_ptr; + + /** + * Stores the inverse of the diagonal + * of the underlying matrix. + */ + VECTOR diagonal_inverse; + + /** + * Internal vector used for + * vmult operation. + */ + mutable VECTOR update1; + + /** + * Internal vector used for + * vmult operation. + */ + mutable VECTOR update2; + + /** + * Stores the additional data + * provided to the initialize + * function. + */ + AdditionalData data; + + /** + * Average of the largest and + * smallest eigenvalue under + * consideration. + */ + double theta; + + /** + * Half the interval length between + * the largest and smallest + * eigenvalue under consideration. + */ + double delta; + + /** + * Stores whether the preconditioner + * has been set up. + */ + bool is_initialized; +}; + + + /*@}*/ /* ---------------------------------- Inline functions ------------------- */ @@ -1289,6 +1499,190 @@ PreconditionedMatrix return dst.l2_norm (); } + + +//--------------------------------------------------------------------------- + +template +inline +PreconditionChebyshev::AdditionalData:: +AdditionalData (const unsigned int degree, + const double smoothing_range, + const bool nonzero_starting, + const unsigned int eig_cg_n_iterations, + const double eig_cg_residual) + : + degree (degree), + smoothing_range (smoothing_range), + nonzero_starting (nonzero_starting), + eig_cg_n_iterations (eig_cg_n_iterations), + eig_cg_residual (eig_cg_residual) +{} + + + +template +inline +PreconditionChebyshev::PreconditionChebyshev () + : + is_initialized (false) +{} + + + +template +inline +void +PreconditionChebyshev::initialize (const MATRIX &matrix, + const AdditionalData &additional_data) +{ + VECTOR diagonal_inv (matrix.m()); + for (unsigned int i=0; i +inline +void +PreconditionChebyshev::initialize (const MATRIX &matrix, + const VECTOR &diagonal_inv, + const AdditionalData &additional_data) +{ + Assert (matrix.m() == matrix.n(), ExcMessage("Matrix not quadratic.")); + matrix_ptr = &matrix; + update1.reinit (diagonal_inv, true); + update2.reinit (diagonal_inv, true); + diagonal_inverse = diagonal_inv; + data = additional_data; + + // calculate largest eigenvalue using a + // hand-tuned CG iteration on the matrix + // weighted by its diagonal. + // + // TODO: can we obtain this with the + // standard CG method? we would need to + // read the logfile in that case, which + // does not seem feasible. + double max_eigenvalue, min_eigenvalue; + { + double eigen_beta_alpha = 0; + + std::vector diagonal; + std::vector offdiagonal; + + VECTOR rhs, g; + rhs.reinit(diagonal_inv, true); + rhs = 1./sqrt(matrix.m()); + g.reinit(diagonal_inv, true); + + int it=0; + double res,gh,alpha,beta; + + g.equ(-1.,rhs); + res = g.l2_norm(); + update2.equ (-1., g); + gh = res*res; + + while (true) + { + it++; + matrix.vmult (update1, update2); + update1.scale (diagonal_inverse); + alpha = update2 * update1; + alpha = gh/alpha; + g.add (alpha, update1); + res = g.l2_norm(); + + if (it > data.eig_cg_n_iterations || res < data.eig_cg_residual) + break; + + beta = gh; + gh = res*res; + beta = gh/beta; + update2.sadd (beta, -1., g); + + diagonal.push_back (1./alpha + eigen_beta_alpha); + eigen_beta_alpha = beta/alpha; + offdiagonal.push_back(std::sqrt(beta)/alpha); + } + + TridiagonalMatrix T(diagonal.size(), true); + for (unsigned int i=0;i 0 ? + max_eigenvalue / data.smoothing_range : + max_eigenvalue / min_eigenvalue); + delta = (beta-alpha)*0.5; + theta = (beta+alpha)*0.5; + is_initialized = true; +} + + + +template +inline +void +PreconditionChebyshev::vmult (VECTOR &dst, + const VECTOR &src) const +{ + Assert (is_initialized, ExcMessage("Preconditioner not initialized")); + double rhok = delta / theta, sigma = theta / delta; + if (data.nonzero_starting && !dst.all_zero()) + { + matrix_ptr->vmult (update1, dst); + update1 -= src; + update1 /= theta; + update1.scale (diagonal_inverse); + dst -= update1; + } + else + { + dst.equ (1./theta, src); + dst.scale (diagonal_inverse); + update1.equ(-1.,dst); + } + + for (unsigned int k=0; kvmult (update2, dst); + update2 -= src; + update2.scale (diagonal_inverse); + const double rhokp = 1./(2.*sigma-rhok); + const double factor1 = rhokp * rhok, factor2 = 2.*rhokp/delta; + rhok = rhokp; + update1.sadd (factor1, factor2, update2); + dst -= update1; + } +} + + + +template +inline +void PreconditionChebyshev::clear () +{ + is_initialized = false; + matrix_ptr = 0; + diagonal_inverse.reinit(0); + update1.reinit(0); + update2.reinit(0); +} + + + #endif // DOXYGEN DEAL_II_NAMESPACE_CLOSE