TensorKrylovSolver: MATRIX-FREE Krylov solver (BiCGStab) with MG preconditioning, for the FULL-TENSOR elliptic operator L(phi) = -div(A grad phi) + kappa phi, A possibly non-symmetric. More...

#include <pops/core/foundation/types.hpp>
#include <pops/mesh/layout/box_array.hpp>
#include <pops/mesh/layout/distribution_mapping.hpp>
#include <pops/mesh/geometry/geometry.hpp>
#include <pops/mesh/storage/mf_arith.hpp>
#include <pops/mesh/storage/multifab.hpp>
#include <pops/mesh/boundary/physical_bc.hpp>
#include <pops/numerics/elliptic/linear/krylov_result.hpp>
#include <pops/numerics/elliptic/mg/geometric_mg.hpp>
#include <pops/numerics/elliptic/poisson/poisson_operator.hpp>
#include <pops/parallel/comm.hpp>
#include <cassert>
#include <cmath>

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Classes
class	pops::TensorKrylovSolver

Namespaces
namespace	pops

Detailed Description

TensorKrylovSolver: MATRIX-FREE Krylov solver (BiCGStab) with MG preconditioning, for the FULL-TENSOR elliptic operator L(phi) = -div(A grad phi) + kappa phi, A possibly non-symmetric.

Layer: include/pops/numerics/elliptic/linear. Role: solve the elliptic problem when A is NON-SYMMETRIC (cross term Axy != Ayx, e.g. the rotation B^{-1} arising from a Schur condensation), the case where the GeometricMG V-cycle ALONE (5-point Gauss-Seidel smoother, diagonal block, explicit cross terms) stalls or diverges. BiCGStab (and not GMRES): FIXED memory footprint, no restart. The matvec is apply_laplacian (full operator, strictly matrix-free); the preconditioner is N V-cycles of GeometricMG on the SYMMETRIC PART (diagonal block). Models the EllipticSolver concept. Contract: convention aligned with poisson_operator.hpp – we solve L_int(phi) = rhs with L_int = div(A grad phi) - kappa phi; the case A = I, kappa = 0 recovers the canonical Laplacian and converges to the SAME solution as GeometricMG (to the tolerance).

Invariants / constraints:

op and precond MUST be DISTINCT GeometricMG objects (assert in the constructor): apply_precond OVERWRITES precond.rhs()/phi() at every iteration; confusing them would destroy the solve iterate;
precond carries the SYMMETRIC part (same eps/eps_y/kappa, set_cross_terms NOT called);
DEVICE/MPI: named functors only; the dot products (dot, norm) are COLLECTIVE (all_reduce_sum) and called on ALL ranks, including a rank WITHOUT a box (no deadlock);
ADDITIVE: no existing path (GeometricMG / Poisson) goes through this header (opt-in).

include/pops/numerics/elliptic/linear/krylov_solver.hpp File Reference¶

Classes

Namespaces

Detailed Description