In the case of adiabatic electrons the gyrokinetic field equation for the electrostatic potential includes an averaging operator acting on flux surfaces. For realistic three-dimensional configurations, as e.g. in stellarator devices, the discretisation of this integro-differential equation leads to very large nearly dense matrices (full matrix approach) which typically cannot be stored in compu...

We consider a family of symmetric matrices A! = A 0 + !B; with a nonnegative deenite matrix A 0 ; a positive deenite matrix B; and a nonnegative parameter ! 1: Small ! leads to a poor conditioned matrix A! with jumps in the coeecients. For solving linear algebraic equations with the matrix A!; we use standard preconditioned iterative methods with the matrix B as a preconditioner. We show that a...

We propose a Preconditioned Locally Harmonic Residual (PLHR) method for computing several interior eigenpairs of a generalized Hermitian eigenvalue problem, without traditional spectral transformations, matrix factorizations, or inversions. PLHR is based on a short-term recurrence, easily extended to a block form, computing eigenpairs simultaneously. PLHR can take advantage of Hermitian positiv...

Many applications based on finite element and finite difference methods include the solution of large sparse linear systems using preconditioned iterative methods. Matrix vector multiplication is one of the key operations that has a significant impact on the performance of any iterative solver. In this paper, recent developments in sparse storage formats on vector machines are reviewed. Then, s...

We study a variant of the Schwarz-preconditioned HMC algorithm. In contrast to the original proposal of Lüscher, we apply the domain decomposition in one lattice direction only. This is sufficient to reduce the condition number of the fermion matrix restricted to the domains compared with the full fermion matrix. For the same linear extension of the domain, less links reside on the boundaries o...

BLOCK TRIANGULAR PRECONDITIONERS FOR -MATRICES AND MARKOV CHAINS MICHELE BENZI AND BORA UÇAR Abstract. We consider preconditioned Krylov subspace methods for solving large sparse linear systems under the assumption that the coefficient matrix is a (possibly singular) -matrix. The matrices are partitioned into block form using graph partitioning. Approximations to the Schur complement are used t...

agonal (scaling) preconditioning is used, the condition number of the preconditioned incremental unknowns matrix associated to the Laplace operator is p(d)O((logd h) ) for the first order incremental unknowns, and q(d)O(| logd h|) for the second order incremental unknowns. For comparison, the condition number of the nodal unknowns matrix associated to the Laplace operator is O(1/h). Therefore, ...

We present nonoverlapping domain decomposition techniques applied to a two-stage NumerovGalerkin finite element model of the shallow water equations over a limited-area domain. The Schur complement matrix formulation is employed and a modified interface matrix approach is proposed to handle the coupling between subdomains. The resulting nonsymmetric Schur complement matrices, modified interface...

This paper presents new implementation of one–sided Jacobi SVD for triangular matrices and its use as the core routine in a new preconditioned Jacobi SVD algorithm, recently proposed by the authors. New pivot strategy exploits the triangular form and uses the fact that the input triangular matrix is the result of rank revealing QR factorization. If used in the preconditioned Jacobi SVD algorith...