A parallel AMG for overlapping and non-overlapping domain decomposition.
A parallel block Lanczos algorithm and its implementation for the evaluation of some eigenvalues of large sparse symmetric matrices on multicomputers
In the present work we describe HPEC (High Performance Eigenvalues Computation), a parallel software package for the evaluation of some eigenvalues of a large sparse symmetric matrix. It implements an efficient and portable Block Lanczos algorithm for distributed memory multicomputers. HPEC is based on basic linear algebra operations for sparse and dense matrices, some of which have been derived by ScaLAPACK library modules. Numerical experiments have been carried out to evaluate HPEC performance...
A parallel Cholesky algorithm for the solution of symmetric linear systems.
A parallel GMRES version for general sparse matrices.
A parallel iterative procedure applicable to the approximate solution of second order partial differential equations by mixed finite element methods.
A parallel method for population balance equations based on the method of characteristics
In this paper, we present a parallel scheme to solve the population balance equations based on the method of characteristics and the finite element discretization. The application of the method of characteristics transform the higher dimensional population balance equation into a series of lower dimensional convection-diffusion-reaction equations which can be solved in a parallel way. Some numerical results are presented to show the accuracy and efficiency.
A parallel method of solution of the differential equations by the formulas containing higher derivatives
A parallel multigrid method using the full domain partition.
A parallel projection method for linear algebraic systems
A direct projection method for solving systems of linear algebraic equations is described. The algorithm is equivalent to the algorithm for minimization of the corresponding quadratic function and can be generalized for the minimization of a strictly convex function.
A Parallel Projection Method for Solving Generalized Linear Least-Squares Problems.
A parallel QR-factorization/solver of quasiseparable matrices.
A parallel splitting-up method for partial differential equations and its applications to Navier-Stokes equations
A parameter choice for Tikhonov regularization for solving nonlinear inverse problems leading to optimal convergence rates
We give a derivation of an a-posteriori strategy for choosing the regularization parameter in Tikhonov regularization for solving nonlinear ill-posed problems, which leads to optimal convergence rates. This strategy requires a special stability estimate for the regularized solutions. A new proof fot this stability estimate is given.
A parameter choice method for Tikhonov regularization.
A parameter robust method for singularly perturbed delay differential equations.
A parameter-free smoothness indicator for high-resolution finite element schemes
This paper presents a postprocessing technique for estimating the local regularity of numerical solutions in high-resolution finite element schemes. A derivative of degree p ≥ 0 is considered to be smooth if a discontinuous linear reconstruction does not create new maxima or minima. The intended use of this criterion is the identification of smooth cells in the context of p-adaptation or selective flux limiting. As a model problem, we consider a 2D convection equation discretized with bilinear finite...
A parameter-free stabilized finite element method for scalar advection-diffusion problems
We formulate and study numerically a new, parameter-free stabilized finite element method for advection-diffusion problems. Using properties of compatible finite element spaces we establish connection between nodal diffusive fluxes and one-dimensional diffusion equations on the edges of the mesh. To define the stabilized method we extend this relationship to the advection-diffusion case by solving simplified one-dimensional versions of the governing equations on the edges. Then we use H(curl)-conforming...
A parameterized lower bound for the smallest singular value.
A parametrized Newton method for nonsmooth equations with finitely many maximum functions
In this paper we propose a parametrized Newton method for nonsmooth equations with finitely many maximum functions. The convergence result of this method is proved and numerical experiments are listed.
A partially ordered space connected with the de la Vallée Poussin problem