Numerical Algorithms
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Circumcentering the Douglas–Rachford method
Numerical Algorithms - Tập 78 - Trang 759-776 - 2017
We introduce and study a geometric modification of the Douglas–Rachford method called the Circumcentered–Douglas–Rachford method. This method iterates by taking the intersection of bisectors of reflection steps for solving certain classes of feasibility problems. The convergence analysis is established for best approximation problems involving two (affine) subspaces and both our theoretical and nu......
Additive block diagonal preconditioning for block two-by-two linear systems of skew-Hamiltonian coefficient matrices
Numerical Algorithms - Tập 62 - Trang 655-675 - 2013
For a class of block two-by-two systems of linear equations with certain skew-Hamiltonian coefficient matrices, we construct additive block diagonal preconditioning matrices and discuss the eigen-properties of the corresponding preconditioned matrices. The additive block diagonal preconditioners can be employed to accelerate the convergence rates of Krylov subspace iteration methods such as MINRES......
Stabilized finite element method for the viscoelastic Oldroyd fluid flows
Numerical Algorithms - Tập 60 Số 1 - Trang 75-100 - 2012
Hermite polynomials on the plane
Numerical Algorithms - Tập 45 - Trang 231-238 - 2007
The space
${\cal P}_n$
of bivariate generalised Hermite polynomials of degree n is invariant under rotations. We exploit this symmetry to construct an orthonormal basis for
${\cal P}_n$
which consists of the ro......
An approximate waves-bordering algorithm for adaptive finite elements analysis
Numerical Algorithms - Tập 21 - Trang 311-322 - 1999
In this paper an Approximate Waves-Bordering algorithm (AWB) is presented. It computes the finite elements linear system solution-update after a refinement/unrefinement step. This is done taking into consideration only the equations that correspond to the nodes whose solution is modified above a certain tolerance and it appears to be very efficient. The algorithm considers an increasing set of equ......
Recurrence relations for semilocal convergence of a fifth-order method in Banach spaces
Numerical Algorithms - - 2012
A priori error estimates of a discontinuous Galerkin method for the Navier-Stokes equations
Numerical Algorithms - - 2023
This-36pt paper considers a discontinuous Galerkin finite element method for the 2D transient and incompressible Navier-Stokes model. Following the analysis of Heywood and Rannacher (SIAM J. Numer. Anal. 19:275–311, 1982), we derive optimal velocity and pressure error estimates in
$$L^{\infty }({\textbf {L}}^{2})$$
......
A numerical method for stationary shock problems with monotonic solutions
Numerical Algorithms - Tập 77 - Trang 1117-1139 - 2017
Numerical methods are considered for singularly perturbed quasilinear problems having interior-shock solutions. It is shown that the direct discretization on a layer-adapted mesh is ineffective for these problems. A special method is proposed for the case when the solution is monotonic: the problem is transformed by interchanging the dependent and independent variables, and it is then discretized ......
Hardware Implementation of Discrete Stochastic Arithmetic
Numerical Algorithms - Tập 37 - Trang 21-33 - 2004
In this paper we present a hardware implementation of the Discrete Stochastic Arithmetic (DSA) which is based on CESTAC (Controle et Estimation STochastique des Arrondis de Calculs), a method of controlling round-off errors in floating-point scientific computations. Real-time software implementation of this method suffers from computation bottlenecks. This paper gives a hardware alternative that w......
On a nonlinear mean and its application to image compression using multiresolution schemes
Numerical Algorithms - Tập 71 Số 4 - Trang 729-752 - 2016
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