SIAM Journal on Scientific Computing

A procedure is presented for characterizing the asymptotic sampling distribution of estimators of the polynomial chaos (PC) coefficients of a second-order nonstationary and non-Gaussian random process by using a collection of observations. The random ...

A multilevel adaptive aggregation method for calculating the stationary probability vector of an irreducible stochastic matrix is described. The method is a special case of the adaptive smoothed aggregation and adaptive algebraic multigrid methods for ...

A new numerical method for solving the generalized regularized long wave equation is devised and analyzed. By using a reproducing kernel function, the numerical solution at each discrete time step is obtained by an explicit integral expression even ...

Spectral element methods on tetrahedra with symmetric collocation points can be accelerated by factorizing the discrete operators according to Hesthaven and Teng [SIAM J. Sci. Comput., 21 (2000), pp. 2352-2380]. While these authors focused on first-...

In this paper we present a new incomplete factorization of a square matrix into triangular factors in which we get standard $LU$ or $LDL^T$ factors (direct factors) and their inverses (inverse factors) at the same time. Algorithmically, we derive this ...

In this paper, we propose a stochastic mixed multiscale finite element method. The proposed method solves the stochastic porous media flow equation on the coarse grid using a set of precomputed basis functions. The precomputed basis functions are ...

We introduce a new method for the calculation of bounds on eigenvalues of Hessian matrices $\nabla^2 \varphi(x)$ of twice continuously differentiable functions $\varphi:U\subseteq\mathbb{R}^n\rightarrow \mathbb{R}$. The computational complexity of the ...

A new approach to derive transparent boundary conditions (TBCs) for dispersive wave, Schrödinger, heat, and drift-diffusion equations is presented. It relies on the pole condition and distinguishes between physically reasonable and unreasonable ...

In a recent paper, the authors introduced the recovery method (local energy matching principle) for solving large systems of lattice equations. The idea is to construct a partial differential equation along with a finite element discretization such that ...

BPcont, a driver for the software package Auto for the numerical continuation of simple branch points of algebraic and boundary-value problems, is described in detail. Simple branch points are points in the continuation space where two solution branches ...

This paper proposes new finite element spaces that can be constructed for agglomerates of standard elements that have certain regular structure. The main requirement is that the agglomerates share faces that have closed boundaries composed of 1-d edges. ...

We consider a norm-preconditioning approach for the solution of discontinuous Galerkin finite element discretizations of second order partial differential equations with a nonnegative characteristic form. Our solution method is a norm-preconditioned ...

We are interested in the numerical approximation of the complex Ginzburg-Landau equation in the large time and space limit. There are two interesting regimes in this problem, one being the large space time limit, and one being the nonlinear Schrödinger ...

In this paper, we consider the unilateral frictional contact problem of a hyperelastic body in the case of large displacements and small strains. In order to retain the linear elasticity framework, we decompose the deformation into a large global ...

In this paper we propose a novel computational technique to solve the Eikonal equation efficiently on parallel architectures. The proposed method manages the list of active nodes and iteratively updates the solutions on those nodes until they converge. ...

We develop a computational method for simulating models of gel dynamics where the gel is described by two phases: a networked polymer and a fluid solvent. The models consist of transport equations for the two phases, two coupled momentum equations, and ...

In this paper, we present a family of domain decomposition based on an Aitken-like acceleration of the Schwarz method seen as an iterative procedure with a linear rate of convergence. This paper is a generalization of the method first introduced at the ...

The VFRoe scheme has been recently introduced by Buffard, Gallouët, and Hérard [Comput. Fluids, 29 (2000), pp. 813-847] to approximate the solutions of the shallow water equations. One of the main interests of this method is to be easily implemented. As ...

The linear sampling method is a qualitative procedure for the visualization of both impenetrable and inhomogeneous scatterers, which requires the regularized solution of a linear ill-posed integral equation of the first kind. An open issue in this ...

Direction numbers for generating Sobol$'$ sequences that satisfy the so-called Property A in up to 1111 dimensions have previously been given in Joe and Kuo [ACM Trans. Math. Software, 29 (2003), pp. 49-57]. However, these Sobol$'$ sequences may have ...

In this paper, we propose iterative algorithms for solving image restoration problems. The iterative algorithms are based on decoupling of deblurring and denoising steps in the restoration process. In the deblurring step, an efficient deblurring method ...

In this article, we propose new parallel algorithms for the construction and 2:1 balance refinement of large linear octrees on distributed memory machines. Such octrees are used in many problems in computational science and engineering, e.g., object ...