Analysis of a Quadratic Programming Decomposition Algorithm

Analysis of a Quadratic Programming Decomposition Algorithm: "G. Bencteux, E. Cances, W. W. Hager, and C. Le Bris

We analyze a decomposition algorithm for minimizing a quadratic objective function, separable in $\mathbf{x}_1$ and $\mathbf{x}_2$, subject to the constraint that $\mathbf{x}_1$ and $\mathbf{x}_2$ are orthogonal vectors on the unit sphere. Our algorithm consists of a local step where we minimize th ... [SIAM J. Numer. Anal. 47, 4517 (2010)] published Wed Feb 17, 2010."

A Convergent Nonconforming Adaptive Finite Element Method with Quasi-Optimal Complexity

A Convergent Nonconforming Adaptive Finite Element Method with Quasi-Optimal Complexity: "Roland Becker, Shipeng Mao, and Zhongci Shi

In this paper, we prove convergence and quasi-optimal complexity of a simple adaptive nonconforming finite element method. In each step of the algorithm, the iterative solution of the discrete system is controlled by an adaptive stopping criterion, and the local refinement is based on either a simp ... [SIAM J. Numer. Anal. 47, 4639 (2010)] published Fri Feb 19, 2010."

Discrete-Ordinate Discontinuous Galerkin Methods for Solving the Radiative Transfer Equation

Discrete-Ordinate Discontinuous Galerkin Methods for Solving the Radiative Transfer Equation: "Weimin Han, Jianguo Huang, and Joseph A. Eichholz

The radiative transfer equation (RTE) occurs in a wide variety of applications. In this paper, we study discrete-ordinate discontinuous Galerkin methods for solving the RTE. The numerical methods are formed in two steps. In the first step, the discrete ordinate technique is applied to discretize th ... [SIAM J. Sci. Comput. 32, 477 (2010)] published Wed Feb 17, 2010."

Algebraic Multigrid for Markov Chains

Algebraic Multigrid for Markov Chains: "H. De Sterck, T. A. Manteuffel, S. F. McCormick, K. Miller, J. Ruge et al.

An algebraic multigrid (AMG) method is presented for the calculation of the stationary probability vector of an irreducible Markov chain. The method is based on standard AMG for nonsingular linear systems, but in a multiplicative, adaptive setting. A modified AMG interpolation formula is proposed t ... [SIAM J. Sci. Comput. 32, 544 (2010)] published Wed Feb 17, 2010."

Accelerated A Posteriori Error Estimation for the Reduced Basis Method with Application to 3D Electromagnetic Scattering Problems

Accelerated A Posteriori Error Estimation for the Reduced Basis Method with Application to 3D Electromagnetic Scattering Problems: "Jan Pomplun and Frank Schmidt

We propose a new method for fast estimation of error bounds for outputs of interest in the reduced basis context, efficiently applicable to real world 3D problems. Geometric parameterizations of complicated 2D, or even simple 3D, structures easily leads to affine expansions consisting of a high num ... [SIAM J. Sci. Comput. 32, 498 (2010)] published Wed Feb 17, 2010."

Fast Evaluation of Volume Potentials in Boundary Element Methods

Fast Evaluation of Volume Potentials in Boundary Element Methods: "G. Of, O. Steinbach, and P. Urthaler

The solution of inhomogeneous partial differential equations by boundary element methods requires the evaluation of volume potentials. A direct standard computation of the classical Newton potentials is possible but expensive. Here, a fast evaluation of the Newton potentials by using the fast multi ... [SIAM J. Sci. Comput. 32, 585 (2010)] published Wed Feb 17, 2010."

Stanford mathematician: In reality, simulation is key to math education

Stanford mathematician: In reality, simulation is key to math education: "(PhysOrg.com) -- Role-playing games such as 'World of Warcraft' could reverse the declining math proficiency of middle school students, Keith Devlin told an audience at the AAAS annual meeting in San Diego."

Rate of convergence for a Galerkin scheme approximating a two-scale reaction-diffusion system with nonlinear transmission condition. (arXiv:1002.3793v1 [math.NA])

Rate of convergence for a Galerkin scheme approximating a two-scale reaction-diffusion system with nonlinear transmission condition. (arXiv:1002.3793v1 [math.NA]): "

We study a two-scale reaction-diffusion system with nonlinear reaction terms
and a nonlinear transmission condition (remotely ressembling Henry's law) posed
at air-liquid interfaces. We prove the rate of convergence of the two-scale
Galerkin method proposed in Muntean & Neuss-Radu (2009) for approximating this
system in the case when both the microstructure and macroscopic domain are
two-dimensional. The main difficulty is created by the presence of a boundary
nonlinear term entering the transmission condition. Besides using the
particular two-scale structure of the system, the ingredients of the proof
include two-scale interpolation-error estimates, an interpolation-trace
inequality, and improved regularity estimates.

"