Acceleration of convergence of a two-level algorithm by smoothing transfer operators
The technique for accelerating the convergence of the algebraic multigrid method is proposed.
Acceleration of implicit schemes for large systems of nonlinear ODEs.
Acceleration of Le Bail fitting method on parallel platforms
Le Bail fitting method is procedure used in the applied crystallography mainly during the crystal structure determination. As in many other applications, there is a need for a great performance and short execution time. In this paper, we describe utilization of parallel computing for mathematical operations used in Le Bail fitting. We present an algorithm implementing this method with highlighted possible approaches to its aforementioned parallelization. Then, we propose a sample parallel version...
Acceleration of nonhyperbolic sequences of Mann.
Acceleration of Runge-Kutta integration schemes.
Acceleration of two-grid stabilized mixed finite element method for the Stokes eigenvalue problem
This paper provides an accelerated two-grid stabilized mixed finite element scheme for the Stokes eigenvalue problem based on the pressure projection. With the scheme, the solution of the Stokes eigenvalue problem on a fine grid is reduced to the solution of the Stokes eigenvalue problem on a much coarser grid and the solution of a linear algebraic system on the fine grid. By solving a slightly different linear problem on the fine grid, the new algorithm significantly improves the theoretical error...
Acceleration properties of the hybrid procedure for solving linear systems
The aim of this paper is to discuss the acceleration properties of the hybrid procedure for solving a system of linear equations. These properties are studied in a general case and in two particular cases which are illustrated by numerical examples.
Accumulation of global error in Lie group methods for linear ordinary differential equations.
Accuracy and Stability of Multistage Multistep Formulas.
Accurate and online-efficient evaluation of the a posteriori error bound in the reduced basis method
The reduced basis method is a model reduction technique yielding substantial savings of computational time when a solution to a parametrized equation has to be computed for many values of the parameter. Certification of the approximation is possible by means of an a posteriori error bound. Under appropriate assumptions, this error bound is computed with an algorithm of complexity independent of the size of the full problem. In practice, the evaluation of the error bound can become very sensitive...
Accurate calculations of Stationary Distributions and Mean First Passage Times in Markov Renewal Processes and Markov Chains
This article describes an accurate procedure for computing the mean first passage times of a finite irreducible Markov chain and a Markov renewal process. The method is a refinement to the Kohlas, Zeit fur Oper Res, 30, 197–207, (1986) procedure. The technique is numerically stable in that it doesn’t involve subtractions. Algebraic expressions for the special cases of one, two, three and four states are derived.Aconsequence of the procedure is that the stationary distribution of the embedded Markov...
Accurate computation of higher Sturm-Liouville eigenvalues.
Accurate numerical discretizations of non-conservative hyperbolic systems
We present an alternative framework for designing efficient numerical schemes for non-conservative hyperbolic systems. This approach is based on the design of entropy conservative discretizations and suitable numerical diffusion operators that mimic the effect of underlying viscous mechanisms. This approach is illustrated by considering two model non-conservative systems: Lagrangian gas dynamics in non-conservative form and a form of isothermal Euler equations. Numerical experiments demonstrating...
Accurate numerical discretizations of non-conservative hyperbolic systems
We present an alternative framework for designing efficient numerical schemes for non-conservative hyperbolic systems. This approach is based on the design of entropy conservative discretizations and suitable numerical diffusion operators that mimic the effect of underlying viscous mechanisms. This approach is illustrated by considering two model non-conservative systems: Lagrangian gas dynamics in non-conservative form and a form of isothermal Euler equations. Numerical experiments demonstrating...
Accurate Test Limits Under Nonnormal Measurement Error.
Accurate WKB Approximation for a 1D Problem with Low Regularity
2000 Mathematics Subject Classification: 34L40, 65L10, 65Z05, 81Q20.This article is concerned with the analysis of the WKB expansion in a classically forbidden region for a one dimensional boundary value Schrodinger equation with a non smooth potential. The assumed regularity of the potential is the one coming from a non linear problem and seems to be the critical one for which a good exponential decay estimate can be proved for the first remainder term. The treatment of the boundary conditions brings...
Active scalars and the Euler equations
Active set and interior methods for nonlinear optimization.
Adams Methods for Neutral Functional Differential Equations.
Adapting meshes and time-steps for phase change problems
We address the numerical approximation of the two-phase Stefan problem and discuss an adaptive finite element method based on rigorous a posteriori error estimation and refinement/coarsening. We also investigate how to restrict coarsening for the resulting method to be stable and convergent. We review implementation issues associated with bisection and conclude with simulations of a persistent corner singularity, for which adaptivity is an essential tool.