We discuss the matrix-free implementation of Discontinuous Galerkin methods for compressible flow problems, i.e. the compressible Navier-Stokes equations. For the spatial discretization the CDG2 method and for temporal discretization an explicit Runge-Kutta method is used. For the presented matrix-free approach we discuss asynchronous communication, shared memory parallelization, and automated ...

The Stokes problem plays an important role in computational fluid dynamics since it is encountered in the time discretization of (incompressible) Navier-Stokes equations by operator-splitting methods [2, 3]. Space discretization of the Stokes problem leads to large scale ill-conditioned systems. The Uzawa (preconditioned) conjugate gradient method is an efficient method for solving the Stokes p...

Abstract: In this paper, we investigate piecewise approximate solution for linear two dimensional Volterra integral equation, based on the interval approximation of the true solution by truncated Chebyshev series. By discretization respect to spatial and time variables, the solution is approximated by using collocation method. Analysis of discretization error is discussed and efficiency of the ...

A semi-Lagrangian method for parabolic problems is proposed, that extends previous work by the authors to achieve a fully conservative, flux-form discretization of linear and nonlinear diffusion equations. A basic consistency and convergence analysis are proposed. Numerical examples validate the proposed method and display its potential for consistent semi-Lagrangian discretization of advection...

. In this paper, we develop a quadratic spline collocation method for integrating the nonlinear partial differential equations (PDEs) of a plug flow reactor model. The method is proposed in order to be used for the operation of control design and/or numerical simulations. We first present the Crank-Nicolson method to temporally discretize the state variable. Then, we develop and analyze the pro...

Many classification algorithms are designed to work with datasets that contain only discrete attributes. Discretization is the process of converting the continuous attributes of the dataset into discrete ones in order to apply some classification algorithm. In this paper we first review previous work in discretization, then we propose a new discretization method based on a distance proposed by ...

Properly addressing the discretization process of continuos valued features is an important problem during decision tree learning. This paper describes four multi-interval discretization methods for induction of decision trees used in dynamic fashion. We compare two known discretization methods to two new methods proposed in this paper based on a histogram based method and a neural net based me...

In this article, we investigate numerical schemes for solving a three component CahnHilliard model. The space discretization is performed by using a Galerkin formulation and the finite element method. Concerning the time discretization, the main difficulty is to write a scheme ensuring, at the discrete level, the decrease of the free energy and thus the stability of the method. We study three d...

Properly addressing the discretization process of continous valued features is an important problem during decision tree learning. This paper describes four multi-interval discretization methods for induction of decision trees used in dynamic fashion. We compare two known discretization methods to two new methods proposed in this paper based on a histogram based method and a neural net based me...