The present paper describes how to apply the Chebyshev orthogonal collocation technique to solve steady-state and unsteady-steady two-dimensional problems. All problems are solved using one single computer algebra, Mathematica . The problems include: (1) steady-state heat transfer in a rectangular bar, (2) steady-state flow in a rectangular duct, (2) steady-state heat transfer in a cooling cyli...

in this work the mathematical model of a spatial pattern inchemical and biological systems is investigated numerically. theproposed model considered as a nonlinear reaction-diffusionequation. a computational approach based on finite difference andrbf-collocation methods is conducted to solve the equation withrespect to the appropriate initial and boundary conditions. theability and robustness o...

For a nonlinear functional f , and a function u from the span of a set of tensor product interpolets, it is shown how to compute the interpolant of f(u) from the span of this set of tensor product interpolets in linear complexity, assuming that the index set has a certain multiple tree structure. Applications are found in the field of (adaptive) tensor product solution methods for semilinear op...

We present in this pedagogical paper an alternative numerical method for the resolution of transport phenomena problems encountered in the teaching of the required course on transport phenomena in the graduate chemical engineering curricula. Based on the Chebyshev orthogonal collocation technique implemented in Matlab and Mathematica , we show how different rather complicated transport phenomen...

Kunert and Martin (2000) determined optimal and efficient block designs in a model for field trials with interference effects, for block sizes up to 4. In this paper we use Kushner’s method (Kushner, 1997) of finding optimal approximate designs to extend the work of Kunert and Martin (2000) to optimal designs with five or more plots per block. We give an overall upper bound at,b,k for the trace...

The aim of this thesis paper, to create a numerical model to examine the residual stresses induced by orthogonal machining in the finished work piece and the model is validated by comparing with experimental result. The finite element method is used to simulate and analyze the residual stresses induced by a orthogonal metal cutting process. A Dynamics explicit time integration technique with Ar...

We consider an elliptic partial differential equation with a random diffusion parameter discretized by stochastic collocation method in the domain and finite element spatial domain. prove for first time convergence of algorithm which adaptively enriches space as well refines meshes.

In this talk we will discuss a nonoverlapping domain decomposition pre-conditioner for the symmetric interior penalty Galerkin method [1, 2, 3]. Thepreconditioner is based on balancing domain decomposition by constraints [4].Theoretical results on the condition number estimate of the preconditioned sys-tem will be presented along with numerical results. References[1] J. ...

In this paper, we introduce and analyze a new low-rank multilevel strategy for the solution of random diffusion problems. Using a standard stochastic collocation scheme, we first approximate the infinite dimensional random problem by a deterministic parameter-dependent problem on a high-dimensional parameter domain. Given a hierarchy of finite element discretizations for the spatial approximati...

In this note, we make a few comments concerning the paper of Hughes and Akin 131. First it is noted that algorithm reported in (31 to produce a new set of functions is subject to the location of collocation points. Second we make a note concerning the rate of convergence of numerical solutions of the finite element method with singular basis functions. 'This author is partially supported by NAS...