Showing papers by "Nathan Ida published in 1995"
01 May 1995
TL;DR: This work proposes a new method in which the relaxation factor is chosen automatically by the computer code, based on the dynamics of the convergence process, and the local application of relaxation factors is introduced, so that different unknowns have different relaxation factors.
Abstract: Application of under and over-relaxation is a very useful technique in solution of nonlinear problems. However, the choice of the relaxation factor is problem dependent and difficult to estimate. In this work we propose a new method in which the relaxation factor is chosen automatically by the computer code, based on the dynamics of the convergence process. In addition, the local application of relaxation factors is introduced, so that different unknowns have different relaxation factors. Two examples are presented to demonstrate the proposed method's efficiency. >
8 citations
01 Feb 1995-Compel-the International Journal for Computation and Mathematics in Electrical and Electronic Engineering
TL;DR: Two different ‘a posteriori’ error estimation techniques are proposed in this paper and the numerical test results and the performance evaluation establish the effectiveness of the proposed error estimates for adaptive mesh refinement.
Abstract: Two different ‘a posteriori’ error estimation techniques are proposed in this paper. The effectiveness of the error estimates in adaptive mesh refinement for 2D and 3D electrostatic problems are also analyzed with numerical test results. The post‐processing method employs an improved solution to estimate the error, whereas the gradient of field method utilizes the gradient of the field solution for estimating the ‘a posterior’ error. The gradient of field method is computationally inexpensive, since it solves a local problem on a patch of elements. The error estimates are tested by solving a set of self‐adjoint boundary value problems in 2D and 3D using a hierarchical minimal tree based mesh refinement algorithm. The numerical test results and the performance evaluation establish the effectiveness of the proposed error estimates for adaptive mesh refinement.
6 citations
01 May 1995
TL;DR: Reliability analysis of two different error estimates with a model problem and numerical test results are reported and a mathematical model for the reliability assessment of an 'a posteriori' error estimate through asymptotic exactness is presented.
Abstract: Optimal performance of an adaptive finite element (FE) computation depends on the availability of a reliable and computationally efficient 'a posteriori' error estimation strategy. The reliability of an error estimate ensures that the quality of the computed solution remains within a specified accuracy and also guarantees that the error estimate applies uniformly over the entire problem domain. Reliability analysis of two different error estimates with a model problem and numerical test results are reported in this paper. A mathematical model for the reliability assessment of an 'a posteriori' error estimate through asymptotic exactness is also presented. The reliability or the performance of two different error estimates is assessed by adaptively solving a linear boundary value problem. >
6 citations