scholarly journals A Least-Squares FEM for the Direct and Inverse Rectangular Cavity Scattering Problem

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Enxi Zheng ◽  
Fuming Ma ◽  
Yujie Wang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Least Squares ◽  
Numerical Experiments ◽  
Bessel Functions ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Rectangular Cavity ◽  
Total Field ◽  
Element Method

This paper is concerned with the scattering problem of a rectangular cavity. We solve this problem by a least-squares nonpolynomial finite element method. In the method, we use Fourier-Bessel functions to capture the behaviors of the total field around corners. And the scattered field towards infinity is represented by a combination of half-space Green functions. Then we analyze the convergence and give an error estimate of the method. By coupling the least-squares nonpolynomial finite element method and the Newton method, we proposed an algorithm for the inverse scattering problem. Numerical experiments are presented to show the effectiveness of our method.

scholarly journals Assessment of Rectangular Cavity in Concrete Gravity Retaining Wall using Finite Element Method

2019 ◽  
Vol 8 (4) ◽  
pp. 2656-2661
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stress Distribution ◽  
Cross Section ◽  
Retaining Wall ◽  
Rectangular Cavity ◽  
Gravity Retaining Wall ◽  
The Cross ◽  
Conditions Of Stability ◽  
Element Method

The design of the Gravity retaining wall (GRW) is a trial and error process. Prevailing conditions of backfill are used to determine the profile of GRW, which proceeds with the selection of provisional dimensions. The optimum section is having factors of safety of stability higher than the allowable values and stresses in the cross-section smaller than permissible. The cross-section is designed to fulfill conditions of stability, subjected to very low stresses. The strength of the material, which is provided in the cross-section remains unutilized. A computer program is developed to find stresses at various locations on the cross-section of GRW using the Finite Element Method (FEM). A discontinuity in the form of a rectangular cavity is introduced in the cross-section of GRW to optimize it. The rectangular cavity is introduced in the cross-section of GRW at different locations. An attempt is made in this paper to find the stress distribution in the gravity retaining wall cross-section and to study the effect of the rectangular cavity on the stress distribution. Two cases representing different locations are considered to study the effect of the cavity. The location of the cavity is distinguished by the parameter w, the effects of cases with varied was 0.2305 (Case-I) and 0.1385 (Case-II) are observed. The cavity, which is provided not only makes the wall structurally efficient but also economically feasible.

scholarly journals Interval study of convergence in the solution of 1D Burgers by least squares finite element method (LSFEM) + Newton linearization

2015 ◽  
Vol 10 (16) ◽  
pp. 522-530 ◽  
Author(s):  
Fernanda Soares de Oliveira e Silva Barbara ◽  
Veloso Garcia Roberta ◽  
Cristiane Pinto Mesquita Pardal Paula ◽  
Claro Romao Estaner
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Least Squares ◽  
Element Method
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