A method for accelerating the iterative solution of a class of Fredholm integral equations

1978 ◽  
Vol 24 (1) ◽  
pp. 5-27 ◽  
Author(s):  
R. C. Allen ◽  
G. M. Wing
Keyword(s):  
Integral Equations ◽  
Iterative Solution ◽  
Fredholm Integral Equations

scholarly journals Study on the Accuracy Improvement of the Second-Kind Fredholm Integral Equations by Using the Buffa-Christiansen Functions with MLFMA

2016 ◽  
Vol 2016 ◽  
pp. 1-7
Author(s):  
Yue-Qian Wu ◽  
Xin-Qing Sheng ◽  
Xing-Yue Guo ◽  
Hai-Jing Zhou
Keyword(s):  
Integral Equations ◽  
Iterative Solution ◽  
Fredholm Integral Equations ◽  
Accuracy Improvement ◽  
Electric Conductor ◽  
Triangular Elements ◽  
Fast Multipole Algorithm ◽  
Magnetic Field Integral Equation ◽  
The Magnetic Field ◽  
Better Than

Former works show that the accuracy of the second-kind integral equations can be improved dramatically by using the rotated Buffa-Christiansen (BC) functions as the testing functions, and sometimes their accuracy can be even better than the first-kind integral equations. When the rotated BC functions are used as the testing functions, the discretization error of the identity operators involved in the second-kind integral equations can be suppressed significantly. However, the sizes of spherical objects which were analyzed are relatively small. Numerical capability of the method of moments (MoM) for solving integral equations with the rotated BC functions is severely limited. Hence, the performance of BC functions for accuracy improvement of electrically large objects is not studied. In this paper, the multilevel fast multipole algorithm (MLFMA) is employed to accelerate iterative solution of the magnetic-field integral equation (MFIE). Then a series of numerical experiments are performed to study accuracy improvement of MFIE in perfect electric conductor (PEC) cases with the rotated BC as testing functions. Numerical results show that the effect of accuracy improvement by using the rotated BC as the testing functions is greatly different with curvilinear or plane triangular elements but falls off when the size of the object is large.

scholarly journals Improved Iterative Solution of Linear Fredholm Integral Equations of Second Kind via Inverse-Free Iterative Schemes

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1747
Author(s):  
José Manuel Gutiérrez ◽  
Miguel Ángel Hernández-Verón ◽  
Eulalia Martínez
Keyword(s):  
Integral Equations ◽  
Theoretical Study ◽  
Iterative Scheme ◽  
Semilocal Convergence ◽  
Iterative Solution ◽  
Fredholm Integral Equations ◽  
Existence Of A Solution ◽  
Separable Kernel ◽  
Starting Point ◽  
Domain Of Existence

This work is devoted to Fredholm integral equations of second kind with non-separable kernels. Our strategy is to approximate the non-separable kernel by using an adequate Taylor’s development. Then, we adapt an already known technique used for separable kernels to our case. First, we study the local convergence of the proposed iterative scheme, so we obtain a ball of starting points around the solution. Then, we complete the theoretical study with the semilocal convergence analysis, that allow us to obtain the domain of existence for the solution in terms of the starting point. In this case, the existence of a solution is deduced. Finally, we illustrate this study with some numerical experiments.

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