Discretization of Electric Current Volume Integral Equation With Piecewise Linear Basis Functions

Integral Equation Analysis with Characteristic Basis Functions

Piecewise Constant Solution of Non Linear Volterra Integral Equation

In this paper, modification in the computational methods, for solving Non-linear Volterra integral equations, is presented. Here, two piecewise constant methods are considered for obtaining the solutions. The first method is based on Walsh Functions (WF) and the second method is via Block Pulse Functions (BPF). Comparison between the two methods is presented by calculating the errors vis-à-vis ...

The reduced basis method for the electric field integral equation

We introduce the Reduced Basis Method (RBM) as an efficient tool for parametrized scattering problems in computational electromagnetics for problems where field solutions are computed using a standard Boundary Element Method (BEM) for the parametrized Electric Field Integral Equation (EFIE). This combination enables an algorithmic cooperation which results in a two step procedure. The first ste...

Certified Reduced Basis Method for the Electric Field Integral Equation

In [5], a reduced basis method (RBM) for the electric field integral equation (EFIE) based on the boundary element method (BEM) is developed, based on a simplified a posteriori error estimator for the Greedy-based snapshot selection. In this paper, we extend this work and propose a certified RBM for the EFIE based on a mathematically rigorous a posteriori estimator. The main difficulty of the c...

Solution of Hallen’s Integral Equation by Using Radial Basis Functions

In this paper, we present a numerical method for solving Hallen’s integral equation based on radial basis functions (RBFs). This method will represent the solution of Hallen’s integral equation by interpolating the radial basis functions based on Legendre-Gauss-Lobatto(LGL) nodes and weights. The numerical results show that the proposed method for Hallen’s integral equation is very accurate and...