Solving the Electric Field Integral Equation using a Sparse Approximate Inverse preconditioned iterative method
نویسنده
چکیده
In this Master's Thesis we discuss the use of a modi ed Sparse Approximate Inverse method for preconditioning of the dense matrices arising in the Boundary Element Method when applied to the Electric Field Integral Equation. In particular we consider the case of a perfect electric conductor. Some general properties of the modi ed Sparse Approximate Inverse for complex symmetric problems are shown. Through experiments we show that for the problems considered the Quasi-Minimal Residual (QMR) method with the modi ed Sparse Approximate Inverse Preconditioner is faster than QMR without any preconditioner and a direct factorization method for large problems. It is also shown that the method can be applied to real industrial applications.
منابع مشابه
Preconditioned Generalized Minimal Residual Method for Solving Fractional Advection-Diffusion Equation
Introduction Fractional differential equations (FDEs) have attracted much attention and have been widely used in the fields of finance, physics, image processing, and biology, etc. It is not always possible to find an analytical solution for such equations. The approximate solution or numerical scheme may be a good approach, particularly, the schemes in numerical linear algebra for solving ...
متن کاملA Fast and Accurate Expansion-Iterative Method for Solving Second Kind Volterra Integral Equations
This article proposes a fast and accurate expansion-iterative method for solving second kind linear Volterra integral equations. The method is based on a special representation of vector forms of triangular functions (TFs) and their operational matrix of integration. By using this approach, solving the integral equation reduces to solve a recurrence relation. The approximate solution of integra...
متن کاملComputational experience with sequential and parallel, preconditioned Jacobi–Davidson for large, sparse symmetric matrices
The Jacobi–Davidson (JD) algorithm was recently proposed for evaluating a number of the eigenvalues of a matrix. JD goes beyond pure Krylov-space techniques; it cleverly expands its search space, by solving the so-called correction equation, thus in principle providing a more powerful method. Preconditioning the Jacobi–Davidson correction equation is mandatory when large, sparse matrices are an...
متن کاملA new iteration method for solving a class of Hammerstein type integral equations system
In this work, a new iterative method is proposed for obtaining the approximate solution of a class of Hammerstein type Integral Equations System. The main structure of this method is based on the Richardson iterative method for solving an algebraic linear system of equations. Some conditions for existence and unique solution of this type equations are imposed. Convergence analysis and error bou...
متن کاملA New Iterative Method For Solving Fuzzy Integral Equations
In the present work, by applying known Bernstein polynomials and their advantageous properties, we establish an efficient iterative algorithm to approximate the numerical solution of fuzzy Fredholm integral equations of the second kind. The convergence of the proposed method is given and the numerical examples illustrate that the proposed iterative algorithm are valid.
متن کامل