Improving the convergence of the iterative solution of matrix equations in the method of moments formulation using extrapolation techniques

To obtain wideband radar cross-section (RCS) frequency response of multiple perfectly electric conducting (PEC) objects, the frequency sweeping by reusing the ultra-wide band characteristic basis functions (UCBFs) is applied. This method, based on the Characteristic Basis Function Method (CBFM), maintains all the benefit of CBFM, especially accelerating the solution of matrix equations generated by the method of moments (MoM) applied to the scatting problems in electromagnetics. Compared with conventional CBFM procedure, reusing the UCBFs without repeating the calculations of them at different frequency points leads to a significant reduction of computational time. Generating UCBFs for highest frequency, reusing UCBFs for lower frequencies and constructing reduced matrix for each frequency are the three keys of this method. Numerical results demonstrated the efficiency of this method.

Download Full-text

A STOPPING CRITERION FOR ITERATIVE SOLUTION OF STOCHASTIC GALERKIN MATRIX EQUATIONS

International Journal for Uncertainty Quantification ◽

10.1615/int.j.uncertaintyquantification.2016016463 ◽

2016 ◽

Vol 6 (3) ◽

pp. 245-269 ◽

Cited By ~ 1

Author(s):

Christophe Audouze ◽

Par Hakansson ◽

Prasanth B. Nair

Keyword(s):

Iterative Solution ◽

Matrix Equations ◽

Stopping Criterion ◽

Stochastic Galerkin

Download Full-text

Characteristic basis function method: A new technique for efficient solution of method of moments matrix equations

Microwave and Optical Technology Letters ◽

10.1002/mop.10685 ◽

2002 ◽

Vol 36 (2) ◽

pp. 95-100 ◽

Cited By ~ 386

Author(s):

V. V. S. Prakash ◽

Raj Mittra

Keyword(s):

Method Of Moments ◽

Basis Function ◽

Function Method ◽

Efficient Solution ◽

New Technique ◽

Matrix Equations ◽

A New Technique

Download Full-text

Highly efficient parallel direct solver for solving dense complex matrix equations from method of moments

The Journal of Engineering ◽

10.1049/joe.2017.0069 ◽

2017 ◽

Vol 2017 (4) ◽

pp. 69-71

Author(s):

Yan Chen ◽

Zhongchao Lin ◽

Yu Zhang ◽

Daniel García Doñoro

Keyword(s):

Method Of Moments ◽

Matrix Equations ◽

Complex Matrix ◽

Direct Solver ◽

Highly Efficient

Download Full-text

Fast Multipole Acceleration of a MoM Code for the Solution of Composed Metallic/Dielectric Scattering Problems

Advances in Radio Science ◽

10.5194/ars-3-189-2005 ◽

2005 ◽

Vol 3 ◽

pp. 189-194 ◽

Cited By ~ 10

Author(s):

U. Jakobus ◽

J. van Tonder

Keyword(s):

Method Of Moments ◽

Equivalence Principle ◽

Fast Multipole Method ◽

Iterative Solution ◽

Potential Saving ◽

Fast Multipole ◽

Scattering Problems ◽

High Permittivity ◽

Metallic Structures ◽

Dielectric Bodies

Abstract. An existing method of moments (MoM) code for the solution of complex scattering bodies has been accelerated by means of a multilevel fast multipole method (MLFMM). We demonstrate the usage of this technique both for metallic structures (wires and surfaces) and for dielectric bodies (volume and surface equivalence principle). Aspects like the effect of the type of integral equation, preconditioning schemes, or iterative solution techniques are discussed. But also limitations are addressed, which are encountered when for instance attempting to model highly lossy dielectric bodies with a high permittivity. Several validation and application examples demonstrate the usefulness of this method, both with regard to the obtained accuracy, but also with respect to the potential saving in memory and run-time as compared to a standard MoM formulation.

Download Full-text