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**Name**:

# Astudy on Hierarchical-Matrix-Based Algorithm for Solving Electromagnetic Problems of the Volume Int

**Author**: XuHongMei

**Tutor**: BaoYaMing

**School**: Nanjing University of Posts and Telecommunications

**Course**: Electromagnetic Field and Microwave Technology

**Keywords**: Method of Moments,Volume Integral Equation,Hierarchical matrix,Degenerate kernel

**CLC**: O175.5

**Type**: Master's thesis

**Year**: 2012

Abstract:

Key technologies in the field of computational electromagnetics , accelerate the numerical solution of fast algorithms for solving electromagnetic scattering problems . Hierarchical matrix (Hierarchical Matrix, referred to as the H matrix ) method is a typical method . Essence , the H - matrix method degradation of the kernel function of the integral equation processing, to realize the separation of variables and the source point of the field point variables , thus reducing the iterative calculation for solving the integral equation , and reduces the amount of storage required by the coefficient matrix . Firstly , the proposed use of the basic geometric scatterer discrete unit point , line, surface , the body 's basic relationship model , and the public face of the two adjacent discrete tetrahedral elements and the surface of the non - public face of the discrete tetrahedral elements quick Find makes the computational complexity of linear order ; Secondly, the triangular surface element combined octree theory triangulation model of public and non- public triangular faces $ renumbered hierarchical way , in order to achieve the H- matrix division of the structure ; , Lagrange polynomial interpolation method degradation medium volume integral equation kernel function , turn on the method of moments impedance matrix approximation , sparse method of moments of the coefficient matrix so as to achieve the purpose . Finally , use the calculation procedure three model problems , the media cube electromagnetic scattering characteristics of dielectric sphere and finite length dielectric cylinder . Numerical results verify the correctness and validity of the proposed algorithm shows that the H matrix fast algorithm to calculate the amount of storage capacity that can be reduced to solving the integral equation , the complexity of the two are close to ¦¯ ? NlogN ? The research content suitable degenerate kernel approximation method combines the the H matrix technology , you can build a high-efficiency electromagnetic fields fast solution methods .

Key technologies in the field of computational electromagnetics , accelerate the numerical solution of fast algorithms for solving electromagnetic scattering problems . Hierarchical matrix (Hierarchical Matrix, referred to as the H matrix ) method is a typical method . Essence , the H - matrix method degradation of the kernel function of the integral equation processing, to realize the separation of variables and the source point of the field point variables , thus reducing the iterative calculation for solving the integral equation , and reduces the amount of storage required by the coefficient matrix . Firstly , the proposed use of the basic geometric scatterer discrete unit point , line, surface , the body 's basic relationship model , and the public face of the two adjacent discrete tetrahedral elements and the surface of the non - public face of the discrete tetrahedral elements quick Find makes the computational complexity of linear order ; Secondly, the triangular surface element combined octree theory triangulation model of public and non- public triangular faces $ renumbered hierarchical way , in order to achieve the H- matrix division of the structure ; , Lagrange polynomial interpolation method degradation medium volume integral equation kernel function , turn on the method of moments impedance matrix approximation , sparse method of moments of the coefficient matrix so as to achieve the purpose . Finally , use the calculation procedure three model problems , the media cube electromagnetic scattering characteristics of dielectric sphere and finite length dielectric cylinder . Numerical results verify the correctness and validity of the proposed algorithm shows that the H matrix fast algorithm to calculate the amount of storage capacity that can be reduced to solving the integral equation , the complexity of the two are close to ¦¯ ? NlogN ? The research content suitable degenerate kernel approximation method combines the the H matrix technology , you can build a high-efficiency electromagnetic fields fast solution methods .

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