Scholarlink

<p>In this paper, we develop an efficient solver for the time-harmonic Maxwell’s equations in the unbounded domain by extending the source transfer domain decomposition method (STDDM) proposed by Chen et al. The basic idea of the method is to decompose the domain into nonoverlapping layers. By constructing the source transfer operator, we ensure that the sources within each layer can be equivalently transferred to the subsequent layer. To obtain the solution, the method repeatedly applies the perfectly matched layer (PML) method, which is defined locally outside only two layers. Through this combination of layer-by-layer processing and the PML method, the solution to the entire problem can be obtained. The main difficulty in proving the convergence of STDDM is to analyze the solutions in the <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10915_2025_2872_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="62" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbf {H(curl)}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="bold">H</mi> <mo stretchy="false">(</mo> <mi mathvariant="bold">curl</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> space. This difficulty is circumvented by using Green’s function of matrix form. Numerical experiments are included, demonstrating that the proposed method can be used as an efficient preconditioner in the preconditioned GMRES method for solving the PML equation of Maxwell’s equations with constant and heterogeneous wave numbers.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

A Source Transfer Domain Decomposition Method for Time-Harmonic Maxwell’s Equations

  • 期刊论文

  • 发表日期：

    2025年3月28日

查看全文
  • Tao Cui,
  • Ziming Wang,
  • Xueshuang Xiang

摘要

In this paper, we develop an efficient solver for the time-harmonic Maxwell’s equations in the unbounded domain by extending the source transfer domain decomposition method (STDDM) proposed by Chen et al. The basic idea of the method is to decompose the domain into nonoverlapping layers. By constructing the source transfer operator, we ensure that the sources within each layer can be equivalently transferred to the subsequent layer. To obtain the solution, the method repeatedly applies the perfectly matched layer (PML) method, which is defined locally outside only two layers. Through this combination of layer-by-layer processing and the PML method, the solution to the entire problem can be obtained. The main difficulty in proving the convergence of STDDM is to analyze the solutions in the \(\mathbf {H(curl)}\) H ( curl ) space. This difficulty is circumvented by using Green’s function of matrix form. Numerical experiments are included, demonstrating that the proposed method can be used as an efficient preconditioner in the preconditioned GMRES method for solving the PML equation of Maxwell’s equations with constant and heterogeneous wave numbers.