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An Optimized Schwarz Method for the Optical Response Model Discretized by HDG Method.

Jia-Fen Chen¹, Xian-Ming Gu², Liang Li³

¹School of Mathematics and Computer Science, Chongqing College of International Business and Economics, Chongqing 401520, China.

Entropy (Basel, Switzerland)

|May 16, 2023

Summary

This summary is machine-generated.

This study introduces an optimized Schwarz domain decomposition method (DDM) for the local optical response model (LORM). The new method enhances computational efficiency for optical response calculations.

Keywords:

Krylov subspace method domain decomposition method hybridizable discontinuous Galerkin method local optical response model optimized Schwarz method

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Area of Science:

Computational physics
Numerical analysis
Materials science

Background:

The local optical response model (LORM) requires efficient numerical solvers.
Domain decomposition methods (DDMs) are effective for large-scale problems.
Existing methods may not be optimal for LORM's specific characteristics.

Purpose of the Study:

To develop and optimize a Schwarz domain decomposition method (DDM) tailored for the local optical response model (LORM).
To improve the computational efficiency and accuracy of LORM simulations.
To investigate and optimize transmission conditions for Schwarz DDM in LORM.

Main Methods:

Hybridizable discontinuous Galerkin (HDG) scheme for discretization on triangular meshes.
Sparse direct solvers for subdomain linear systems.
Krylov subspace methods for accelerating interface system solutions.
Analysis of the spectral radius of the Schwarz iteration matrix.

Main Results:

An optimized parameter for the transmission condition was proposed, differing from classical electromagnetic problems.
The proposed optimized Schwarz DDM effectively solves the LORM.
Numerical results demonstrate the method's effectiveness and efficiency.

Conclusions:

The optimized Schwarz DDM with HDG discretization provides an effective approach for LORM.
The proposed transmission condition parameter is crucial for the method's performance.
This work contributes to more efficient simulations in optical response modeling.