Convergence rate for numerical computation of the lattice Green's function

Area of Science:

• Materials Science
• Condensed Matter Physics
• Computational Materials Science

Background:

• Flexible boundary-condition methods are crucial for simulating isolated defects within bulk materials.
• Accurate modeling requires handling the bulk lattice Green's function, which involves complex projections for infinite lattices.
• Understanding convergence rates is key to efficient and reliable computational methods.

Purpose of the Study:

• To compare the convergence rates of three distinct techniques for flexible boundary-condition methods.
• To evaluate these methods for both elastically isotropic and anisotropic material cases.
• To identify the most efficient technique for defect modeling.

Main Methods:

• Calculation of convergence rates for relative displacement, elastic Green's function correction, and discontinuity correction techniques.
• Application of these methods to elastically isotropic and anisotropic lattice systems.
• Analysis of computational efficiency based on convergence speed.

Main Results:

• The discontinuity correction method demonstrated the most rapid convergence across different elastic properties.
• Relative displacement and elastic Green's function correction showed slower convergence rates.
• Convergence rates varied between isotropic and anisotropic cases, with discontinuity correction remaining superior.

Conclusions:

• The discontinuity correction method is the most efficient technique for flexible boundary-condition modeling of defects.
• This finding has significant implications for computational materials science, enabling faster and more accurate simulations.
• The study provides a clear benchmark for selecting appropriate methods in defect analysis.