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Area of Science:

  • Computational electrostatics
  • Numerical methods for electromagnetics
  • Surface charge method

Background:

  • Flat triangle approximations in electrostatics lead to diverging electric fields.
  • Integrating charge density over curved surfaces is computationally challenging.
  • Need for accurate methods to handle curved surfaces in electrostatics.

Purpose of the Study:

  • Introduce curved areal elements for electrostatics.
  • Develop a framework for the surface charge method using curved patches.
  • Provide analytical control over accuracy in surface charge calculations.

Main Methods:

  • Utilizing spherical triangles as curved areal elements.
  • Analytical expansion in powers of arc length and curvature.
  • Developing higher-order correction terms for accuracy.

Main Results:

  • Demonstrated analytical control over accuracy using curvature-dependent expansions.
  • Provided detailed methods for incorporating higher-order corrections.
  • Established groundwork for applying the surface charge method with curved patches.

Conclusions:

  • Curved areal elements offer a viable solution to diverging fields in electrostatics.
  • The presented analytical approach allows for controlled accuracy in surface charge calculations.
  • This work enables more precise electrostatics simulations on curved surfaces.