High order integration schemes on the unit sphere

Key Points

• The study aims to enhance numerical integration techniques on the unit sphere by refining high order schemes.
• Developed a new refining method for numerical integration schemes.
• Focused on integration over the unit sphere with a specific symmetry.
• Generated new integration schemes up to order 59 based on intuitive guesses.
• Introduced new high order integration schemes beyond previously established limits.
• Validated the method's effectiveness in improving integration accuracy.
• Demonstrated the ability to create integration schemes from initial rough ideas.