Numerical computation is one of the reliable ways to solve partial differential equations. In the past three decades, with the rapid growth of computer processing power and storage space, numerical computation has been successfully applied to many fields. It provides strong support for researchers to solve complex engineering practical problems and analyze complex physical phenomena. Most of the existing numerical methods are element-based, among which the finite element method is the most famous. Modern numerical analysis technology is developing towards high efficiency, high accuracy, low cost and high performance, while the traditional analysis technology has been unable to meet the requirements. The first step in industrial manufacturing is engineering design, and the most basic tool of engineering design is calculation and analysis software, and calculation method is the most critical core problem in calculation and analysis software. At present, the software industry of our country is almost completely monopolized by foreign software products. The serious lack of domestic computing simulation software with completely independent intellectual property rights will surely become the biggest weakness in the implementation of the intelligent manufacturing 2025 in China. The research and development of advanced core adaptive computing methods and analysis technology with completely independent intellectual property rights play an important role in improving the development level of engineering analysis software in China and cultivating the ability of independent research and development.