High performance implementation of 3D FEM for nonlocal Poisson problem with different ball approximation strategies

Nonlocality brings many challenges to the implementation of finite element methods (FEM) for nonlocal problems, such as large number of queries and invoke operations on the meshes. Besides, the interactions are usually limited to Euclidean balls, so direct numerical integrals often introduce numerical errors. The issues of interactions between the ball and finite elements have to be carefully dealt with, such as using ball approximation strategies. In this paper, an efficient representation and construction methods for approximate balls are presented based on combinatorial map, and an efficient parallel algorithm is also designed for assembly of nonlocal linear systems. Specifically, a new ball approximation method based on Monte Carlo integrals, i.e., the fullcaps method, is also proposed to compute numerical integrals over the intersection region of an element with the ball

Bollinger Bands Trading Strategy Based on Wavelet Analysis

With the popularization of the concept of quantitative investment and the introduction of stock index futures in China, the research on the quantitative trading strategies of stock index futures is emerging gradually. This paper takes the CSI 300 stock index futures as the research object and sets up the Bollinger Bands trading strategy to test it, while considering the factors such as returns, retracement and income risk ratio, etc. Furthermore, the paper uses the wavelet noise reduction to process the data of price and the Bollinger Bands trading strategy to test the processed data. Compared with the results of the first test, the Bollinger Band trading strategy based on wavelet analysis has greater returns, less risk and better applicability