Numerical manifold method with local pixel representation of finite covers for two-dimensional problems having complex discontinuities

Numerical manifold method (NMM) based on finite covers provides a powerful tool for the analysis of engineering problems having complex discontinuities. However, the complicated geometric/topology operations and the block cutting procedure for generating physical covers seriously hinder the engineering practice of the NMM. In this work, local temporary pixels are constructed on the mathematical covers, and the seed filling method is employed to generate the pixel-represented physical covers cut by discontinuities. In this way, the geometric algorithm and block cutting procedure involved in conventional NMM are completely avoided, and the discontinuities and the manifold element integrals are still expressed in an accurate form. The proposed method has the merits of simple in principle and convenient for numerical implementation, which can simplify the physical cover generation process, so as to facilitate and promote the further application of the NMM in engineering practice.

Automated summary

The proposed method in this work simplifies the process of generating physical covers by constructing local temporary pixels on mathematical covers and employing the seed filling method. This approach avoids the use of complex geometric algorithms and block cutting procedures, making it easier to further apply NMM in engineering practice.