MULTILEVEL DECOMPOSITION FOR ADAPTIVE NUMERICAL MODELINGOF COMPLEX PHYSICAL PROCESSES

Abstract

Relevance. Numerical modeling of complex physical processes is an important tool in scientific research and engineering applications. Traditional methods based on uniform discretization often have high computational cost, especially for problems with significant spatiotemporal heterogeneities. Optimization of computational resources is a key factor in ensuring the efficiency and accuracy of numerical analysis.

Purpose. The study is aimed at developing and implementing a multilevel decomposition method for adaptive numerical modeling, which allows automatically changing the level of detail depending on the local features of physical processes, while ensuring high accuracy of calculations with minimal computational costs.

Method. The proposed model is based on the criteria for adaptive domain partitioning, which are based on the analysis of the gradient of the state function and a posteriori error estimates. An algorithm for adaptively changing the levels of detail is implemented, which includes mesh initialization, local gradient calculation, decision-making on splitting or merging cells, and updating the mesh structure. The method is verified on the diffusion problem with a comparison of analytical and reference numerical solutions.

Results. The results obtained show that the use of multilevel decomposition allows achieving accuracy equivalent to uniform splitting with high resolution, while reducing the amount of calculations by 4-5 times. Numerical experiments confirmed the effectiveness of the proposed method for modeling diffusion processes, and also demonstrated its potential application for heat transfer problems and laser-induced changes in films.

Conclusions. The implemented multilevel decomposition method provides an effective balance between accuracy and performance. It can be integrated with modern numerical methods, such as FDTD, FEM, and RCWA, which expands the possibilities of its application in modeling problems of complex physical systems.